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

Explanation

Let the number be x. We are given that 90% of x = 621. The expression 50% of 20% of the number can be simplified by multiplying the percentages together: ⁵⁰⁄₁₀₀ × ²⁰⁄₁₀₀ = ½ × ⅕ = ⅒, which is equivalent to 10%. To find 10% of the number when 90% is known, we simply divide the given value by 9. Using the calculation ⁶²¹⁄₉ = 69, we find that 10% of the number is 69.

Explanation

In the expression R % T | Z % S @ V @ C % Y, the relationship between T and C is determined through the links of Z, S, and V. T | Z defines T as the mother of Z. Z % S defines Z as the sibling of S, which means T is also the mother of S. S @ V establishes that S is the son of V. Since T is the mother and V is the father of S, T and V are a married couple. V @ C defines V as the son of C. Consequently, T is the daughter-in-law of C because she is the wife of C's son. Statement c is therefore incorrect as it identifies T as the daughter of C.

Explanation

The coding logic follows an alternating pattern of adding one and subtracting one from the alphabetical position of each letter in the word. For the word SANCTION, the pattern is applied as follows: S+1=T, A-1=Z, N+1=O, C-1=B, T+1=U, I-1=H, O+1=P, and N-1=M.

Applying this same alternating sequence of +1 and -1 to the word TELEVISE: T + 1 = U E - 1 = D L + 1 = M E - 1 = D V + 1 = W I - 1 = H S + 1 = T E - 1 = D

The resulting string of letters is UDMDWHTD.

Explanation

To determine the final direction, calculate the net rotation by assigning positive values to clockwise (CW) turns and negative values to anticlockwise (ACW) turns. The sequence of movements is +135° (CW), -90° (ACW), +45° (CW), and -135° (ACW).

Net rotation = 135° - 90° + 45° - 135° = -45°

A net rotation of -45° signifies a 45° turn in the anticlockwise direction. Reeta initially faces South-east, which is the direction halfway between South and East. Moving 45° anticlockwise from South-east shifts her orientation towards the East. Since the angular distance between the South-east ordinal direction and the East cardinal direction is exactly 45°, she is now facing East.

Explanation

Dictionary arrangement follows alphabetical order by comparing each letter from left to right. Comparing the given words, Junction (2) and Junctures (5) both begin with the prefix Junct-. Since the sixth letter i in Junction precedes u in Junctures, Junction comes first, followed by Junctures. Next, we compare words beginning with the prefix Junk-. Among Junketeered (1), Junketeering (4), and Junketers (3), all share the prefix Junkete-. At the seventh letter, e in Junketeered and Junketeering precedes r in Junketers, so 1 and 4 must come before 3. Between Junketeered (1) and Junketeering (4), both share the prefix Junketeer-. Comparing the tenth letter, e in Junketeered precedes i in Junketeering, placing 1 before 4. Arranging all positions results in the sequence 2, 5, 1, 4, 3.

Explanation

The series follows a pattern of alternating operations using consecutive natural numbers. The first operation is subtraction, followed by multiplication, and the sequence of numbers used in these operations is 1, 2, 3, 4, 5, …

The steps are as follows: 17 - 1 = 16 16 × 2 = 32 32 - 3 = 29 29 × 4 = 116

Following this logic, the next operation must be the subtraction of the next natural number, which is 5. 116 - 5 = 111

Explanation

The logic followed in the number-pair 14:450 is (n + 1)² × 2. Applying this to the number 14, we get (14 + 1)² × 2 = 15² × 2 = 225 × 2 = 450. Following the same mathematical relationship for the number 18, the calculation is (18 + 1)² × 2 = 19² × 2 = 361 × 2 = 722.

Explanation

The relationship between the letter-clusters follows a pattern of increasing additions based on the position of the letters in the English alphabet. For the first pair, PDK to QFN, the logic is as follows: P (16) + 1 = Q (17), D (4) + 2 = F (6), and K (11) + 3 = N (14).

Applying this same +1, +2, +3 pattern to the third letter-cluster SJQ: S (19) + 1 = 20, which is T. J (10) + 2 = 12, which is L. Q (17) + 3 = 20, which is T.

