SSC CGL Tier 1 2023 General Intelligence & Reasoning Questions with Solutions

Explanation

The logic applied to the numbers in the given pairs follows the mathematical pattern n : n² × (n - 1).

For the first pair: 17 : 17² × (17 - 1) 17 : 289 × 16 = 4624

For the third pair: 13 : 13² × (13 - 1) 13 : 169 × 12 = 2028

To find the missing term x in the second pair x : 180, we solve the equation x² × (x - 1) = 180. Testing the value 6: 6² × (6 - 1) = 36 × 5 = 180

The value 6 satisfies the established pattern, making it the correct related term.

Explanation

The letters common to the words SLAP and PAST are S, A, and P. By comparing their respective numerical codes 3160 and 6071, the common digits between the two codes are identified as 1, 6, and 0. This indicates that the set of letters {S, A, P} corresponds to the set of digits {1, 6, 0} in some order. Since L is the only letter in SLAP that does not appear in PAST, its code must be the only digit in 3160 that does not appear in 6071. Excluding the common digits 1, 6, and 0 from the code for SLAP leaves the digit 3.

Explanation

The series follows a specific pattern of positional shifts for each letter in the clusters. By converting the letters into their numerical positions in the English alphabet (A=1, B=2, ..., Z=26), we can identify the following transformations:

For the first letter of each cluster: W (23), U (21), S (19), ? (17), O (15). The pattern is -2. 19 - 2 = 17, which corresponds to the letter Q.

For the second letter of each cluster: T (20), R (18), P (16), ? (14), L (12). The pattern is -2. 16 - 2 = 14, which corresponds to the letter N.

For the third letter of each cluster: D (4), G (7), J (10), ? (13), P (16). The pattern is +3. 10 + 3 = 13, which corresponds to the letter M.

For the fourth letter of each cluster: H (8), K (11), N (14), ? (17), T (20). The pattern is +3. 14 + 3 = 17, which corresponds to the letter Q.

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

Explanation

The relationship followed in the given sets (5, 13, 16) and (4, 11, 14) is defined by the formula: Third Number = 2 × (Second Number - First Number)

Substituting the values for the first example set (5, 13, 16), we get 2 × (13 - 5) = 2 × 8 = 16. For the second example set (4, 11, 14), the calculation is 2 × (11 - 4) = 2 × 7 = 14.

In the set (9, 21, 26), applying the same mathematical rule results in 2 × (21 - 9) = 2 × 12 = 24. The third number in this set is 26, which does not equal the required value of 24.

Explanation

The arithmetic operators in the expression are replaced according to the provided instructions: - becomes ×, + becomes -, × becomes ÷, and ÷ becomes +.

Original expression: 26 - 13 + 144 × 18 ÷ 81

After substituting the symbols: 26 × 13 - 144 ÷ 18 + 81

Applying the BODMAS rule, division is performed first: 144 ÷ 18 = 8

Next, the multiplication is carried out: 26 × 13 = 338

The expression now becomes: 338 - 8 + 81

Finally, performing the addition and subtraction: 330 + 81 = 411

Explanation

The mathematical relationship between the numbers in the provided sets follows the formula n₃ = n₁{n₂} × 10, where n₁, n₂, and n₃ represent the first, second, and third numbers respectively.

For the first set (60, 15, 40): n₃ = ⁶⁰⁄₁₅ × 10 = 4 × 10 = 40

For the second set (100, 50, 20): n₃ = ¹⁰⁰⁄₅₀ × 10 = 2 × 10 = 20

Applying this logic to the set (200, 40, 50) in option a: n₃ = ²⁰⁰⁄₄₀ × 10 = 5 × 10 = 50

The calculation yields 50, which is the third number in the set, confirming that it follows the same pattern as the given examples.

Explanation

The expression segment S - K establishes that S is the mother of K. The preceding segment R + S indicates that R is the brother of S. By linking these two relationships, it is determined that R is the brother of K's mother, S. Therefore, R is the maternal uncle of K, which is described as K's mother's brother.

Explanation

The series follows an alternating pattern of multiplying by 3 and adding 3: 2 * 3 = 6, 6 + 3 = 9, 9 * 3 = 27, 27 + 3 = 30, and 30 * 3 = 90. Following this logic, the next operation is addition (90 + 3), which results in 93.

Explanation

The mathematical operation followed in the number-pairs is y = (x × 2) + 4, where x represents the first number and y represents the second number. For the pair 18:42, applying this formula results in 18 × 2 + 4 = 36 + 4 = 40. Since the second number provided in this pair is 42 rather than 40, it does not conform to the logic established by the other pairs in the set.

