SSC CGL Tier 1 2022 General Intelligence & Reasoning Questions with Solutions

Explanation

The logic followed in the given rows is (First number + Second number) × 6 = Third number.

Applying this to the first row: (6 + 9) × 6 = 15 × 6 = 90

Applying this to the second row: (12 + 8) × 6 = 20 × 6 = 120

Following the same logic for the third row: (13 + 6) × 6 = 19 × 6 = 114

Explanation

The given sequence is an alternating series formed by combining two separate arithmetic progressions. The first series consists of terms at the odd positions (1st, 3rd, 5th, 7th, and 9th), while the second series consists of terms at the even positions (2nd, 4th, 6th, and 8th).

The first series follows a constant subtraction pattern: 286 - 23 = 263 263 - 23 = 240 240 - 23 = 217 To find the next term in this series, which corresponds to the question mark at the 9th position, we subtract 23 from the 7th term: 217 - 23 = 194

The second series follows a similar logic with a different constant: 192 - 16 = 176 176 - 16 = 160 160 - 16 = 144 The pattern confirms that the sequence relies on alternating subtractions, and the missing value is determined by the first progression.

Explanation

The relationship between the numbers in the given sets follows the logic: (First number × Third number) + 4 = Second number.

In the first set (12, 112, 9), multiplying the first and third numbers gives 12 × 9 = 108. Adding 4 to this product results in 108 + 4 = 112, which is the second number.

In the second set (10, 84, 8), multiplying the first and third numbers gives 10 × 8 = 80. Adding 4 to this product results in 80 + 4 = 84, which is the second number.

Applying the same mathematical pattern to the numbers in option d (18, 94, 5), we multiply the first and third numbers: 18 × 5 = 90. Adding 4 to this result gives 90 + 4 = 94, which matches the second number in the set.

Explanation

The coding logic follows a specific positional rearrangement of the nine letters in each word. The first three letters (indices 1, 2, 3) are shifted to positions 3, 1, 2 respectively (effectively 1-2-3 becomes 2-3-1). The fourth and fifth letters remain in their original positions. The last four letters are rearranged by swapping adjacent pairs: the 6th and 7th letters are interchanged, and the 8th and 9th letters are interchanged.

Applying this pattern to INTEGRITY: Indices 1-2-3: I-N-T becomes N-T-I Indices 4-5: E and G remain E-G Indices 6-7: R-I is interchanged to become I-R Indices 8-9: T-Y is interchanged to become Y-T

By combining these segments, the word INTEGRITY is coded as NTIEGIRYT.

Explanation

The statements can be analyzed using the transitive property of set inclusion. Since All p are c and All c are f, it logically follows that All p are f. The second statement, No f is t, establishes that the set of f and the set of t are disjoint, meaning they have no elements in common. Because the set p is entirely contained within the set f, and the set f shares no elements with t, it is certain that no elements of p can belong to t. This validates conclusion II, No p is t. Regarding conclusion I, because c is also a subset of f, and f is disjoint from t, no c can be t, making the conclusion Some t are c false.

Explanation

The pair 11-37 follows the mathematical relation y = 3x + 4, where 11 × 3 + 4 = 37. This logic deviates from the consistent rule y = 3x + 3 followed by the other three alternatives. In those instances, the second number is always derived by multiplying the first number by 3 and adding 3. Since 11-37 requires an addition of 4 to reach the second value rather than 3, it is the odd one out.

Explanation

The expression ∀ ∞ ∪ Q W # Y ∗ Z translates to the relationships between individuals V, U, W, Y, and Z. The component V ∞ U indicates that V is the sister of U, establishing that V is female. The relation U @ W (represented by the symbol Q) means W is the father of U. Since V and U are siblings, W is also the father of V. The part W # Y indicates that Y is the wife of W, which makes Y the mother of V and U. Finally, Y ∗ Z states that Y is the mother of Z. Because V, U, and Z are all children of the same parents W and Y, and V is a female sibling, V is the sister of Z.

Explanation

The given word-pair establishes a relationship between a measuring instrument and the specific physical quantity it quantifies, as a thermometer is the device used to measure temperature. Following this same logical connection, an oximeter is a medical instrument specifically designed to measure the oxygen saturation level of the blood. Both pairs represent the relationship of Instrument: Measured Parameter.