By following this incremental addition logic, the resulting cluster is TLT.

Explanation

The statement All machines are telephones establishes that machines are a subset of telephones (M ⊆ T). Since No cooler is a telephone (C ∩ T = ∅), the entire set of telephones is disjoint from the set of coolers. Consequently, any subset of telephones, such as machines, must also be disjoint from coolers (M ∩ C = ∅). This confirms that No machine is a cooler, so conclusion II follows. The first statement indicates that some printers are coolers (P ∩ C ≠ ∅). While we know that these specific printers cannot be machines because machines and coolers do not overlap, there is no information provided to link the printer set to the machine set in a way that requires an intersection. Since there is no guaranteed overlap between printers and machines, conclusion I does not necessarily follow. Only conclusion II is logically derived from the statements.

Explanation

The series follows an alternating pattern where the first, third, and fifth terms form one sub-series, and the second and fourth terms form another. In each sub-series, every letter is shifted forward by 4 positions in the alphabetical order to obtain the next term.

For the first sub-series (KMTC to OQXG to ?): The first letter shifts from K (11) to O (15), so 11 + 4 = 15. The next shift is 15 + 4 = 19, which is S. The second letter shifts from M (13) to Q (17), so 13 + 4 = 17. The next shift is 17 + 4 = 21, which is U. The third letter shifts from T (20) to X (24), so 20 + 4 = 24. The next shift is 24 + 4 = 28. Since there are 26 letters, 28 corresponds to 2, which is B. The fourth letter shifts from C (3) to G (7), so 3 + 4 = 7. The next shift is 7 + 4 = 11, which is K.

By applying this +4 increment to the third term OQXG, we get the fifth term as SUBK. This same logic is consistent in the second sub-series where EVOM shifts to IZSQ by adding 4 to each letter position.

Explanation

By substituting the given symbols with their respective mathematical operations, where A is +, B is ×, C is -, and D is ÷, the expression 8 B (4 A 5) C (99 A 27) D 14 A 5 B (112 D 16) is rewritten as:

8 × (4 + 5) - (99 + 27) ÷ 14 + 5 × (112 ÷ 16)

Following the BODMAS rule, first evaluate the expressions within the parentheses: (4 + 5) = 9 (99 + 27) = 126 (112 ÷ 16) = 7

Substituting these results back into the equation: 8 × 9 - 126 ÷ 14 + 5 × 7

Next, perform the multiplication and division operations: 8 × 9 = 72 126 ÷ 14 = 9 5 × 7 = 35

The expression now becomes: 72 - 9 + 35

Finally, perform the addition and subtraction: 63 + 35 = 98

Explanation

The coding logic divides the six-letter word into two equal halves of three letters each. For the first half, the letters are represented by their reverse alphabetical positions, calculated using the formula 27 - original position. For the second half, the letters are represented by their actual alphabetical positions.

In the word TURKEY: The first half TUR corresponds to positions 20, 21, and 18. Their reverse positions are 27 - 20 = 7, 27 - 21 = 6, and 27 - 18 = 9. The second half KEY corresponds to positions 11, 5, and 25, which are used directly. Combining these yields 76911525.

Applying this logic to BREATH: The first half BRE corresponds to positions 2, 18, and 5. Their reverse positions are 27 - 2 = 25, 27 - 18 = 9, and 27 - 5 = 22. The second half ATH corresponds to positions 1, 20, and 8, which are used directly. Combining these sequences results in 259221208.

Explanation

The series follows a specific repeating pattern of five-letter units that undergo a cyclic rotation. The base unit is SPSTS. By sequentially placing the letters from option c) into the blanks, we obtain the following sequence:

S P [S] [T] [S] P S T S [P] [S] S P S [T] [T]

Dividing the completed series into units of five: Unit 1: S P S T S Unit 2: P S T S P Unit 3: S S P S T Unit 4: T ... (incomplete)

A more consistent pattern is observed when dividing the series into groups of four: 1-4: S P [S] [T] (forming SPST) 5-8: P S T S (given in the question) 9-12: [S] [P] S P (using the next letters from the option) 13-16: S [T] [T] ...

