Explanation

From the conditions, Floor(G) - Floor(A) = 4 and (7 - Floor(A)) = (Floor(G) - 1), which gives Floor(A) + Floor(G) = 8. Solving these simultaneous equations yields G on floor 6 and A on floor 2.

Since B is immediately below F, C is two floors above F, and floors 2 and 6 are already occupied by A and G, F must be on floor 5. Consequently, B is on floor 4 and C is on floor 7.

Since three people live between F (floor 5) and D, D must be on floor 1 (5 - 4 = 1). The remaining person, E, occupies the odd-numbered floor 3. Therefore, D lives on the lowermost floor (floor 1).

Explanation

From the conditions, if G is on floor g and A is on floor a, then g - a = 4 and 7 - a = g - 1, which gives a + g = 8. Solving these gives G on floor 6 and A on floor 2.

Since C lives two floors above F, B lives just below F, and three people live between F and D, setting F on floor 5 gives C on floor 7, B on floor 4, and D on floor 1. Placing the remaining person E on floor 3 satisfies the condition that E lives on an odd-numbered floor.

The final floor arrangement from top to bottom (floors 7 to 1) is C, G, F, B, E, A, D. Thus, three people (G, F, and B) live between C (floor 7) and E (floor 3).

Explanation

From the conditions, let the floor numbers of G and A be g and a respectively. The number of people living above A equals the number living below G, so 7 - a = g - 1, which gives a + g = 8. Since A lives four floors below G, g - a = 4. Solving these two equations gives G on floor 6 and A on floor 2.

C lives two floors above F, and B lives just below F, occupying the relative structure C (floor k + 2), F (floor k), and B (floor k - 1). With floor 6 occupied by G, setting k = 5 places C on floor 7, F on floor 5, and B on floor 4.

Three people live between F and D, placing D on floor 1 (since 5 - 4 = 1). The remaining person, E, sits on the remaining odd-numbered floor 3. Therefore, the complete arrangement from floor 7 to floor 1 is C, G, F, B, E, A, D, placing B on the fourth floor.

Explanation

From the conditions, G - A = 4 and (7 - A) = (G - 1), which gives G + A = 8. Solving these gives G on floor 6 and A on floor 2.

The block containing C, F, and B requires C at floor k + 2, F at floor k, and B at floor k - 1. Since three people live between F and D, |F - D| = 4. Placing F on floor 5 satisfies all conditions: C is on floor 7, B is on floor 4, D is on floor 1, and the remaining odd floor 3 is occupied by E. Therefore, C lives on the seventh floor.

Explanation

From the conditions Floor(G) − Floor(A) = 4 and 7 − Floor(A) = Floor(G) − 1, we get Floor(G) + Floor(A) = 8, which yields G on floor 6 and A on floor 2.

Since C lives two floors above F, B lives just below F, and three people live between F and D, placing F on floor 5 gives C on floor 7, B on floor 4, and D on floor 1 (three floors 2, 3, 4 between F and D).

The remaining person E is placed on floor 3, satisfying the condition of living on an odd-numbered floor. Floor 4 is occupied by B and floor 3 directly below it is occupied by E.

Explanation

In Step I, the digits of each number in the input are reversed: 56 becomes 65 37 becomes 73 18 becomes 81 38 becomes 83 79 becomes 97 63 becomes 36 85 becomes 58

Step III arranges all the numbers obtained in Step I in ascending order: 36, 58, 65, 73, 81, 83, 97

The sum of all the numbers in Step III is: 36 + 58 + 65 + 73 + 81 + 83 + 97 = 493

Explanation

In Step I, the digits of each number in the input are reversed: 56 becomes 65, 37 becomes 73, 18 becomes 81, 38 becomes 83, 79 becomes 97, 63 becomes 36, and 85 becomes 58.

The highest number in Step I is 97. Dividing 97 by 3 gives 97 = 3 × 32 + 1, which leaves a remainder of 1.

Explanation

In Step I, the digits of each number in the input are reversed: 56 becomes 65 37 becomes 73 18 becomes 81 38 becomes 83 79 becomes 97 63 becomes 36 85 becomes 58

Step II merely rearranges the positions of the numbers obtained in Step I without modifying their values. Therefore, the set of numbers in Step II is {65, 73, 81, 83, 97, 36, 58}.

The highest number in Step II is 97 and the least number is 36. Difference = 97 - 36 = 61

Explanation

Step I reverses the digits of each number in the input: 65, 73, 81, 83, 97, 36, 58. Step II reverses the first three numbers, keeps the middle number intact, and reverses the last three numbers: 81, 73, 65, 83, 58, 36, 97. Step III arranges all the numbers in ascending order: 36, 58, 65, 73, 81, 83, 97. Step IV replaces each number with the sum of its digits: 3 + 6 = 9 5 + 8 = 13 6 + 5 = 11 7 + 3 = 10 8 + 1 = 9 8 + 3 = 11 9 + 7 = 16

The numbers generated in Step IV are 9, 13, 11, 10, 9, 11, 16. In this sequence, both 9 and 11 appear twice.

Explanation

The given machine rearrangement follows a specific rule across steps: Step I: The digits of each input number are reversed. Step II: The first three numbers and the last three numbers are reversed in their respective sub-groups, while the middle number retains its position. Step III: All the numbers from the previous step are arranged in ascending order. Step IV: The sum of digits of each number in Step III is computed to obtain the final sequence.

Applying this logic to the given input 56 37 18 38 79 63 85: Step I: 65 73 81 83 97 36 58 Step II: 81 73 65 83 58 36 97 Step III: 36 58 65 73 81 83 97 Step IV: 9 13 11 10 9 11 16

The final step contains the numbers 9, 13, 11, 10, 9, 11, and 16, of which 13 is present.

Explanation

In the family of six members (A, B, C, D, L, X): A, D, and L are siblings. Since A is unmarried, B is the brother-in-law of A by being married to A's sister D. L is married to X, making X the sister-in-law of D. Because C is the daughter of D, and B is the husband of D, B is the father of C.

Explanation

A is a male, unmarried, and the brother of D. Since B is the brother-in-law of A, B is a male married to D, who is female. C is the daughter of D and B. X is the sister-in-law of D and is married to L. In this six-member family structure, X is the sister of D's husband B, making X the sister-in-law of D and L her husband. Thus, X is the sister of B.

Explanation

Since A is unmarried, B being the brother-in-law of A means B is married to A's sister D, which establishes B as male and D as female.

L is married to X, who is the sister-in-law of D (wife of D's brother L). Thus, X is female and L is male.

C is the daughter of D, so C is female. A is explicitly given as a male brother.

The gender breakdown of the six members is: Males: A, B, L Females: D, X, C

The family contains 3 male members.

Explanation

Arranging the 8 persons clockwise at positions 1 through 8:

Position 1: R faces outside Position 2: P faces inside Position 3: S faces outside Position 4: W faces outside Position 5: U faces inside Position 6: T faces inside Position 7: Q faces outside Position 8: V faces outside

All given conditions are satisfied: R faces outside at position 1, placing V to its immediate left at position 8 (facing outside). The person opposite V is W at position 4, who faces outside. Q is at position 7 facing outside, making R second to its right, and W at position 4 has Q third to its right. P is at position 2 (one seat away from V and not to the immediate left of Q) facing inside, which places U third to its left at position 5 (facing inside). S is at position 3 facing outside, placing U second to its right, and S is second to the right of U. T occupies the remaining position 6 and faces inside.

Counting the individuals facing outside: R, V, W, Q, and S, giving a total of 5 people.