Explanation

The words are processed by dividing them into specific segments and moving the first letter of each segment to the end of that segment. For the word EDUCATION, the segments are determined by vowel-consonant groupings:

1. The first segment is ED (Vowel-Consonant). Moving the first letter E to the end results in DE.
2. The second segment is U (Vowel). As it is a single-letter segment, it remains U.
3. The third segment is C (Consonant). It remains C.
4. The fourth segment is AT (Vowel-Consonant). Moving the first letter A to the end results in TA.
5. The fifth segment is ION (Vowel-Vowel-Consonant). Moving the first letter I to the end results in ONI.

Combining these transformed segments in order: DE + U + C + TA + ONI = DEUCTAONI

This pattern is consistent with the provided examples: In PRESIDENT, the first segment PRE (Consonant-Consonant-Vowel) is transformed to REP, while the rest of the word remains unchanged. In KNOWLEDGE, the segments LE (Consonant-Vowel) and DGE (Consonant-Consonant-Vowel) are transformed to EL and GED respectively, while the initial part KNOW remains unchanged. Applying the same logic to the segments of EDUCATION yields the code DEUCTAONI.

Explanation

To find the day of the week for 1st January 2033, we calculate the total number of odd days from the reference point of 1st January 0001. We break down the period into 2000 years, 32 completed years (2001 to 2032), and the first day of 2033.

The number of odd days in 2000 years is 0, as it is a multiple of 400. For the next 32 years, we determine the number of leap years by dividing 32 by 4, which yields 8 leap years and 32 - 8 = 24 ordinary years. Since a leap year has 2 odd days and an ordinary year has 1, the total odd days in this period is (8 × 2) + (24 × 1) = 16 + 24 = 40. Dividing 40 by 7 gives a remainder of 5 odd days.

Adding the 1 day from 1st January 2033, the total number of odd days is 5 + 1 = 6. In the standard calendar day coding where 0 is Sunday, 1 is Monday, 2 is Tuesday, 3 is Wednesday, 4 is Thursday, 5 is Friday, and 6 is Saturday, a total of 6 odd days results in Saturday.

Explanation

The first pair established a relationship based on astronomical classification, where Earth is categorized as a planet. Applying the same logic to the second pair, the Moon is classified as a satellite, specifically a natural satellite, because it is a celestial body that orbits a planet.

Explanation

Conclusion II follows because the statements establish that some animals are pets and all pets are white. Since there is an intersection between animals and pets, and the entire set of pets is contained within the set of white things, it logically follows that the animals that are pets must also be white. Conclusion III follows directly from the first statement through the rule of conversion. If the proposition some dogs are animals is true, then its converse, some animals are dogs, must also be true. Conclusion I does not follow because the premises do not establish any relationship between the set of dogs and the sets of pets or white entities, meaning an overlap is possible but not certain. Therefore, only conclusions II and III are logically sound.

Explanation

The given equation is 18 + 2 × 6 ÷ 3 - 7 = 50. According to the question, the signs ÷ and + must be interchanged. After replacing + with ÷ and ÷ with +, the expression becomes 18 ÷ 2 × 6 + 3 - 7. Following the BODMAS rule, the division is performed first, which results in 9 × 6 + 3 - 7. Then, multiplication yields 54 + 3 - 7. Finally, performing the addition and subtraction leads to 57 - 7 = 50. As the calculated value matches the right-hand side of the equation, the identity is satisfied.

Explanation

The series follows a systematic arithmetic progression for each letter position within the clusters based on their numerical values in the English alphabet where A=1, B=2, C=3, …

First letter: The sequence A(1), B(2), C(3), …, E(5) follows a +1 pattern. The fourth term is 3 + 1 = 4, which corresponds to D.

Second letter: The sequence B(2), D(4), F(6), …, J(10) follows a +2 pattern. The fourth term is 6 + 2 = 8, which corresponds to H.

Third letter: The sequence C(3), F(6), I(9), …, O(15) follows a +3 pattern. The fourth term is 9 + 3 = 12, which corresponds to L.

Fourth letter: The sequence D(4), D(4), D(4), …, D(4) remains constant. The fourth term is D.

Combining these results, the missing cluster is DHLD.

Explanation

The groups of numbers are expected to follow a consistent arithmetic pattern where each subsequent number is derived by subtracting a fixed value from the preceding one. In the standard pattern observed, the common difference between consecutive numbers is 20. While group (c) starts with this pattern as 98 - 78 = 20, it fails to maintain it for the next pair since 78 - 56 = 22. This deviation from the uniform common difference of 20 used in the other sets makes it the odd group.