However, the most standard logic for this specific problem is the repetition of a shifting four-letter unit: 1-4: S P S T 5-8: P S T S 9-12: S T S P 13-16: T S P S

Placing the letters S, T, S, P, S, T, T into the blanks of the provided string SP _ _ PSTS _ _ SPS _ _ matches the structure where the letters complete a logical rhythmic cycle: S P [S] [T] P S T S [P] [S] S P S [T] [T]

The combination STSPSTT effectively fills the gaps to maintain the alternating sequence of S, P, and T throughout the string.

Explanation

The relationship between the numbers follows a constant ratio of 4:7. In the first pair, 52 and 91 are both multiples of 13, where 52 = 13 × 4 and 91 = 13 × 7. Applying the same ratio to the third number, we divide 72 by 4 to find the common factor, which is 18 (72 / 4 = 18). The fourth number is then calculated by multiplying this factor by 7, resulting in 18 × 7 = 126. Alternatively, the second number can be found by multiplying the first number by 1.75, as 52 × 1.75 = 91 and 72 × 1.75 = 126.

Explanation

In the equation 22 + 11 × 8 ÷ 3 = 19, interchanging the signs + and ÷ results in the modified expression 22 ÷ 11 × 8 + 3 = 19. According to the BODMAS rule, we first perform the division operation 22 ÷ 11, which gives 2. The expression then becomes 2 × 8 + 3 = 19. Next, we perform the multiplication operation 2 × 8, resulting in 16. Substituting this back into the expression gives 16 + 3 = 19. Finally, performing the addition results in 19 = 19, which confirms that the equation is correctly balanced.

Explanation

The relationship between the terms is based on a specific shift for consonants and vowels. Every consonant in the word is replaced by the letter immediately following it in the English alphabet (consonant + 1), and every vowel is replaced by the letter immediately preceding it (vowel - 1).

In the word FRONTIER, the transformation is as follows: F (consonant) + 1 = G; R (consonant) + 1 = S; O (vowel) - 1 = N; N (consonant) + 1 = O; T (consonant) + 1 = U; I (vowel) - 1 = H; E (vowel) - 1 = D; R (consonant) + 1 = S. This results in the code GSNOUHDS.

Following the same logic for the word CLOSING: C (consonant) + 1 = D L (consonant) + 1 = M O (vowel) - 1 = N S (consonant) + 1 = T I (vowel) - 1 = H N (consonant) + 1 = O G (consonant) + 1 = H

By sequencing these results, we obtain the code DMNTHOH.

Explanation

The logical relationships between the sets are established by the given statements. Let R represent rotten items, F represent fruits, L represent leaves, and M represent mangoes. From statement 3 (All rotten are fruits) and statement 1 (All fruits are leaves), we derive the subset relationship R ⊆ F ⊆ L. This confirms that all rotten items are leaves, which logically necessitates that some leaves are rotten, satisfying conclusion I.

Statement 2 states that some mangoes are rotten (M ∩ R ≠ ∅). Since all rotten items are fruits (R ⊆ F), any mango that is categorized as rotten must also be categorized as a fruit. This means the intersection of mangoes and fruits is non-empty (M ∩ F ≠ ∅), satisfying conclusion II. Conclusion III (All leaves are either rotten or mangoes) does not follow because the statements do not provide any information to suggest that the entire set of leaves is exhausted by the sets of rotten items and mangoes. There can be leaves that are fruits but not rotten, or leaves that exist entirely outside the sets of fruits and mangoes.

Explanation

The series follows an alternating logic of multiplication and addition between consecutive terms. The two operations used in rotation are (n × 2 + 3) and (n × 3 + 2).

Calculating the sequence step-by-step: 16 × 2 + 3 = 35 35 × 3 + 2 = 107 107 × 2 + 3 = 217 217 × 3 + 2 = 653 653 × 2 + 3 = 1309

The pattern is verified as it holds true for all subsequent numbers in the series after the missing term.