Explanation

Placing Q facing outside at position 1, R sits second to the right of Q at position 3 facing outside. V is to the immediate left of R at position 2 facing outside. Since W faces outside with Q sitting third to its right, W is at position 6. P sits at position 4 facing inside, leaving one person between V and P while avoiding the seat immediately to the left of Q. U sits third to the left of P at position 7 facing inside. S sits at position 5 facing outside, satisfying the condition that S and U are second to the right of each other. T occupies position 8 facing inside. In this arrangement, the person sitting opposite to V at position 2 is W at position 6.

Explanation

Placing the eight persons in clockwise order around the table: Q (facing outside) is at position 1, V (facing outside) at position 2, R (facing outside) at position 3, P (facing inside) at position 4, S (facing outside) at position 5, W (facing outside) at position 6, U (facing inside) at position 7, and T (facing inside) at position 8.

Since Q faces outside the table, the direction to the left of Q corresponds to the counter-clockwise direction. Moving 3 positions counter-clockwise from position 1 leads to position 6, which is occupied by W.

Explanation

Based on the direct condition given in the problem statement, U sits third to the left of P.

Explanation

Placing the eight people in clockwise order around the circle: Position 1: W (facing outside) Position 2: U (facing inside) Position 3: T (facing inside) Position 4: Q (facing outside) Position 5: V (facing outside) Position 6: R (facing outside) Position 7: P (facing inside) Position 8: S (facing outside)

In this arrangement: S and Q sit diametrically opposite to each other (positions 8 and 4). R and U sit diametrically opposite to each other (positions 6 and 2). P and T sit diametrically opposite to each other (positions 7 and 3). W and V sit diametrically opposite to each other (positions 1 and 5).

P and U sit at positions 7 and 2, which are not opposite to each other. Hence, PU does not belong to the group.

Explanation

Decoding the symbols according to the given definitions: @ represents ≤

represents =

; represents < % represents > & represents ≥

The given statement translates to: A ≤ B > C ≤ M < N ≤ O ≥ P ≥ K

For Conclusion I (A ≥ O): The path between A and O is A ≤ B > C ≤ M < N ≤ O. The presence of opposing relational signs (≤ and >) means no definite relation can be established between A and O.

For Conclusion II (B ≥ P): The path between B and P is B > C ≤ M < N ≤ O ≥ P. The presence of opposing relational signs (> and ≤) means no definite relation can be established between B and P.

Since neither conclusion definitely follows, neither I nor II is true.

Explanation

Decoding the symbols gives: & represents ≥ % represents >

represents =

; represents <

The combined statement becomes: P ≥ Q ≥ R ≥ S > T > O > M = I

For conclusion I, P < O is false because traversing the inequality chain gives P > O. For conclusion II, Q > T is definitely true because Q ≥ R ≥ S > T establishes that Q is strictly greater than T.

Explanation

Decoding the given symbols gives @ as ≤, # as =, % as >, and & as ≥. Combining the given statement yields the single chain L ≤ M ≤ O = R > P ≥ K.

For conclusion I, the relation between L and R simplifies to L ≤ R, meaning L < R is not definitely true as L can be equal to R.

For conclusion II, comparing M and K involves opposite relation signs across R (M ≤ R and R > P ≥ K), so no definite relationship can be established between M and K.

Thus, neither conclusion I nor II follows.

Explanation

Decoding the given symbols: @ denotes ≤

denotes =

; denotes < & denotes ≥

Combining the given statements yields the chain: I ≥ J ≥ O = L < M ≤ P < A ≤ F

Evaluating Conclusion I (O < F): From the chain, O = L < M ≤ P < A ≤ F. Because all relational signs between O and F point in the same direction and include strict less-than signs (<), O < F is definitely true.

Evaluating Conclusion II (J < A): The segment linking J and A is J ≥ O = L < M ≤ P < A. The signs between J and A face opposite directions (J ≥ L and L < A), meaning no definite inequality relationship can be established between J and A.

Explanation

Decoding the given relational symbols into standard inequalities: & represents ≥ % represents > @ represents ≤ = represents =

Combining the statement segments: Z ≥ X > Y > P ≥ L L ≤ O ≤ R = S

For conclusion I (Z % L, meaning Z > L): Following the chain Z ≥ X > Y > P ≥ L, the presence of strict inequalities (>) guarantees that Z > L. Thus, conclusion I is definitely true.

For conclusion II (S % L, meaning S > L): Following the chain L ≤ O ≤ R = S yields L ≤ S, or S ≥ L. Because S may be equal to L, S > L is not definitively true.

Explanation

The 1st, 3rd, 5th, and 7th letters of the word ABSOLUTE are A, S, L, and T, respectively. Using each letter exactly once, multiple meaningful English words can be formed, including SALT, LAST, and SLAT. As more than one valid word can be formed from this combination, the required choice is Z.

Explanation

B presents in May on an odd date, fixing B on May 13. Two people present between B and C, and C does not present in or after June, fixing C on March 26. Only two meetings are scheduled after J, which places J on June 26. E and I present in the same month with E before I, which fills April with E on April 13 and I on April 26. A presents before D, and D cannot present in the same month as J or after J, placing A on March 13 and D on May 26. F and G present on the same date (13th) but in different months, and G and H cannot present in the same month, which fixes G on June 13, F on July 13, and H on July 26.

The complete chronological order is: March 13: A March 26: C April 13: E April 26: I May 13: B May 26: D June 13: G June 26: J July 13: F July 26: H

Explanation

Ten slots are arranged chronologically across March, April, May, June, and July on the 13th and 26th of each month.

B is on May 13th. With two people between B and C, and C presenting before June, C is scheduled on March 26th. J is on June 26th as only two meetings follow it. E and I present in the same month with E before I, which requires a completely open month (April or July).

D presents before J, and A must present before D. Because March 26th is occupied by C, E and I cannot be placed in March. D cannot take the first slot of the schedule on March 13th because A must precede D. Consequently, A presents on 13th March.

Explanation

Working through the scheduling clues: "B has the meeting in May but not on the even date" fixes B on 13th May, since the only two dates available are the 13th and 26th. Combined with "A has a meeting before D, who will not present with or after J", the unique schedule that satisfies every clue is March = A/C, April = E/I, May = B/D, June = G/J, July = F/H. That places D on 26th May. Among the persons offered as options, only D falls in May.

Explanation

Based on the given conditions, the schedule for the ten presentations is determined as follows:

B presents in May on an odd date, so B presents on May 13th. Two people present between B and C, and C cannot present in or after June, which places C on March 26th. Only two meetings are scheduled after J, meaning J presents on June 26th. E and I present in the same month with E before I, placing E on April 13th and I on April 26th. A presents before D, and D cannot present with or after J (not in June or July). This fixes A on March 13th and D on May 26th. F and G present on the same date, leaving June 13th and July 13th for them. Since G and H cannot present in the same month, H presents on July 26th, F on July 13th, and G on June 13th.

The complete schedule in chronological order is: March 13: A March 26: C April 13: E April 26: I May 13: B May 26: D June 13: G June 26: J July 13: F July 26: H

The people who have their meetings between E (April 13) and G (June 13) are I, B, and D, making a total of three people.

Explanation

B presents in May on an odd date, fixing B on May 13. Two people present between B and C, and C does not present in or after June, placing C on March 26. Only two meetings occur after J, so J presents on June 26.

E and I present in the same month with E before I, meaning they must take both the 13th and 26th of a completely vacant month. With D presenting before J and after A, remaining date and month constraints for F, G, and H place E on April 13 and I on April 26. Thus, I presents in April.

Explanation

The coding rule shifts each letter forward by one position (+1) in the English alphabet: T (+1) = U E (+1) = F A (+1) = B R (+1) = S

Applying this transformation to TEAR gives UFBS.