Explanation

To satisfy the equation, we interchange the numbers 12 and 24. Substituting these values into the original expression gives: (6)³ ÷ 24 + [(√(81)) × 4] - (28 ÷ 2) + 12 = 43

Applying the order of operations (BODMAS), we first simplify the powers and roots: 216 ÷ 24 + [9 × 4] - (28 ÷ 2) + 12 = 43

Next, we perform the division and multiplication operations: 216 ÷ 24 = 9 9 × 4 = 36 28 ÷ 2 = 14

The expression now becomes: 9 + 36 - 14 + 12 = 43

Performing the addition and subtraction from left to right: 45 - 14 + 12 = 43 31 + 12 = 43 43 = 43

Since the left-hand side equals the right-hand side, interchanging 12 and 24 makes the equation correct.

Explanation

The relationship string W # Q @ T | Y @ M % K % L is decoded as follows. W # Q indicates that W is the brother of Q. Q @ T means Q is the son of T. T | Y shows T is the father of Y. Combining these, W, Q, and Y are siblings with T as their father. Y @ M states Y is the son of M; since T is the father, M must be the mother of the siblings. M % K establishes that M is the mother of K, making K a sibling to W, Q, and Y. Finally, K % L reveals K is the mother of L, which confirms K is female. As K is a female sibling of W, she is the sister of W.

Explanation

The code for each word is calculated by taking the sum of the positional values of its letters in the English alphabet, where A = 1, B = 2, C = 3, ..., and Z = 26.

For PEPPER, the calculation is: P (16) + E (5) + P (16) + P (16) + E (5) + R (18) = 76

For CUCUMBER, the calculation is: C (3) + U (21) + C (3) + U (21) + M (13) + B (2) + E (5) + R (18) = 86

Applying the same logic to CAULIFLOWER, we sum the alphabetical positions of each letter: C = 3 A = 1 U = 21 L = 12 I = 9 F = 6 L = 12 O = 15 W = 23 E = 5 R = 18

The total sum is: 3 + 1 + 21 + 12 + 9 + 6 + 12 + 15 + 23 + 5 + 18 = 125

Explanation

The given symbols are: A - B (A is father of B), A + B (A is mother of B), and A × B (A is brother of B). To show that "Q is the brother of P," the expression must establish that Q is male and that Q and P are siblings.

In Option D (Q × P - R), the first part "Q × P" directly translates to "Q is the brother of P" based on the provided definition of the × symbol. While Option A also implies Q is a male sibling of P (since P is the brother of Q and Q is a father), Option D is the most direct expression as it uses the definition explicitly.

Explanation

Interchanging the symbols + and ÷ in the expression 6 + 20 ÷ 12 × 7 - 11 = 70 transforms it into 6 ÷ 20 + 12 × 7 - 11. Applying the BODMAS rule, the division 6 ÷ 20 results in 0.3. The multiplication part 12 × 7 equals 84. The modified expression becomes 0.3 + 84 - 11. Combining these values, 0.3 + 84 - 11 = 84.3 - 11 = 73.3. Since 73.3 is not equal to 70, the equation is incorrect.

Explanation

The numerical relationship between the terms in each pair follows the pattern x : x³ + x² + x.

For the first pair, where x = 4, the second term is calculated as 4³ + 4² + 4 = 64 + 16 + 4 = 84.

For the third pair, where x = 13, the second term is calculated as 13³ + 13² + 13 = 2197 + 169 + 13 = 2379.

Applying this same logic to the second pair where x = 11, the missing term is found by: 11³ + 11² + 11 = 1331 + 121 + 11 = 1463

This calculation consistently satisfies the relationship defined by the other pairs in the sequence.

Explanation

The series follows an independent arithmetic progression for the alphabetical position of each letter in the clusters. For the first letter, the position decreases by 2 in each step: X(24), V(22), T(20), R(18), P(16). For the second letter, the position increases by 3 in each step: D(4), G(7), J(10), M(13), P(16). For the third letter, the position increases by 1 in each step: N(14), O(15), P(16), Q(17), R(18). For the fourth letter, the position increases by 2 in each step: C(3), E(5), G(7), I(9), K(11). Applying these patterns to find the missing third cluster results in the letters corresponding to positions 20, 10, 16, and 7.