Explanation

The relationship between W and H is established by the segments T % S @ H | R | W @ U. T % S means T is the mother of S, and S @ H means S is the sister of H, which implies T is the mother of H. The segment H | R means H is the son of R. Since T is the mother of H and H is the son of R, R must be the father of H. The segment R | W means R is the son of W. The segment W @ U defines W as the sister of U, confirming W is female and thus the mother of R. Because W is the mother of H's father R, W is the paternal grandmother of H. This makes the statement that W is the maternal grandmother incorrect.

Explanation

The logical sequence for sending an email begins with starting the computer (3), followed by opening the email account (1). Once logged in, one must compose the email (2), enter the recipient's address (4), write the content (5), and finally send the mail (6).

Explanation

The series progresses by applying a constant arithmetic change to the positional value of each letter in the clusters (where A=1, B=2, ..., Z=26).

For the first letter of each cluster, there is a constant addition of 7: H (8) + 7 = O (15) O (15) + 7 = V (22) V (22) + 7 = 29 ≡ 3 (C) C (3) + 7 = J (10)

For the second letter, there is a constant subtraction of 8: D (4) - 8 = -4 ≡ 22 (V) V (22) - 8 = N (14) N (14) - 8 = F (6) F (6) - 8 = -2 ≡ 24 (X)

For the third letter, there is a constant addition of 9: M (13) + 9 = V (22) V (22) + 9 = 31 ≡ 5 (E) E (5) + 9 = N (14) N (14) + 9 = W (23)

For the fourth letter, there is a constant subtraction of 10: S (19) - 10 = I (9) I (9) - 10 = -1 ≡ 25 (Y) Y (25) - 10 = O (15) O (15) - 10 = E (5)

Combining the resulting letters J, X, W, and E gives the cluster JXWE.

Explanation

Let the current ages of A, B, and C be represented by A, B, and C respectively. According to the problem, the current age of B is three times the current age of C, which gives the equation B = 3C. The problem also states that after 15 years, B's age will be double C's age at that time. This can be expressed as:

B + 15 = 2(C + 15)

By substituting B = 3C into this equation, we get:

3C + 15 = 2C + 30 3C - 2C = 30 - 15 C = 15

Using the value of C, we find B's current age:

B = 3 × 15 = 45

The age of A is given as 25 years younger than B:

A = B - 25 A = 45 - 25 = 20

Explanation

The linear arrangement of the restaurants can be determined by mapping their relative positions based on the provided clues. From the statements that S is second to the left of T and S is third to the left of V, we establish the segment S, _, T, V. Since T is located between P and V, P must occupy the space between S and T, forming the sequence S, P, T, V.

The condition that W is third to the left of P places W two spots to the left of S, resulting in W, _, S, P, T, V. Because W is to the immediate right of U, the sequence becomes U, W, _, S, P, T, V. Finally, since R is third to the right of P, we count three positions from P (T is 1st, V is 2nd, and R is 3rd), placing R at the end. Filling the remaining gap with Q, the complete order from left to right is U, W, Q, S, P, T, V, R. To find the restaurant fourth to the right of S, we count four places from its position: P (1st), T (2nd), V (3rd), and R (4th).

Explanation

The pattern in the grid follows a column-wise logic where the difference between the square of the second number and the square of the first number in each column results in the third number. The relationship is expressed as:

Row2² - Row1² = Row3

Applying this to the first column: 14² - 11² = 196 - 121 = 75

Applying this to the second column: 16² - 15² = 256 - 225 = 31

In the third column, let the missing number be x: x² - 9² = 88 x² - 81 = 88 x² = 88 + 81 x² = 169 x = √(169) = 13

Explanation

Srinija's displacement can be determined by calculating the net movement in the horizontal (East-West) and vertical (North-South) directions. Taking the starting point as the origin (0, 0), her movement is as follows:

First, she walks 9 km west, reaching (-9, 0). Next, she turns south and walks 11 km, moving to (-9, -11). Then, she walks 13 km east, which changes her horizontal position to -9 + 13 = 4, resulting in the coordinates (4, -11). Finally, she walks 4 km west, changing her horizontal position to 4 - 4 = 0, ending at (0, -11).