Explanation

The statement only a few DH is UV implies that some DH is UV and some DH is not UV. Since OJ is a subset of DH, it is possible for the entirety of OJ to be inside UV while other elements of DH remain outside UV. Because all OJ being UV is possible, the definite conclusion that some OJ are not UV does not follow. Furthermore, there is no direct or indirect negative relation between UV and XP, making the overlap of UV and XP a valid possibility. Therefore, only conclusion II follows.

Explanation

Both conclusions logically follow from the given statements. Hence, both I and II follow.

Explanation

Only conclusion I logically follows from the given statements; conclusion II does not follow. Hence, only I follows.

Explanation

Statements: Some P is M; Only a few M is T (so M and T overlap partially); All T is B. Conclusion I claims "Some P is T" — this needs P's overlap with M to lie specifically inside the M∩T region. Conclusion II claims "All M is B is a possibility" — since All T is B, the M∩T portion already lies inside B, and nothing prevents the rest of M from lying inside B too, so it is a valid possibility.

Explanation

From statement I, taking M as the origin (0, 0), T is located at (0, -30). U is 10m east of M at (10, 0), and Q is 20m south of U at (10, -20). Since Q is 15m east of V, V is located at (-5, -20). Relative to T(0, -30), V is 5m west and 10m north, placing V in the north-west direction of T. Thus, statement I alone is sufficient.

From statement II, taking T as the origin (0, 0), D is located at (0, 40). Since V is 30m west of D, V is located at (-30, 40). Relative to T(0, 0), V is 30m west and 40m north, placing V in the north-west direction of T. Thus, statement II alone is also sufficient.

Explanation

In Statement I, the only condition involving R is that T does not sit opposite R, which leaves multiple available positions for R around the circle. In Statement II, R is not mentioned at all. Combining both statements still leaves the exact position of R unconstrained among the remaining unoccupied positions, making it impossible to uniquely determine the relative position of Z with respect to R. Thus, the data in both statements together is not sufficient.

Explanation

From statement II, R is the father of L and T is the daughter of R, meaning T and L are siblings. O is the father-in-law of L, and P has a mother-in-law.

From statement I, L is married to P, which means O is the father of P. Since the family consists of seven people (L, P, N, W, T, R, O), R is married to N, and O is married to W.

Because N has only one daughter and one son, and T is the daughter, L must be the son. Consequently, P is female and is the daughter of O and W. Thus, L is uniquely identified as the son-in-law of W. Both statements together are necessary to determine this relationship.

Explanation

Since all persons face south, U sitting fourth to the right of M places U at a distance of 4 positions from M. Two people sitting between S and U means S is at a distance of 3 positions from U. This allows two possible relative positions for S: either 1 position from M (immediate neighbors) or 7 positions from M.

Because both statements specify that S and M are not immediate neighbors, S must be positioned 7 places away from M. The number of people sitting between M and S is 7 − 1 = 6.

Since this deduction can be made independently from the conditions given in Statement I as well as in Statement II, either statement alone is sufficient to answer the question.

Explanation

From statement I, since A5 is taller than only A6, A6 is the shortest and A5 is the second shortest. Among the remaining four persons, A2 > A4 > {A1, A3}, which uniquely places A2 as the tallest.

From statement II, since A6 is taller than only A4, A4 is the shortest and A6 is the second shortest. Among the remaining four persons {A1, A2, A3, A5}, the given relation is A1 > A5 > A3. Since A1 is not the tallest, A2 must be the tallest.

Therefore, either statement alone is sufficient to determine who is the tallest.

Explanation

Assumption I is valid: the accused might flee the country to avoid appearing for the court hearings after getting bail. Assumption II is also valid: an angry mob might take it upon itself to punish the poachers, which would be an illegal act. Since both assumptions hold, both I and II are implicit.

Explanation

There is no direct evidence to establish both assumptions simultaneously, but one of the two possibilities must be true: either people are using expired cards, or the machine itself is not working properly. Hence, either assumption I or II is implicit.

Explanation

There is no evidence supporting assumption I, so it does not hold. However, it is reasonable to assume that people below the poverty line may not be able to afford the price set by the government, and that local hospitals are charging a lower price specifically to help such people get vaccinated. This supports assumption II. Hence, only II is implicit.

Explanation

The statement describes an unannounced disruption of water supply. Course I (wait a little, since technicians may already be resolving it) is a sensible, measured response. Course II (enquire with the department) is equally sensible. The two are not mutually exclusive — an affected person can reasonably do both. Since neither action is impractical or overreactive, both courses of action follow.

Explanation

Rusticating the student would be too severe a punishment and could ruin his future, so course of action I does not follow. Instead, the principal should give the student a warning and may also call his guardian to discuss the matter. Hence, only course of action II follows.

Explanation

Assign each letter of ADAPTATION its alphabetical position: A(1), D(4), A(1), P(16), T(20), A(1), T(20), I(9), O(15), N(14).

Checking pairs in both forward and backward directions: Forward direction: No pair has an alphabetical difference matching the distance between their positions in the word. Backward direction: Moving from right to left, N (position 10) and O (position 9) are consecutive letters with zero intervening letters, matching their adjacent arrangement in the English alphabet.

Thus, only one such pair (N-O) exists.

Explanation

Arranging the five positions in each row from West to East (1 to 5):

For Row 2 (facing North), Y is at position 1 and W is second to the right at position 3. Since the person opposite Y is to the immediate right of B (facing South), B sits at position 2 in Row 1. More than one person sits to the left of B, which holds true.

E sits second to the right of D and not at an end, placing D at position 5 and E at position 3 in Row 1. The person opposite E (position 3 in Row 2) sits immediate right of V, so V is at position 2. Two people sit between V and X, placing X at position 5 in Row 2. The remaining spot in Row 2 is occupied by U at position 4.

Since U does not sit opposite C, A sits at position 4 and C sits at position 1 in Row 1.

The final arrangements from position 1 to 5 are: Row 1 (facing South): C, B, E, A, D Row 2 (facing North): Y, V, W, U, X

Since C is at position 1 in Row 1, the person sitting diagonally opposite to C is at position 5 in Row 2, which is X.

Explanation

Arranging the five positions from left to right (positions 1 to 5) according to the given clues:

Row 1 (facing South): Position 1 = C, Position 2 = B, Position 3 = E, Position 4 = A, Position 5 = D. Row 2 (facing North): Position 1 = Y, Position 2 = V, Position 3 = W, Position 4 = U, Position 5 = X.

Since persons in Row 2 face North, the right direction corresponds to increasing position numbers. W sits at position 3, so the person sitting immediately to the right of W is at position 4, who is U.

Explanation

Row 1 faces South and Row 2 faces North.

From the condition that W sits second to the right of Y and the person opposite Y sits immediate right of B (with more than one person to the left of B), Y must be at position 1 and B at position 2, placing W at position 3.

E sits second to the right of D (pos(E) = pos(D) - 2) and not at an end, which fixes D at position 5 and E at position 3 in Row 1. The person opposite E (position 3) is immediate right of V, placing V at position 2. Two persons sit between V and X, placing X at position 5, and U at position 4 in Row 2. Since U does not sit opposite C, C is at position 1 and A is at position 4 in Row 1.

The final arrangement from positions 1 to 5 is: Row 1 (South-facing): C, B, E, A, D Row 2 (North-facing): Y, V, W, U, X

Thus, B sits opposite V.

Explanation

Number the five positions from 1 to 5 from west to east.

In Row 2 (facing north), Y is at position 1, V is at position 2, W is at position 3, U is at position 4, and X is at position 5.

In Row 1 (facing south), C is at position 1, B is at position 2, E is at position 3, A is at position 4, and D is at position 5.