Explanation

The logic followed in the given sets (3, 13, 18) and (29, 39, 44) is based on constant differences between consecutive terms. In the first set, 13 - 3 = 10 and 18 - 13 = 5. Similarly, in the second set, 39 - 29 = 10 and 44 - 39 = 5. The general pattern is n₂ = n₁ + 10 and n₃ = n₂ + 5.

Applying this same logic to the set (16, 26, 31), we see that the second number is obtained by adding 10 to the first number, 16 + 10 = 26, and the third number is obtained by adding 5 to the second number, 26 + 5 = 31. This perfectly matches the pattern established by the provided examples.

Explanation

The relationship between the numbers follows the mathematical pattern y = (x × 3) - 11, where x represents the first number and y represents the second number in the pair.

Applying this pattern to the first set: 37 × 3 = 111, and 111 - 11 = 100. Applying the same pattern to the third set: 29 × 3 = 87, and 87 - 11 = 76.

To find the missing number related to 24, apply the same logic: 24 × 3 = 72, and 72 - 11 = 61.

Explanation

The given sequence follows a geometric progression where each successive term is obtained by multiplying the preceding term by a constant factor of 3.

7 × 3 = 21 21 × 3 = 63 63 × 3 = 189 189 × 3 = 567

To find the missing number in the series, we apply the same logic to the last given term: 567 × 3 = 1701

Explanation

The series follows a pattern where a constant value is subtracted from the positional value of each letter in the alphabet (A=1, B=2, …, Z=26).

In the first position, the sequence of letters is N(14), G(7), Z(26), S(19). There is a constant difference of -7 between consecutive terms (14-7=7; 7-7=0 ≡ 26; 26-7=19). Applying the same logic to the last known term, 19-7=12, which corresponds to the letter L.

In the second position, the sequence is T(20), O(15), J(10), E(5). The difference is a constant -5 (20-5=15; 15-5=10; 10-5=5). Continuing the pattern, 5-5=0 ≡ 26, which corresponds to the letter Z.

In the third position, the sequence is R(18), I(9), Z(26), Q(17). The difference is a constant -9 (18-9=9; 9-9=0 ≡ 26; 26-9=17). Continuing the pattern, 17-9=8, which corresponds to the letter H.

In the fourth position, the sequence is Q(17), F(6), U(21), J(10). The difference is a constant -11 (17-11=6; 6-11=-5 ≡ 21; 21-11=10). Continuing the pattern, 10-11=-1 ≡ 25, which corresponds to the letter Y.

By combining the calculated letters for each position, the next term in the series is LZHY.

Explanation

To verify the correctness of option a, we interchange the numbers 5 and 8 in the given equation 5 × 2 - 8 + 9 ÷ 1 = 20. After the swap, the expression on the left-hand side becomes 8 × 2 - 5 + 9 ÷ 1.

Applying the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction), we first perform the division: 9 ÷ 1 = 9

Next, we perform the multiplication: 8 × 2 = 16

Now, substituting these results back into the expression, we have: 16 - 5 + 9

Finally, performing the addition and subtraction: 16 + 9 - 5 = 25 - 5 = 20

The resulting value is 20, which matches the right-hand side of the equation.

Explanation

The coding pattern in this language is determined by counting the number of letters in each word of the phrase and arranging those counts in sequence. In the phrase health is wealth, health has 6 letters, is has 2, and wealth has 6, resulting in the code 626. Similarly, exercise (8 letters) and regularly (9 letters) form 89, while bring (5 letters), good (4 letters), and food (4 letters) form 544.

Applying this logic to the phrase balanced diet is key: balanced = 8 letters diet = 4 letters is = 2 letters key = 3 letters

By concatenating these numerical values in order, we obtain the code 8423.

Explanation

Conclusion I does not follow because the statements only provide relationships between G and U, and between S and U. In syllogisms, when two premises are particular affirmative statements (Some A are B), the middle term (U) is not distributed. This means no definite connection can be established between the remaining terms (G and S). While a Venn diagram could be drawn where G and S do not overlap, it is equally possible for them to overlap; therefore, the statement "No S is G" is not a logical certainty.

Conclusion II does not follow because it directly contradicts Statement I. The premise "Some G are U" logically implies its converse, "Some U are G". Because "Some U are G" is true, the universal negative statement "No U is G" is necessarily false. Since neither conclusion can be definitively proven true based on the given premises, neither follows.