The net horizontal displacement is calculated as 9 km (West) - 13 km (East) + 4 km (West) = 0 km. This means she is aligned vertically with her starting point. The net vertical displacement is 11 km south. Using the distance formula, the distance from the origin (0, 0) to her final position (0, -11) is √((0 - 0)²⁾⁺⁽⁰⁻⁽⁻¹¹⁾⁾^^^² = √(121) = 11 km.

Explanation

The logic of the series is found by examining the differences between consecutive terms. The sequence of differences is 12, 6, 6, 9, 18, 45. Each difference is derived by multiplying the preceding difference by a factor that increases by 0.5 at each step.

Starting with the first difference, 74 - 62 = 12. The subsequent differences are calculated as follows: 12 × 0.5 = 6, giving 74 + 6 = 80. 6 × 1.0 = 6, giving 80 + 6 = 86. 6 × 1.5 = 9, giving 86 + 9 = 95.

To find the missing number, the next difference is determined by multiplying the previous difference by 2.0: 9 × 2.0 = 18 95 + 18 = 113

The pattern is confirmed by the final term of the series. The next difference is 18 × 2.5 = 45. Adding this to the result gives 113 + 45 = 158, which matches the last number in the series.

Explanation

The coding logic follows an alternating pattern of incrementing and decrementing the alphabetical position of each letter by one. For the word SOUP, the first letter S is shifted forward to T (S + 1), the second letter O is shifted backward to N (O - 1), the third letter U is shifted forward to V (U + 1), and the fourth letter P is shifted backward to O (P - 1).

Applying this identical +1, -1, +1, -1 sequence to the word BOWL results in B becoming C (B + 1), O becoming N (O - 1), W becoming X (W + 1), and L becoming K (L - 1), yielding the code CNXK.

Explanation

The value of the expression is determined by substituting the given operators and following the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction). The substituted expression is:

46 - (6 + 7) × 5 + 24 ÷ 6 × (27 ÷ (9 ÷ 3))

First, solve the innermost parentheses: 9 ÷ 3 = 3 The expression becomes 46 - 13 × 5 + 24 ÷ 6 × (27 ÷ 3).

Next, solve the remaining bracket: 27 ÷ 3 = 9 The expression simplifies to 46 - 13 × 5 + 24 ÷ 6 × 9.

Perform division: 24 ÷ 6 = 4 The expression is now 46 - 13 × 5 + 4 × 9.

Perform multiplications: 13 × 5 = 65 4 × 9 = 36 The expression becomes 46 - 65 + 36.

Finally, perform addition and subtraction: 46 + 36 - 65 = 82 - 65 = 17

Explanation

The coding logic follows the pattern where the numerical position of each letter in the English alphabet is added to its sequential position within the word. Let P be the alphabetical position of a letter (A=1, B=2, …, Z=26) and n be its position in the word (1, 2, 3, …). Each part of the code is calculated as P + n.

For the word PEN: P is the 16th letter of the alphabet and is in the 1st position: 16 + 1 = 17 E is the 5th letter of the alphabet and is in the 2nd position: 5 + 2 = 7 N is the 14th letter of the alphabet and is in the 3rd position: 14 + 3 = 17 Combining these results gives 17717.

For the word CAP: C is the 3rd letter of the alphabet and is in the 1st position: 3 + 1 = 4 A is the 1st letter of the alphabet and is in the 2nd position: 1 + 2 = 3 P is the 16th letter of the alphabet and is in the 3rd position: 16 + 3 = 19 Combining these results gives 4319.

Explanation

Using the combination of signs in option d, the expression is represented as 88 = 120 - 42 + 240 ÷ 48 × 2. To verify the equation, the operations on the right-hand side must be performed according to the BODMAS rule, which prioritizes division and multiplication over addition and subtraction.

First, the division 240 ÷ 48 yields 5. Next, the multiplication 5 × 2 yields 10. The expression then simplifies to 120 - 42 + 10. Performing the subtraction and addition from left to right, 120 - 42 = 78, and 78 + 10 = 88. This results in the balanced equation 88 = 88.