For a south-facing row, the left direction corresponds to moving towards higher position numbers. Since B is at position 2, the person sitting first to the left of B is E at position 3, and the person sitting second to the left of B is A at position 4.

Explanation

Arranging the ten persons according to the given conditions gives two parallel rows: Row 1 (facing South, positions 1 to 5 from left to right): C, B, E, A, D Row 2 (facing North, positions 1 to 5 from left to right): Y, V, W, U, X

The directly opposite pairs are C and Y at position 1, B and V at position 2, E and W at position 3, A and U at position 4, and D and X at position 5. In the given pair AW, A sits opposite U while W sits opposite E, making it the only pair that does not sit directly opposite each other.

Explanation

The differences between consecutive terms follow the rule d(n) = n² + 1: 11 - 9 = 2 = 1² + 1 16 - 11 = 5 = 2² + 1 26 - 16 = 10 = 3² + 1

The next difference must be 4² + 1 = 17. Adding this to the preceding term gives: 26 + 17 = 43

Verifying the subsequent term with the next difference (5² + 1 = 26): 43 + 26 = 69

Explanation

The pattern in the given sequence is formed by alternately adding and subtracting consecutive powers of 3:

40 + 3⁰ = 40 + 1 = 41 41 - 3¹ = 41 - 3 = 38 38 + 3² = 38 + 9 = 47 47 - 3³ = 47 - 27 = 20 20 + 3⁴ = 20 + 81 = 101

Applying the operation 47 - 27 yields 20.

Explanation

Calculate the difference between consecutive terms: 168 − 165 = 3 165 − 154 = 11 (difference increases by 8) 154 − 136 = 18 (difference increases by 7) 136 − 112 = 24 (difference increases by 6)

The second differences are 8, 7, 6, so the next second difference is 5. Next first-order difference = 24 + 5 = 29.

Next term = 112 − 29 = 83.

Explanation

The given series can be separated into two alternating arithmetic sub-series:

Odd-positioned terms decrease by 0.8: 3.3, 2.5, 1.7 (since 3.3 - 0.8 = 2.5 and 2.5 - 0.8 = 1.7)

Even-positioned terms increase by 0.8: x, 4.9, 5.7 (since 4.9 + 0.8 = 5.7)

Solving for the missing second term x: x = 4.9 - 0.8 = 4.1

Alternatively, the consecutive differences follow an alternating sign pattern with increments of 0.8: +0.8, -1.6, +2.4, -3.2, +4.0 3.3 + 0.8 = 4.1

Explanation

The pattern in the series is based on successive multiplication by decreasing factors: 12 × 2.5 = 30 30 × 2.0 = 60 60 × 1.5 = 90 90 × 1.0 = 90 90 × 0.5 = 45

The multiplying factor decreases by 0.5 at each successive step (× 2.5, × 2.0, × 1.5, × 1.0, × 0.5), giving the missing number as 90 × 1.0 = 90.

Explanation

Number of students failed in class V = Students appeared - Students passed = 124 - 96 = 28. Number of students appeared in class VIII = 188. Required ratio = 28 : 188 = 7 : 47.

Explanation

Number of students who did not appear in the examination: Class VI = 148 − 97 = 51 Class VII = 196 − 150 = 46 Class VIII = 208 − 188 = 20

Total non-appearing students from classes VI, VII, and VIII together = 51 + 46 + 20 = 117

Students registered from class VIII = 208

Required percentage = (117 / 208) × 100% = (9 / 16) × 100% = 56.25%

Explanation

Number of failed students in a class = Students appeared - Students passed.

For Class V: 124 - 96 = 28 For Class VI: 97 - 81 = 16 For Class VII: 150 - 142 = 8 For Class VIII: 188 - 160 = 28

Total failed students = 28 + 16 + 8 + 28 = 80 Average number of failed students = 80 / 4 = 20

Explanation

Total students who appeared from class VIII = 188. Since male and female students appeared in equal numbers: Number of male students appeared = 188 / 2 = 94.

Total students passed from class VIII = 160. Number of female students passed = 88. Number of male students passed = Total passed - Female passed = 160 - 88 = 72.

Number of male students failed = Male students appeared - Male students passed = 94 - 72 = 22.

Explanation

Total number of students registered for exams from Class V and Class VII together = 175 + 196 = 371.

Total number of students appeared for exams from Class VI and Class VIII together = 97 + 188 = 285.

Required difference = 371 − 285 = 86.

Explanation

Initial quantity of milk = 120 litres. Initial quantity of water = 120 × (100 - 40)% = 120 × 0.60 = 72 litres.

Since only milk is added to the mixture, the quantity of water remains unchanged at 72 litres.

In the resultant mixture, the ratio of milk to water is 7 : 3. Quantity of water = 3 parts = 72 litres 1 part = 72 / 3 = 24 litres

Quantity of milk in the resultant mixture = 7 parts = 7 × 24 = 168 litres.

Explanation

Ratio of efficiency of B to A = 120 : 100 = 6 : 5. Since time taken is inversely proportional to efficiency: Time taken by A alone = 35 × (6 / 5) = 42 days.

Let the total work be LCM(42, 35, 30) = 210 units. Efficiency of A = 210 / 42 = 5 units/day Efficiency of B = 210 / 35 = 6 units/day Efficiency of (A + C) = 210 / 30 = 7 units/day Efficiency of C = 7 - 5 = 2 units/day

Work completed by A in 18 days = 18 × 5 = 90 units. Remaining work = 210 - 90 = 120 units. Combined efficiency of B and C = 6 + 2 = 8 units/day. Time taken by B and C together = 120 / 8 = 15 days.

Explanation

Let the speed of the boat in still water be 5x and the speed of the stream be x. Downstream speed = 5x + x = 6x km/h Upstream speed = 5x - x = 4x km/h

Given the difference in time taken: 240 / (4x) - 240 / (6x) = 5 60/x - 40/x = 5 20/x = 5 x = 4

Speed of the boat in still water = 5 × 4 = 20 km/h.

Time taken to cover 80 km in still water = 80 / 20 = 4 hours.

Explanation

Simple Interest SI = (P × R × T) / 100.

For Scheme A: SI₁ = [(x + 400) × 15 × 5] / 100 = 0.75(x + 400) = 0.75x + 300

For Scheme B: SI₂ = [(x - 600) × 20 × 6] / 100 = 1.20(x - 600) = 1.20x - 720

Given that total interest is Rs. 6600: SI₁ + SI₂ = 6600 (0.75x + 300) + (1.20x - 720) = 6600 1.95x - 420 = 6600 1.95x = 7020 x = 7020 / 1.95 = 3600

Explanation

Initial investment of P = Rs. 16000 for 12 months Initial investment of Q = Rs. 20000 for 12 months Investment of R = (16000 + 20000) / 2 = Rs. 18000 for 8 months

Ratio of profit shares of P, Q, and R: P : Q : R = (16000 × 12) : (20000 × 12) : (18000 × 8) = 192000 : 240000 : 144000 = 4 : 5 : 3

Total ratio units = 4 + 5 + 3 = 12

Profit share of R = (3 / 12) × 5400 = ¼ × 5400 = Rs. 1350

Explanation

Let the total income of Priya be X.

Spending on rent and food = 20% + 25% = 45% of X. Remaining income = 100% − 45% = 55% of X.

From the remaining income, spending on transportation and entertainment = 24% + 32% = 56%. Savings = (100% − 56%) of remaining income = 44% of (55% of X).

0.44 × 0.55 × X = 12100 0.242 × X = 12100 X = 12100 / 0.242 = ₹50,000

Remaining income = 55% of 50,000 = ₹27,500. Amount spent on transportation = 24% of 27,500 = 0.24 × 27,500 = ₹6600.