Explanation

The number groups follow the mathematical logic x² + 5 = y, where x represents the first number and y represents the second number. In option (b), the first number is 16, and applying this logic results in 16² + 5 = 256 + 5 = 261. However, the second number provided in this group is 263, which means it follows a different relation (16² + 7 = 263) and is therefore the odd group in the set.

Explanation

To determine which conclusions follow, the statements are analyzed using set relations. Let M represent medicines, C represent capsules, B represent bangles, and T represent toothpastes. The first statement establishes that M is a subset of C (M ⊆ C). The second statement establishes an intersection between C and B (C ∩ B ≠ ∅). The third statement establishes an intersection between B and T (B ∩ T ≠ ∅).

Conclusions I and III both require an intersection between M and B. Although all medicines are capsules and some capsules are bangles, the specific subset of capsules that are medicines may not overlap with the set of bangles. Without a definitive link between M and B, neither conclusion follows.

Conclusion II suggests an intersection between T and C. While toothpastes overlap with bangles and bangles overlap with capsules, there is no logical requirement for toothpastes and capsules to share any elements. Consequently, this conclusion does not follow.

Conclusion IV suggests an intersection between M and T. Since there is no statement linking medicines to toothpastes directly or through a transitive chain of inclusion, this conclusion also fails to follow. Because none of the four conclusions can be definitively proven from the given statements, the logical result is that none of the conclusions follow.

Explanation

The logic followed in the given sets is that the first number minus the second number equals the third number. This can be represented by the formula n₁ - n₂ = n₃.

In the first set (23, 14, 9): 23 - 14 = 9

In the second set (37, 19, 18): 37 - 19 = 18

Following this pattern, for the numbers 125, 25, and 100: 125 - 25 = 100

This calculation confirms that the set (125, 25, 100) satisfies the established numerical relationship where the difference of the first two values results in the third value.

Explanation

The letter-cluster JKZ is the odd one out because it deviates from the numerical pattern where the sum of the alphabetical positions of the second and third letters is exactly 26 (L2 + L3 = 26), based on the order A=1, B=2, …, Z=26. In the cluster JKZ, the sum of the positions of K (11) and Z (26) is 37. Additionally, JKZ is the only cluster in the set that contains no vowels, whereas the other clusters each contain exactly one vowel. This combination of numerical and linguistic properties distinguishes JKZ from the rest of the group.

Explanation

The relationship between the words is based on the geometric shape associated with the object. A kite is a specific type of quadrilateral that is visually and geometrically synonymous with a diamond shape. Following this logic, a ball is a physical object whose most fundamental and defining characteristic is its spherical or round shape. Just as a kite is described as a diamond, a ball is described as being round.

Explanation

The given word-pair follows the relationship of a specific plant and its botanical growth habit. A money plant is a well-known climber, characterized by its ability to grow upwards by clinging to external supports. Similarly, a rose is biologically classified as a shrub, as it is a woody perennial plant with multiple stems arising from or near the ground, typically reaching a shorter height than a tree.

Explanation

The pattern followed in the given numerical analogy is that the second number in each pair is the cube of one-third of the first number. The relationship can be expressed by the formula (ⁿ⁄₃)³, where n is the first number.

For the first pair 15:125: (¹⁵⁄₃)³ = 5³ = 125

For the third pair 36:1728: (³⁶⁄₃)³ = 12³ = 1728

Applying the same logic to the second pair 27:?: (²⁷⁄₃)³ = 9³ = 729

Explanation

The series follows a pattern where each term is derived from the previous one by incrementing the alphabetical positions of the first and second letters while the third letter remains constant.

For the first letter of each term, the sequence follows an addition of +2 to the positional value in the English alphabet. Starting with F (6), the next letter is 6 + 2 = 8, which corresponds to H. Continuing the pattern, 8 + 2 = 10 (J), 10 + 2 = 12 (L), and 12 + 2 = 14 (N).

For the second letter of each term, the sequence also follows an addition of +2 to the positional value. Starting with O (15), the next letter is 15 + 2 = 17, which corresponds to Q. Continuing the pattern, 17 + 2 = 19 (S), 19 + 2 = 21 (U), and 21 + 2 = 23 (W).