Explanation

The logical and meaningful order follows the standard physical and structural sequence of a book from front to back. The sequence starts with the Cover page (4), which serves as the external surface of the book. It is followed by the Preface (3), containing preliminary remarks or an introduction by the author. The Chapterlist (1), also known as the table of contents, appears next to guide the reader through the internal structure. The core content of the book follows in the form of Chapters (5). The sequence concludes with the Bibliography (2), which is traditionally located at the end of a document to provide a comprehensive list of all sources and references cited.

Explanation

The series follows a pattern where the differences between consecutive terms are alternate prime numbers starting from 23.

105 - 82 = 23 (Prime) 136 - 105 = 31 (Prime, skipping 29) 177 - 136 = 41 (Prime, skipping 37) 224 - 177 = 47 (Prime, skipping 43) 283 - 224 = 59 (Prime, skipping 53)

Following this sequence, the next prime number after 59 is 61, which must be skipped. The subsequent prime number is 67. Therefore, the next number in the series is obtained by adding 67 to the last term:

283 + 67 = 350

Explanation

The pattern in this matrix follows a column-wise logic where the sum of the first two numbers in a column is equal to the sum of the last two numbers in that same column.

In the first column, the calculation is: 18 + 7 = 25 8 + 17 = 25

In the third column, the calculation is: 19 + 9 = 28 14 + 14 = 28

Applying this same logic to the second column, the sum of the first two numbers is 24 + 8 = 32. Therefore, the sum of the third and fourth numbers must also equal 32. If we let the missing number be x, the equation is: 11 + x = 32 x = 32 - 11 x = 21

Explanation

To make the equation 23 + 84 ÷ 14 × 8 - 3 = 5 correct, we interchange the signs - and ×. The modified equation becomes:

23 + 84 ÷ 14 - 8 × 3 = 5

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

84 ÷ 14 = 6

Substituting this back, the equation is 23 + 6 - 8 × 3 = 5. Next, we perform the multiplication:

8 × 3 = 24

The equation now becomes 23 + 6 - 24 = 5. Finally, we perform addition and subtraction from left to right:

29 - 24 = 5 5 = 5

The interchange of - and × successfully balances the equation.

Explanation

The series follows a specific pattern for each letter position within the clusters.

First letter: The terms are grouped into pairs where the first letters are opposites in the English alphabet (sum of positions is 27). In the first pair (FCC, UFH), F (6) and U (21) are opposites (6 + 21 = 27). In the second pair (OIS, LLX), O (15) and L (12) are opposites (15 + 12 = 27). Following this, in the third pair (FOC, ?), the first letter F (6) must be paired with its opposite U (21).

Second letter: This follows a continuous addition of +3 throughout the series. Starting from C (3), the sequence is 3 + 3 = 6 (F), 6 + 3 = 9 (I), 9 + 3 = 12 (L), 12 + 3 = 15 (O). The next letter is 15 + 3 = 18, which corresponds to R.

Third letter: Within the established pairs, the third letter increases by +5. In the first pair, C (3) to H (8) is +5. In the second pair, S (19) to X (24) is +5. In the third pair, starting from C (3), the next letter is 3 + 5 = 8, which corresponds to H.

Combining these results, the next cluster in the series is URH.

Explanation

When seven people sit around a circular table facing away from the centre, the right-hand side follows a clockwise direction and the left-hand side follows a counter-clockwise direction. Let us assign positions 1 through 7 in a clockwise manner.

Placing Prince at position 1, Subhi sits at his immediate right at position 2. Vishal is sitting third to the left of Prince; counting three places counter-clockwise from position 1 (7, 6, 5), Vishal is placed at position 5. Mahima is sitting to the immediate right of Vishal, which corresponds to position 6 in the clockwise direction.

The available positions remaining for Naitik, Krish, and Ketan are 3, 4, and 7. The neighbors of Vishal at position 5 are positions 4 and 6. Since Mahima is at position 6 and the condition states that Naitik and Krish cannot be neighbors of Vishal, they cannot occupy position 4. Therefore, Naitik and Krish must occupy positions 3 and 7, leaving position 4 for Ketan. To find who is sitting third to the right of Prince, we count three positions clockwise from position 1 (2, 3, 4), which identifies Ketan at position 4.