Explanation

From equation I: x² - 16x + 64 = 0 (x - 8)² = 0 x = 8

From equation II: y² = 64 y = +8, -8

Comparing the values: For y = 8, x = y For y = -8, x > y

Combining both conditions gives x ≥ y.

Explanation

For equation I: x² - 3x + 2 = 0 (x - 1)(x - 2) = 0 x = 1, 2

For equation II: y² - 8y + 15 = 0 (y - 3)(y - 5) = 0 y = 3, 5

Comparing the roots: 1 < 3, 1 < 5, 2 < 3, and 2 < 5. Since every possible value of x is strictly less than every value of y, the relationship is x < y.

Explanation

For the quadratic equation x² + 11x + 28 = 0, factoring gives (x + 7)(x + 4) = 0, yielding roots x = -7 and x = -4.

For the quadratic equation y² + 12y + 32 = 0, factoring gives (y + 8)(y + 4) = 0, yielding roots y = -8 and y = -4.

Comparing the roots: When x = -7 and y = -8, x > y. When x = -7 and y = -4, x < y. When x = -4 and y = -8, x > y. When x = -4 and y = -4, x = y.

Because both x > y and x < y hold for different pairs of roots, the relationship between x and y cannot be established.

Explanation

For equation I: x² - x - 72 = 0 (x - 9)(x + 8) = 0 x = 9, -8

For equation II: y² - 8y - 20 = 0 (y - 10)(y + 2) = 0 y = 10, -2

Comparing the values: When x = 9 and y = 10, x < y. When x = 9 and y = -2, x > y.

Because the comparison produces both x < y and x > y, no definitive relationship between x and y can be established.

Explanation

For equation I: 6x² - 19x + 15 = 0 Splitting the middle term: 6x² - 9x - 10x + 15 = 0 3x(2x - 3) - 5(2x - 3) = 0 (3x - 5)(2x - 3) = 0 x = 5/3, 3/2 (or x = 1.67, 1.5)

For equation II: 3y² - 11y + 10 = 0 Splitting the middle term: 3y² - 6y - 5y + 10 = 0 3y(y - 2) - 5(y - 2) = 0 (3y - 5)(y - 2) = 0 y = 5/3, 2 (or y = 1.67, 2)

Comparing the roots: 3/2 < 5/3 and 3/2 < 2 5/3 = 5/3 and 5/3 < 2

Combining these comparisons gives x ≤ y.

Explanation

From the main question, R = Q + 12, so finding Q gives the age of R.

Statement I gives P - Q = 8, which is insufficient on its own to find Q. Statement II gives (P - 4) / (Q - 4) = 13/11, which also cannot determine Q alone.

Combining both statements, the age difference between P and Q remains 8 at all times. Thus, 4 years ago, the difference between their ratio units was 13x - 11x = 2x = 8, which yields x = 4. Therefore, Q's age 4 years ago was 11 × 4 = 44 years, making Q's present age 48 years. The present age of R is 48 + 12 = 60 years. Both statements together are necessary to answer the question.

Explanation

Total monthly income of A, B, and C is A + B + C = 3 × 8000 = 24000.

From Statement I: (A + B) - C = 10000. Adding this to A + B + C = 24000 gives 2(A + B) = 34000, which yields A + B = 17000 and C = 7000. This provides only the sum of the incomes of A and B, so B's income cannot be determined uniquely.

From Statement II: Expenditure of B = 0.45 × (Income of A). This introduces B's expenditure and does not give B's savings or any direct equation for B's income.

Combining both statements still does not provide sufficient data to calculate the individual income of B.

Explanation

From Statement I, the ratio of efficiencies of A, B, and C is 2 : 1 : 5. This gives the relative work rates but no absolute value, making Statement I alone insufficient.

From Statement II, the total time taken by A, B, and C together is 7.5 days, which is insufficient alone without individual or relative rates.

Combining both statements: Let the efficiencies of A, B, and C be 2x, x, and 5x units/day respectively. Combined efficiency = 2x + x + 5x = 8x units/day. Total work = Combined efficiency × Time = 8x × 7.5 = 60x units. Time taken by C alone = Total work / Efficiency of C = 60x / 5x = 12 days.

Both statements together are necessary to answer the question.

Explanation

Total initial age = 18 × 20 = 360 years. Total age after two persons join = 20 × (20 + 1) = 20 × 21 = 420 years. Sum of ages of the two persons = 420 - 360 = 60 years.

Let their ages be 7x and 5x. 7x + 5x = 60 12x = 60 x = 5

Difference between their ages = 7x - 5x = 2x = 2 × 5 = 10 years.

Explanation

Total number of balls = 8 + 12 = 20. Total ways to choose 2 balls out of 20 = ²⁰C₂ = (20 × 19) / 2 = 190.

Number of ways to choose 2 white balls = ⁸C₂ = (8 × 7) / 2 = 28. Number of ways to choose 2 green balls = ¹²C₂ = (12 × 11) / 2 = 66.

Total favorable outcomes = 28 + 66 = 94. Required probability = 94 / 190 = 47 / 95.

Explanation

Simple Interest formula: SI = (P × R × T) / 100 Given SI = ₹1200, T = 4 years, and R = 12%: 1200 = (P × 12 × 4) / 100 P = (1200 × 100) / 48 = ₹2500

For compound interest, time is half the initial period (T = 2 years) at R = 12%: Effective compound interest rate = 12 + 12 + (12 × 12) / 100 = 25.44% CI = 2500 × 25.44 / 100 = 25 × 25.44 = ₹636

Explanation

Let the two numbers be 8x and 11x.

According to the given condition: (8x + 3) / (11x + 3) = 3 / 4 4(8x + 3) = 3(11x + 3) 32x + 12 = 33x + 9 x = 3

The original numbers are: 8 × 3 = 24 11 × 3 = 33

Adding 9 to each number: 24 + 9 = 33 33 + 9 = 42

The new ratio is: 33 / 42 = 11 / 14

Explanation

Rate of work done by A in 1 day = 1/42

Since B is 40% more efficient than A: Rate of work done by B in 1 day = 1.4 × (1/42) = 14/420 = 1/30

Combined rate of B and C in 1 day = 1/12

Rate of work done by C alone in 1 day = (Combined rate of B and C) - (Rate of B) = 1/12 - 1/30 = (5 - 2)/60 = 3/60 = 1/20

Time taken by C alone to complete the work = 20 days.

Explanation

Let the cost price of each mobile be CP.

Difference in selling prices = (20% - 16%) of CP = 4% of CP 4% of CP = ₹200 CP = 200 / 0.04 = ₹5000

Selling price of the mobile sold at 20% profit: SP = 120% of CP = 1.20 × 5000 = ₹6000

Explanation

Let the number of shoes sold by shop B in week III and week II be 4x and 3x, respectively.

Shoes sold by shop A in week II = (1 − 0.375) × 4x = 2.5x Shoes sold by shop A in week I = 2.5x − 20 Shoes sold by shop A in week III = 620 − 4x

Since the total shoes sold by shop A in all three weeks is 680: (2.5x − 20) + 2.5x + (620 − 4x) = 680 x + 600 = 680 x = 80

Shoes sold by shop A in week III = 620 − 4(80) = 620 − 320 = 300

Explanation

Let the shoes sold by shop B in week III and week II be 4x and 3x respectively.

Then, shoes sold by shop A in week II = 4x × (1 − 0.375) = 2.5x. Shoes sold by shop A in week I = 2.5x − 20. Shoes sold by shop A in week III = 620 − B_III = 620 − 4x.

Total shoes sold by shop A across three weeks: (2.5x − 20) + 2.5x + (620 − 4x) = 680 x + 600 = 680 x = 80

Shoes sold by shop A in week I = 2.5(80) − 20 = 180. Shoes sold by shop B in week I = 460.