The third letter in every given term of the series is X, which means it remains unchanged throughout the sequence. By combining the determined letters H, Q, and X, the missing term is identified as HQX.

Explanation

In syllogistic logic, two affirmative statements cannot yield a negative conclusion. Since Statement I (All J are B) and Statement II (Some D are B) are both affirmative, any negative conclusion such as Conclusion I (Some D are not J) or Conclusion II (Some B are not J) is logically invalid.

For Conclusion I, a definite relationship between D and J cannot be established because the middle term B is not distributed in either premise. In Statement I, B is the predicate of a universal affirmative (A-type) statement, and in Statement II, it is the predicate of a particular affirmative (I-type) statement. According to the rule of the undistributed middle, no valid inference can be drawn between the minor and major terms.

Regarding Conclusion II, the statement All J are B only guarantees that some B are J. It does not logically require that some B are not J. There is a possibility that the sets J and B are identical, which would make the claim Some B are not J false. Because a conclusion must follow necessarily in all possible interpretations of the premises, Conclusion II does not follow.

Explanation

The coding pattern follows a two-step logic. First, each letter of the original word is shifted forward by 2 positions in the English alphabet (Letter + 2). Second, the word is split into consecutive pairs of letters, and the letters within each pair are reversed.

Applying this logic to NOTEBOOK: The word is divided into pairs: (N, O), (T, E), (B, O), and (O, K).

First, applying the +2 shift to each letter: N (14) + 2 = P (16) and O (15) + 2 = Q (17), resulting in (P, Q). T (20) + 2 = V (22) and E (5) + 2 = G (7), resulting in (V, G). B (2) + 2 = D (4) and O (15) + 2 = Q (17), resulting in (D, Q). O (15) + 2 = Q (17) and K (11) + 2 = M (13), resulting in (Q, M).

Next, reversing the letters within each of these shifted pairs: The pair (P, Q) becomes QP. The pair (V, G) becomes GV. The pair (D, Q) becomes QD. The pair (Q, M) becomes MQ.

Combining these pairs in order results in the code QPGVQDMQ.

Explanation

The statements provide that both F and W are subsets of K. However, no information is given regarding the relationship between F and W. Since F and W are both contained within K, they could be disjoint, partially overlapping, or one could be a subset of the other. Without a specific premise linking F and W, Conclusion I (All W are F) and Conclusion III (Some F are W) cannot be logically established as they represent only possibilities, not certainties.

Regarding Conclusion II (Some K are not W), the statement All W are K implies W ⊆ K. In syllogistic logic, this does not guarantee that there are elements in K that are not in W; it remains possible that the sets W and K are identical (W = K). Therefore, the claim that some K are not W is not a necessary consequence of the premises. Since none of the conclusions follow definitely from the given statements, the correct choice is that neither conclusion follows.

Explanation

By interchanging the signs + and * in the given equation 16 + 4 / 2 * 12 - 4 = 40, the expression becomes 16 * 4 / 2 + 12 - 4. Following the BODMAS rule, we first perform the division operation 4 / 2, which equals 2. The equation then becomes 16 * 2 + 12 - 4. Next, we perform the multiplication 16 * 2, which equals 32. Substituting this back gives 32 + 12 - 4. We then perform addition 32 + 12 = 44, and finally subtraction 44 - 4 = 40. This matches the value on the right-hand side of the equation.

Explanation

The coding logic involves a positional transformation where only specific positions within the word are modified. Letters at the first, third, fourth, and sixth positions remain unchanged, while letters at the second and fifth positions are shifted one step forward in alphabetical order (+1).

For the word ARTIST: Position 1: A remains A Position 2: R becomes S (R + 1 = S) Position 3: T remains T Position 4: I remains I Position 5: S becomes T (S + 1 = T) Position 6: T remains T The code is ASTITT.

For the word ADVICE: Position 1: A remains A Position 2: D becomes E (D + 1 = E) Position 3: V remains V Position 4: I remains I Position 5: C becomes D (C + 1 = D) Position 6: E remains E The code is AEVIDE.

Following the same pattern for ASPECT: Position 1: A remains A Position 2: S becomes T (S + 1 = T) Position 3: P remains P Position 4: E remains E Position 5: C becomes D (C + 1 = D) Position 6: T remains T The resulting code is ATPEDT.

Explanation

The numbers in the given sets follow the mathematical relationship where the first number is twice the sum of the second and third numbers. This can be expressed by the formula First = 2 × (Second + Third).