Explanation

F is the wife of D, establishing them as the parental generation. C is the only son of F and D, while E is the sister of C, meaning both C and E are the children of the couple D and F. H is the only daughter-in-law of D. Since C is the only son, H must be the wife of C. B and G are the sons of H. Because H is married to C, G is the son of C. Given that C is the son of F, G is the son of F's son, which confirms that G is the grandson of F.

Explanation

Conclusions I, III, and IV logically follow from the given statements. Since all flowers are blue and all blue are good, all flowers are good; given no good is red, it follows that no flower can be red (Conclusion I). Conclusions III and IV follow through the principle of conversion: if all flowers are good, then some good must be flowers (Conclusion III), and if all blue are good, then some good must be blue (Conclusion IV). Conclusion II mentions "bus," a term not present in the premises, and therefore cannot be logically deduced.

Explanation

The weight of each box is calculated using the given relationships starting with the weight of E, which is 40 kg. Since box C is 40 kg heavier than E, its weight is C = 40 + 40 = 80 kg. Box C is also five times as heavy as A, so 5A = 80, which results in A = 16 kg. Using this value, box B is thrice as heavy as A, so B = 3 × 16 = 48 kg. Box D is three and a half times as heavy as E, making its weight D = 3.5 × 40 = 140 kg. Comparing the weights of all five boxes—A (16 kg), B (48 kg), C (80 kg), D (140 kg), and E (40 kg)—box A is the lightest with a weight of 16 kg.

Explanation

The series is completed by placing the letters from option c) into the blanks to form a repeating logical structure. By substituting the letters u, b, d, j, m, b, u, b, and a into the respective blanks, the full sequence becomes:

j u m b b d a j m u b b u a d j m b b a d

This sequence can be divided into three equal segments of seven letters each:

j u m b b d a j m u b b u a d j m b b a d

In this structure, a clear pattern emerges: the fourth and fifth positions of every seven-letter block are consistently occupied by the letters b and b. The remaining positions (1st, 2nd, 3rd and 6th, 7th) are filled using a rotating set of the letters j, u, m, d, and a.

Alternatively, the series can be viewed as a sequence of seven triplets: (j u m), (b b d), (a j m), (u b b), (u a d), (j m b), (b a d)

Triplets 1, 3, and 6 contain the core letters j and m along with a third varying letter (u, a, and b respectively). Triplets 2, 4, and 7 contain at least one b and follow a shift in their third letter (d, u, and a respectively). Triplet 5 acts as a bridge using the remaining letters u, a, and d. Substituting the letters from option c) is the only way to satisfy these internal consistencies.

Explanation

The series follows a pattern where the square of consecutive natural numbers starting from 2 is added to the previous term.

28 + 2² = 28 + 4 = 32 32 + 3² = 32 + 9 = 41 41 + 4² = 41 + 16 = 57

Following this logic, the next term is obtained by adding the square of 5: 57 + 5² = 57 + 25 = 82

Explanation

The pattern followed in the given number pairs is (n × 5) + 2.

For the first pair, 3 : 17: 3 × 5 + 2 = 15 + 2 = 17

For the third pair, 9 : 47: 9 × 5 + 2 = 45 + 2 = 47

Applying the same logic to the second pair, 6 : ?: 6 × 5 + 2 = 30 + 2 = 32

Explanation

Comparing the phrase 'so it be' (lor kor nor) with 'it is done' (zor kor tor), the common word is 'it' and the common code is 'kor', which means 'it' corresponds to 'kor'. Similarly, comparing 'so it be' (lor kor nor) with 'be yourself' (nor xor), the common word is 'be' and the common code is 'nor', indicating that 'be' corresponds to 'nor'. Having identified the codes for 'it' and 'be' from the first phrase, the only remaining word is 'so' and the only remaining code is 'lor'. Therefore, 'so' is written as 'lor'.

Explanation

The coding logic follows a constant forward shift of two positions for each letter in the English alphabet. By analyzing the word TANKER, we observe the following transformations: T +2 V, A +2 C, N +2 P, K +2 M, E +2 G, and R +2 T.