Total shoes sold by shop A and B together in week I = 180 + 460 = 640.

Explanation

Let the shoes sold by shop B in week III be 4x and in week II be 3x.

Shoes sold by shop A in week II: A_II = 4x × (1 - 0.375) = 4x × (5/8) = 2.5x

Shoes sold by shop A in week I: A_I = 2.5x - 20

Shoes sold by shop A in week III: A_III = 620 - B_III = 620 - 4x

Summing the sales for shop A over the three weeks: A_I + A_II + A_III = 680 (2.5x - 20) + 2.5x + (620 - 4x) = 680 x + 600 = 680 x = 80

Calculating the required values: A_II = 2.5 × 80 = 200 A_III = 620 - 4 × 80 = 300

Ratio of sales by shop A in week II to week III: A_II : A_III = 200 : 300 = 2 : 3

Explanation

Let the number of shoes sold by shop B in week III and week II be 4x and 3x respectively.

Shop A sold 37.5% (or 3/8) less shoes than shop B in week III: A in week II = 4x × (1 − 3/8) = 2.5x A in week I = 2.5x − 20 A in week III = 680 − (A in week I + A in week II) = 680 − (5x − 20) = 700 − 5x

Given that the total shoes sold by A and B together in week III is 620: (700 − 5x) + 4x = 620 x = 80

Calculating the required values: Shoes sold by shop A in week II = 2.5 × 80 = 200 Shoes sold by shop B in week II = 3 × 80 = 240 Total shoes sold by shops A and B in week II = 200 + 240 = 440 Shoes sold by shop A in week III = 700 − 5(80) = 300 Total shoes sold by shop A in weeks II and III together = 200 + 300 = 500

Required percentage = (440 / 500) × 100 = 88%

Explanation

Let the number of shoes sold by shop B in week III be 4x. Shoes sold by shop B in week II = 3x. Shoes sold by shop A in week II = (1 - 0.375) × 4x = (5/8) × 4x = 2.5x. Shoes sold by shop A in week I = 2.5x - 20. Shoes sold by shop A in week III = 620 - 4x.

Total shoes sold by shop A in three weeks: (2.5x - 20) + 2.5x + (620 - 4x) = 680 x + 600 = 680 x = 80

Thus, shoes sold by shop B in week III = 4 × 80 = 320.

Total shoes sold by shop B in weeks I, III, and IV = 3 × 370 = 1110. Given shoes sold by shop B in week I = 460: Shoes sold by shop B in week IV = 1110 - (460 + 320) = 1110 - 780 = 330.

Explanation

Round each decimal to its nearest integer for quick estimation: 5.89 ≈ 6 14.01 ≈ 14 203.999 ≈ 204

Substitute these values into the given equation: ? + 6 × 14 = 204 ? + 84 = 204 ? = 204 - 84 = 120

Explanation

Approximating the numbers to their nearest integers: 2731.04 ≈ 2730 91.03 ≈ 91 474.91 ≈ 475 18.97 ≈ 19

Substituting these values into the given equation: 2730 ÷ 91 = 475 ÷ 19 + ? 30 = 25 + ? ? = 30 - 25 = 5

Explanation

Applying the approximation to the given expression, the value works out to 149. Hence, option B is correct.

Explanation

Approximating each term to the nearest whole number: 249.01 ≈ 249 14.89 ≈ 15 26.03 ≈ 26 3.01 ≈ 3

Substitute the approximated values into the expression: (249 - 15) ÷ (26 × 3) = 234 ÷ 78 = 3

Explanation

Approximating the given decimal numbers to the nearest integers: 64.01 ≈ 64 19.98 ≈ 20 9.01 ≈ 9

Substituting these values into the equation: (64 × 20) ÷ 32 = ? ÷ 9 (2 × 20) = ? ÷ 9 40 = ? ÷ 9 ? = 40 × 9 = 360

Explanation

Circumference of a circle = 2πr. 2 × (22/7) × r = 88 r = 14 cm

Given the ratio of length, breadth, and radius is 5 : 4 : 2: Common ratio multiplier x = 14 / 2 = 7 cm. Length = 5 × 7 = 35 cm Breadth = 4 × 7 = 28 cm

Area of rectangle = Length × Breadth = 35 × 28 = 980 cm².

Explanation

Since the savings rate of B is 45% and the combined savings rate of A and B is also 45%, the savings rate of A must equal 45%.

Total Expenditure = Total Income × (1 - 0.45) = 0.55 × Total Income 1980 = 0.55 × Total Income Total Income = 1980 / 0.55 = Rs. 3600

Let Income of B be x, then Income of A = 0.8x. Total Income = x + 0.8x = 1.8x = 3600 x = 2000

Income of A = 0.8 × 2000 = Rs. 1600 Saving of A = 45% of 1600 = 0.45 × 1600 = Rs. 720

Explanation

Marked Price (MP) = CP × (1 + 75/100) = 800 × 1.75 = Rs. 1400.

Selling Price (SP) = MP × (1 - 20/100) × (1 - 40/100) SP = 1400 × (4/5) × (3/5) = 1400 × (12/25) = 56 × 12 = Rs. 672.

Explanation

Let the present ages of A and B be 5x and 9x respectively.

After 5 years, the sum of their ages = 2 × 40 = 80 years. (5x + 5) + (9x + 5) = 80 14x + 10 = 80 14x = 70 x = 5

Present age of B = 9 × 5 = 45 years. Present age of C = Present age of B - 9 = 45 - 9 = 36 years.

Explanation

Convert the train speed to meters per second: 72 × (5/18) = 20 m/s. The length of the train is Speed × Time = 20 × 14 = 280 m. The length of the platform is half the train length: 280 / 2 = 140 m. Total distance to cross the platform is the sum of their lengths: 280 + 140 = 420 m. Time taken = Total distance / Speed = 420 / 20 = 21 seconds. Shortcut: Since speed is constant, time is directly proportional to distance. Time taken = 14 + (14 / 2) = 21 seconds.

Explanation

The phrasal verb "get away with" is an English idiom that means to escape punishment, blame, or legal consequences for an improper or illegal action. In the past tense, "got away with murder" is the standard idiomatic expression used to describe someone who has evaded justice for a crime.

Explanation

The phrasal verb "get along with" means to have a friendly, smooth, or harmonious relationship with someone. In the given sentence, "getting along well with each other" accurately conveys that the cousins share a good relationship, making the original construction grammatically sound, idiomatic, and meaningful.

Explanation

The idiomatic expression give up hope means to abandon all expectation or cease hoping for something. In the given context, the subject stopped believing that he would ever conduct the experiment successfully, making gave up the appropriate phrasal verb.

Explanation

The phrase "let down" functions as a noun phrase denoting a disappointment or an anticlimax, particularly when an outcome fails to meet high expectations or extensive preparation. In the given sentence, characterizing the final presentation as "a huge let down" after months of dedicated effort is idiomatically and contextually accurate.

Explanation

The idiomatic phrasal verb meaning to tolerate, endure, or bear an unpleasant situation or behavior is "put up with". Following the preposition "of" in the phrase "tired of", the gerund form "putting up with" correctly completes the construction.

Explanation

Statement I is true: the passage notes that after a death, the household was "making do without an earner," showing that the main cause of the decline in income is the loss of an earner rather than the one-time cost of the funeral. Statement II is true: the passage states that despite biomedical advances there is still no cure or vaccine, and the fall in death rates is credited instead to "life-prolonging treatments." Statement III is not supported: the passage only mentions that victims faced stigma, without specifying that religious communities in Africa branded them as "dirty." Hence, both I and II are true.