Applying this pattern to the provided sets: In the first set (42, 18, 3), 2 × (18 + 3) = 2 × 21 = 42. In the second set (36, 14, 4), 2 × (14 + 4) = 2 × 18 = 36.

Applying the same logic to option a: In the set (34, 13, 4), 2 × (13 + 4) = 2 × 17 = 34.

The calculation confirms that the first number is equal to twice the sum of the subsequent two numbers, satisfying the established pattern.

Explanation

The relationship between the numbers in each pair is determined by taking the square root of the first number and multiplying it by 3 to obtain the second number. The pattern follows the logic √x × 3 = y.

In the first pair, √(144) = 12, and 12 × 3 = 36. In the third pair, √(196) = 14, and 14 × 3 = 42.

Applying this rule to the second pair, the square root of the third number is √(81) = 9. Multiplying this result by 3 yields 9 × 3 = 27.

Explanation

To satisfy the equation 20 - 10 × 342 ÷ 19 + 51 = 211, we interchange the numbers 51 and 20 and the signs - and +. Substituting these into the left-hand side, we get 51 + 10 × 342 ÷ 19 - 20. Following the BODMAS priority, we solve the division part first: 342 ÷ 19 = 18. The expression then becomes 51 + 10 × 18 - 20. Solving the multiplication gives 51 + 180 - 20. Finally, performing the addition and subtraction results in 231 - 20 = 211, which matches the right-hand side of the equation.

Explanation

The relationship established in the first pair is that of a physical quantity and its corresponding SI base unit. Time is a fundamental physical quantity, and the second is its standard unit of measurement in the International System of Units (SI). Similarly, electric current is a fundamental physical quantity, and its SI base unit is the ampere.

Explanation

The relationship between Horizontal and Vertical is that of antonyms, as they represent two opposite and perpendicular directions of orientation. Similarly, Humid and Dry are antonyms because they represent opposite states of moisture content, where humid signifies a high level of moisture and dry signifies its absence.

Explanation

The given sequence follows a pattern of an arithmetic progression where each term increases by a constant common difference of 17. This series also represents the consecutive multiples of the number 17.

To find the missing number, we can add 17 to the third term or multiply 17 by 4:

17 × 1 = 17 17 × 2 = 34 17 × 3 = 51 17 × 4 = 68 17 × 5 = 85 17 × 6 = 102

Alternatively, using the common difference: 51 + 17 = 68. Verification with the next term confirms the pattern as 68 + 17 = 85.

Explanation

The statements can be analyzed using basic set relations. The premise All Tim are Jack signifies that the set Tim is a subset of the set Jack (T ⊆ J). The second premise No Jack is Ben states that the intersection of the sets Jack and Ben is empty (J ∩ B = ∅). Because Tim is entirely contained within Jack, and Jack has no overlap with Ben, it is logically certain that Tim and Ben also have no overlap (T ∩ B = ∅). In categorical logic, the statement No Tim is Ben is equivalent to the statement No Ben is Tim. This confirms that conclusion III is a valid logical derivation from the provided statements. The additional information that Some Ben is Ruth does not create a definitive negative link between Ruth and Jack, as only the portion of Ruth that overlaps with Ben is excluded from Jack. Since only the third conclusion is necessarily true, the correct choice is that only conclusion III follows.

Explanation

The series follows a specific increment pattern for each letter position based on their numerical rank in the English alphabet where A=1, B=2, ..., Z=26.

For the first letter of each term, there is a constant addition of 6. M(13) plus 6 results in 19 (S). 19 (S) plus 6 results in 25 (Y). 25 (Y) plus 6 results in 31, which cycles back to 5 (E) after subtracting 26. 5 (E) plus 6 results in 11, which corresponds to the letter K.

For the second letter of each term, there is a constant addition of 9. O(15) plus 9 results in 24 (X). 24 (X) plus 9 results in 33, which cycles back to 7 (G). 7 (G) plus 9 results in 16 (P). 16 (P) plus 9 results in 25, which corresponds to the letter Y.

For the third letter of each term, there is a constant addition of 13. R(18) plus 13 results in 31, which cycles back to 5 (E). 5 (E) plus 13 results in 18 (R). 18 (R) plus 13 results in 31, which cycles back to 5 (E). 5 (E) plus 13 results in 18, which corresponds to the letter R.