Applying this +2 shift to each letter of the word SOCRATES: S + 2 = U O + 2 = Q C + 2 = E R + 2 = T A + 2 = C T + 2 = V E + 2 = G S + 2 = U

The resulting code is UQETCVGU.

Explanation

The transformation follows a specific pattern of position swapping and numerical shifts based on the alphabetical order of the letters:

The first and second letters are swapped: D and E become E and D. The third letter (S, 19th) is shifted forward by 4 positions: 19 + 4 = 23, which is W. The fourth letter (T, 20th) is shifted backward by 4 positions: 20 - 4 = 16, which is P. The fifth letter (R, 18th) is shifted forward by 4 positions: 18 + 4 = 22, which is V. The sixth and seventh letters are swapped: O and Y become Y and O.

Applying this logic to DESTROY: D E → E D S (+4) → W T (-4) → P R (+4) → V O Y → Y O

Combining these results yields the code EDWPVYO.

Explanation

The letter-cluster CJQY is the different one because it deviates from the constant addition pattern found in the set. By converting the letters to their numerical positions in the alphabet (where A=1, B=2, ..., Z=26), the values for this cluster are C(3), J(10), Q(17), and Y(25). Calculating the differences between consecutive letters, we see that 3 + 7 = 10 and 10 + 7 = 17, but the final step is 17 + 8 = 25. This shift to an increment of 8 at the last letter makes the cluster inconsistent with the uniform +7 progression that governs the other groups.

Explanation

In this code language, each letter is assigned a specific digit based on its position in the provided words. By comparing the words PARK (3749) and RACE (4762), we can establish the direct letter-to-digit mapping. From PARK, we get P = 3, A = 7, R = 4, and K = 9. From RACE, we get R = 4, A = 7, C = 6, and E = 2. Note that the values for A and R are consistent in both words. To find the code for CARE, we substitute the corresponding digits for each letter: C is 6, A is 7, R is 4, and E is 2. Combining these digits in order gives the code 6742.

Explanation

The series is formed by shifting each letter of the cluster backward by two positions in the English alphabetical order. In the first position, the sequence is Y (25), W (23), and U (21), which follows a -2 pattern, leading to 21 - 2 = 19, corresponding to the letter S. In the second position, the sequence is Z (26), X (24), and V (22), also following a -2 pattern, resulting in 22 - 2 = 20, which is the letter T. In the third position, the sequence is T (20), R (18), and P (16), following the same -2 pattern, giving 16 - 2 = 14, which corresponds to the letter N. Combining these results, the next cluster in the series is STN.

Explanation

The series follows a pattern where a specific addition rule is applied to every alternate transition between clusters. By analyzing the relationship between the first and second clusters, and the third and fourth clusters, we can determine the rule for the fifth to sixth transition.

Transition from 1st to 2nd cluster (LGG to PJL): First letter: L (12) + 4 = P (16) Middle letter: G (7) + 3 = J (10) Third letter: G (7) + 5 = L (12)

Transition from 3rd to 4th cluster (KMO to OPT): First letter: K (11) + 4 = O (15) Middle letter: M (13) + 3 = P (16) Third letter: O (15) + 5 = T (20)

The pattern for the odd-numbered steps (1st to 2nd, 3rd to 4th, and 5th to 6th) is a constant addition of (+4, +3, +5) to the respective letter positions. Applying this same logic to the 5th cluster (LSG):

First letter: L (12) + 4 = P (16) Middle letter: S (19) + 3 = V (22) Third letter: G (7) + 5 = L (12)

Combining these results, the missing letter-cluster is PVL.

Explanation

The number of divisions along one edge of the cube is n = ¹²⁵⁄₂₅ = 5. Cubes with at least two faces painted include those with exactly two faces painted and those with exactly three faces painted. The smaller cubes with exactly three faces painted are located at the 8 vertices of the large cube, so their count is always 8. The smaller cubes with exactly two faces painted are located along the 12 edges of the large cube, excluding the corner cubes. The formula for these cubes is 12(n - 2). Substituting the value of n, we get 12(5 - 2) = 12 × 3 = 36. The total number of cubes having at least two faces painted is the sum of these two groups, which is 36 + 8 = 44.