Explanation

Statement I is not supported: the passage notes that women were more likely to get tested, implying men are less likely to, but this is unrelated to whether someone is the first in the household to test positive. Statement II is true: some traditional religions viewed an early death as a break in the ancestral chain, and since AIDS causes early death, the blame falls on the disease. Statement III is true: the passage notes that the stigma discouraged open conversations about HIV/AIDS, leaving patients to suffer in silence and pushing them away from their families. Statement IV is true: being the first in the family to test positive could lead to being accused of bringing the disease into the household, reflecting a persisting fear and a lack of empathy from family members. Hence, II, III and IV are true.

Explanation

According to the fourth paragraph of the passage, while poverty affected access to expensive treatments, it does not account for the high prevalence and severity of HIV across Africa. The author demonstrates this by noting that other poor regions around the world, such as Central America, South Asia, and the Caribbean, were significantly less affected, whereas Botswana and South Africa, two of the wealthiest nations on the African continent, were among the hardest hit. This evidence shows that the epidemic was not limited to poor localities.

Explanation

The first paragraph explains that the HIV/AIDS crisis served as a formative experience for leading medical figures and physicians responding to modern health crises like COVID-19, making it a foundational reference point for the medical community in handling large-scale epidemics.

Explanation

The idiomatic expression "earned his spurs" means to gain initial recognition, establish a reputation, or demonstrate competence and capability in a particular field or role. In the context of the passage, it signifies that Anthony Fauci demonstrated his ability and expertise in managing major infectious disease outbreaks through his formative work during the American AIDS crisis.

Explanation

The quote highlights that Africa experienced the most devastating consequences because the epidemic originated and emerged there before appearing elsewhere. Being the first region to encounter the virus meant that health authorities had no pre-existing guidelines, treatment protocols, or historical models to reference, allowing the disease to spread rapidly before effective containment strategies could be established.

Explanation

The passage gives two examples of religious leaders acting in similar, misleading ways: in America, many viewed HIV/AIDS as punishment for sin, with churches opposing condoms and refusing to bury AIDS victims, while in Malawi, hundreds of thousands turned to a healer who claimed ancestral spirits had shown him a tree-bark cure. This shows religious leaders across the globe holding similar perspectives. The passage describes these views rather than showing religion bringing people together, so option A does not fit, and it says nothing to support option D. Hence, the correct answer is that religious leaders across the globe hold similar perspectives.

Explanation

In the seventh paragraph, the phrase "making do without an earner" describes how impoverished households manage to cope, subsist, and sustain their daily living after losing an income-earning family member. The idiomatic expression denotes managing with whatever limited resources are available to ensure continued existence and survival.

Explanation

In the passage, flocked describes large numbers of people gathering or congregating together toward a single destination or person. The exact opposite of congregating or gathering together in a mass is to scatter, break up, and move away in various directions, which is defined by dispersed.

Explanation

In the sentence "The worst of the pandemic may be over, but its effects endure", the verb endure means to continue to exist or remain in effect over a prolonged duration. Persist denotes the exact same meaning of continuing firmly or obstinately in a state or existing continuously.

Explanation

The adjective critical means essential or vitally important, which fits the context of personal protective equipment being indispensable for healthcare workers and individuals fighting a disease outbreak. Other options do not fit grammatically or logically to describe the crucial role of protective gear.

Explanation

The phrasal verb "dispose of" means to discard or get rid of something. In passive voice, the past participle "disposed" correctly pairs with the preposition "of" to describe the proper discarding of personal protective equipment such as masks and gloves to prevent environmental harm.

Explanation

The sentence discusses how waste management does not follow a uniform standard around the world, which is why waste can end up in nature. The idea being conveyed is that waste disposal is not handled in a systemic (uniform, standardized) way everywhere. Hence, "systemic" is the correct word.

Explanation

In the clause where the blank appears, a singular subject is needed to agree with the singular verb is rare. The gerund littering functions as an uncountable noun referring to the improper disposal of waste in public areas, fitting both the grammatical structure and the context of urban cleanliness.

Explanation

The phrase pose a threat to is a standard English collocation meaning to cause risk, danger, or harm. In the context of environmental pollution in water bodies, discarded personal protective equipment directly endangers aquatic organisms and marine ecosystems. Since the blank is preceded by the indefinite article a and followed by the preposition to, a singular countable noun representing danger or hazard is required.

Explanation

In the sentence "It depends on the chemical additives used to ___ them," the structure requires an infinitive of purpose formed by "to" followed by the base form of the verb. The base verb "produce" correctly completes the infinitive construction, explaining the purpose for which the chemical additives are used during manufacturing.

Explanation

In the sentence discussing environmental efforts during an emergency, the verb backtrack fits grammatically and contextually to indicate that sustainability practices regress or lose progress during a crisis. It correctly functions as the plural present-tense verb agreeing with the subject sustainability practices.

Explanation

The sentence discusses the development of environmentally friendly solutions to tackle the problem of non-recyclable and non-reusable medical protective equipment. The adjective sustainable modifies a plural subject that performs the action are emerging, for which innovations is the contextually and grammatically precise fit.

Explanation

The prepositional phrase into the middle of the road is grammatically sound, uses the appropriate preposition into to indicate movement toward the interior of an area, and contains no structural, lexical, or punctuation errors. In the other segments, the spelling though is used incorrectly in place of the preposition through, the preposition on is incorrectly used instead of over, and the singular noun head incorrectly replaces the plural heads when referring to multiple people in a crowd.

Explanation

The clause follows standard subject-verb agreement where the plural noun accounts correctly pairs with the plural passive verb are maintained, followed by a comma and the subject of the main clause, everyone. The sentence establishes a real conditional in the present tense, making this segment grammatically sound.

Explanation

The phrase correctly uses the conjunction "whether" followed by the infinitive structure "to launch" to express an indirect question of choice or deliberation, along with the proper modifier "Jupiter space" preceding the noun in the predicate.

Explanation

Part A is error-free. In part B, "for" is incorrect; it should be replaced with "of," since "of" expresses the relationship between a part and a whole. In part C, "reserve" is incorrect; the plural form "reserves" should be used after a fraction. In part D, "a" is incorrect; "the" should be used before a superlative form. Hence, part A is the correct answer.

Explanation

The phrase making money from live is grammatically sound, using the correct present participle form after the past continuous auxiliary to denote an ongoing activity. In the rest of the sentence, the relative pronoun who is required for people rather than which, the auxiliary did must be followed by the base verb hesitate instead of the past tense hesitated, and the idiomatic phrasal verb for contributing money is chip in rather than chip up.

Explanation

Proximity is a noun that means nearness in space, time, or relationship. In the first sentence, the phrase in close proximity is used correctly to describe physical closeness among individuals. In the third sentence, proximity sensor is a standard technical term referring to a device that detects the presence of nearby objects without physical contact.

Explanation

The verb "predate" means to exist or occur at a date earlier than something else. In statement II, it correctly conveys that the blue beads may have existed prior to Christopher Columbus' arrival. In statement III, it is accurately used to indicate that the economic struggles existed long before the onset of the COVID-19 pandemic.

Explanation

"Vague" (adjective) means of uncertain, indefinite, or unclear character or meaning, describing unfocused or imprecise thinking or communication. "Vagueness" (noun) means a lack of certainty, distinctness, or preciseness in thought or communication. Statement I correctly uses "vague" to denote uncertainty about the goal. Statement II correctly uses "vagueness" to denote a lack of clarity about the surroundings. Statement III correctly uses "vagueness" to denote a lack of distinctness and certainty. Hence, all three statements — I, II, and III — are correct.

Explanation

The adjective volatile means liable to change rapidly and unpredictably, characterized by wide fluctuations or instability. In the first statement, volatile correctly functions as an adjective describing the unstable, rapidly shifting movement of gold prices. In the second statement, volatile is used accurately to convey the unpredictable price swings of Bitcoin that hinder its reliability as a payment instrument. In the third statement, the word is used inappropriately both contextually and in its derived noun form, where certainty or uncertainty of paternity is the intended biological concept.

Explanation

Ambiguity is a noun that refers to the quality of being open to more than one interpretation, or an inexactness and uncertainty in meaning. In statement I, it correctly describes an unclear legal provision regarding the age limit for adoption. In statement III, it is used appropriately to signify an unclear or confusing detail in a corporate report that creates doubt among shareholders. Statement II improperly uses the adjective ambiguous in a context that requires a parallel noun denoting an activity or pursuit alongside meditation.

Explanation

The passage does not state that businesses prioritize AI schematics over making profits, as it only mentions challenges in finding suitable applications and adopting the technology. Regarding Moravec's paradox, the text highlights that machines find complex arithmetic and formal logic easy compared to biological intelligence, not that biological intelligence is entirely incapable of processing them. Additionally, the passage mentions the gradual adoption of electrification across decades without asserting that nineteenth-century businesses lacked irrational exuberance. Because all three statements are unsubstantiated by the text, none of the given statements are correct.

Explanation

Go has only two possible outcomes — win or lose — both of which are easily identified, and while individual games can play out in countless unique ways, the underlying rules remain few and clearly specified. Customer calls, on the other hand, have no such pre-defined conditions and can go in many, many more possible directions. Since AI works well under clearly specified, limited conditions like those in Go but not in the open-ended, unpredictable nature of customer calls, the given inference is definitely true.

Explanation

The passage states, "A more subtle problem is that of deciding what to use AI for." "Subtle" means not obvious, or nuanced; its opposite is "blatant," meaning obvious or glaringly conspicuous. Hence, "blatant" is the correct answer.

Explanation

Statement I is not supported: the passage does not mention any increase in maintenance costs due to AI. Statement II is true: machines find complex arithmetic and formal logic easy but struggle with tasks like coordinated movement and locomotion, showing that AI finds it difficult to handle tasks that aren't purely logical. Statement III is true: two-fifths of organisations with "significant investments" in AI had yet to report any benefits at all, indicating an absence of returns. Statement IV is true: internet giants are staffed by programmers and already sit on huge piles of user-generated data, but "not everyone is so lucky," showing that the data required to build effective AI isn't equally available to all organisations. Hence, II, III and IV are true.

Explanation

An informative tone is characterized by an objective presentation of facts, data, and analytical insights intended to educate the reader on a particular subject. Throughout the passage, the author details survey findings from Boston Consulting Group, MIT, and PwC, draws historical parallels to factory electrification, and explains technical concepts such as Moravec's paradox with clear examples. The primary intent is to provide knowledge and explain why artificial intelligence adoption is difficult for traditional firms.

Explanation

"Academia" refers to the community concerned with research, education, and scholarship. This indicates that most recruits to the AI sector come straight out of college or academic backgrounds, implying that "old and experienced experts" are not readily available in this field — otherwise, academia would not be such a fertile (affording abundant possibilities for growth) recruiting ground. Hence, AI, being a new technology, doesn't have old and experienced experts is the correct inference.

Explanation

In the context of the passage, the word deploy refers to putting a tool, system, or technology into active and effective operation within an organization. Utilizing technology means bringing it into service to achieve functional outcomes, which directly matches the intended meaning of implementing and using artificial intelligence systems across businesses.

Explanation

Statement I is true: the passage notes that after a death, the household was "making do without an earner," showing that the main cause of the decline in income is the loss of an earner rather than the one-time cost of the funeral. Statement II is true: the passage states that despite biomedical advances there is still no cure or vaccine, and the fall in death rates is credited instead to "life-prolonging treatments." Statement III is not supported: the passage only mentions that victims faced stigma, without specifying that religious communities in Africa branded them as "dirty." Hence, both I and II are true.

Explanation

The noun phrase requires sector after agriculture, while the comparative adjective bigger must be modified by the adverb slightly, requiring an exchange between A and B. Similarly, economic modifies recovery strategy, requiring an exchange between D and E to form the correct phrase economic recovery strategy. The restored sentence reads: The agriculture sector, which has received a slightly bigger share of the budget, remains vital to the country's economic recovery strategy.

Explanation

Exchanging priorities (1) with wealthiest (4) and tipping (2) with humans (3) restores the intended meaning and grammatical structure of the sentence. The modified sentence reads: "Three-quarters of people in the world's wealthiest nations believe humans are pushing the planet towards a dangerous tipping point and support a shift of priorities away from economic profit." Here, "wealthiest nations" correctly modifies the country type, "humans are pushing" provides the proper subject-verb agreement, "tipping point" forms the standard idiomatic environmental phrase, and "shift of priorities" logically fits the desired transition away from pure economic profit.

Explanation

The adjective popular correctly describes the widespread recognition of Sudoku outside Japan, forming the phrase became popular outside Japan. Correspondingly, mental appropriately modifies faculties, forming the standard English collocation mental faculties to refer to cognitive abilities kept sharp by solving puzzles. Swapping words 1 and 4 produces a coherent and grammatically meaningful sentence.

Explanation

In the given sentence, the subject "Research" requires the singular present tense verb "suggests" to introduce the subordinate clause beginning with "that". Correspondingly, the noun phrase "with its ... wildfires" requires the participial adjective "accompanying" to describe the wildfires that occur alongside drought. Swapping words (1) and (2) produces the coherent sentence: "Research suggests that water problems - drought, with its accompanying wildfires, and flooding - are likely to become much worse around the world as climate breakdown takes hold."

Explanation

All highlighted words are in their grammatically and contextually appropriate positions. Midday properly denotes the time of day, already serves as an adverb modifying the progressive verb lashing to indicate ongoing rainfall, flash pairs directly with floods to form the standard term flash floods, and mudslides appropriately names the concurrent geological hazard affecting road travel.

Explanation

Part B connects directly with Part D to complete the prepositional phrase describing the Strategic Partnership (SP) model as a component of the Defence Procurement Procedure (DPP). Part C connects smoothly with Part F using the coordinating conjunction 'and', maintaining parallel present perfect verb structures ('have finalised' and 'has been completed'). Part A cannot pair with Part E because the simple present tense 'is repeatedly delayed' is grammatically incompatible with the time duration 'over the last couple of years', which requires the present perfect tense. Thus, only pairs B-D and C-F form meaningful and grammatically sound sentences.

Explanation

Fragment B correctly combines with fragment F to form a grammatically sound and meaningful cause-and-effect sentence describing how decreased network reliability leads customers to seek alternative providers.

Fragment C correctly combines with fragment D, where the modal verb 'will' in C is followed by the base verb phrase 'be sworn in and begin their terms as lawmakers' in D to complete the predicate for 'the new members of parliament'.

Fragment A ends with the indefinite article 'an', requiring a noun starting with a vowel sound, which does not match any of the given second-half fragments.

Explanation

Connecting fragment B with fragment E produces a grammatically coherent sentence: "Historians researching contemporary events have traditionally banked on newspapers and magazines as primary sources." The plural subject "Historians researching contemporary events" uses the auxiliary verb "have", which naturally links to the adverb and past participle phrase "traditionally banked on" to complete the predicate in the present perfect tense.

Explanation

Fragment A connects appropriately with F because the noun remnants is correctly complemented by the prepositional phrase of concoctions that had meat and fish, forming a complete and meaningful sentence about paleobiological findings. Fragment C connects with D because the adjective certain seamlessly modifies the noun phrase political parties, forming a grammatically sound clause describing historical opposition to office computerization.