Explanation

The relationship between the first pair of words is based on synonymy or closely related characteristics. Fair refers to being just, unbiased, or impartial, which is a core attribute of being Righteous, meaning morally upright or virtuous. In the same way, Cunning describes the trait of being crafty, artful, or guileful in achieving one's ends. Deceit is the practice of propogating beliefs that are not true, which is the defining characteristic or synonymous behavior of someone who is Cunning. Therefore, the analogy follows a pattern where the second word represents the quality or state associated with the first word.

Explanation

The numbers in each given set follow an arithmetic progression with a common difference of 8. In the first set (15, 23, 31), the difference between the second and first terms is 23 - 15 = 8, and the difference between the third and second terms is 31 - 23 = 8. In the second set (33, 41, 49), the same logic applies as 41 - 33 = 8 and 49 - 41 = 8. The set (20, 28, 36) follows this identical pattern where 20 + 8 = 28 and 28 + 8 = 36.

Explanation

The numerical relationship in the given sets (x, y) follows the pattern y = (x + 1)² + 1. For the first set (7, 65), the operation is (7 + 1)² + 1 = 8² + 1 = 64 + 1 = 65. Similarly, for the second set (11, 145), the operation is (11 + 1)² + 1 = 12² + 1 = 144 + 1 = 145.

Applying this logic to the set (8, 82), the calculation is (8 + 1)² + 1 = 9² + 1 = 81 + 1 = 82. This identifies the set that shares the same mathematical property as the provided examples.

Explanation

To make the equation 50 - 25 ÷ 5 × 3 + 6 = 59 correct, interchange the - and + signs. The revised equation is 50 + 25 ÷ 5 × 3 - 6 = 59. Following the BODMAS rule, first solve the division part: 25 ÷ 5 = 5. Then, solve the multiplication: 5 × 3 = 15. The expression now reads 50 + 15 - 6. Adding 50 and 15 yields 65. Finally, subtracting 6 from 65 results in 59, which matches the right-hand side of the equation.

Explanation

To arrange the words in dictionary order, compare them letter by letter. Dedicated (4) and Defiance (2) start with De-. In the third letter, d comes before f, so Dedicated (4) precedes Defiance (2).

Next, examine words starting with Di-: Diabolical (6), Differentiate (5), and Dither (1). Sorting by their third letters (a, f, t), Diabolical (6) comes first, followed by Differentiate (5), and then Dither (1).

Finally, Dramatic (3) begins with Dr-. Since r comes after e and i in the alphabet, it is the last word in the sequence. Combining these groups, the correct alphabetical order is 4, 2, 6, 5, 1, 3.

Explanation

The coding logic used in this language is the square of the number of letters present in the word. For the word PEN, there are 3 letters, and 3² = 9. Similarly, the word PAPER contains 5 letters, and 5² = 25. Applying the same logic to the word CHAPTER, which consists of 7 letters (C, H, A, P, T, E, R), the code is determined by 7² = 49.

Explanation

The coding scheme follows an alternating pattern of adding 2 and 3 to the alphabetical positions of the letters in each word.

In APRIL, the transformation is: A (1) + 2 = 3 (C) P (16) + 3 = 19 (S) R (18) + 2 = 20 (T) I (9) + 3 = 12 (L) L (12) + 2 = 14 (N)

In MARCH, the transformation is: M (13) + 2 = 15 (O) A (1) + 3 = 4 (D) R (18) + 2 = 20 (T) C (3) + 3 = 6 (F) H (8) + 2 = 10 (J)

Applying the same logic (+2, +3, +2, +3) to JUNE: J (10) + 2 = 12 (L) U (21) + 3 = 24 (X) N (14) + 2 = 16 (P) E (5) + 3 = 8 (H)

The resulting code for JUNE is LXPH.

Explanation

In each of the given letter-clusters, the first and second letters are consecutive in alphabetical order. The distinction lies in the movement from the second letter to the third. In the clusters OPK, ABY, and IJG, the sequence moves forward by one position and then moves backward to the third letter: 15 → 16 → 11 (a decrease of 5), 1 → 2 → 25 (a circular decrease of 3), and 9 → 10 → 7 (a decrease of 3).

Conversely, in the cluster LMO, both movements are in the forward direction: 12 → 13 → 15 (an increase of 1 followed by an increase of 2). Furthermore, LMO is the only cluster that starts with a consonant and ends with a vowel, while the other three clusters begin with a vowel and end with a consonant. These combined patterns identify LMO as the cluster that does not belong to the group.

Explanation

The series is formed by dividing the letters into groups of four. The pattern consists of a base four-letter block that alternates with its reverse sequence.

Base block: L M N L Reverse block: N M L N

The complete series follows the sequence: (L M N L) / (N M L N) / (L M N L) / (N M L N) ...

By placing the letters from option c (M, N, L, L, N) into the blanks of the series L _ N L _ M _ N _ M N L _, we complete the pattern as follows:

First group (1-4): L (M) N L → L M N L (Base block) Second group (5-8): (N) M (L) N → N M L N (Reverse block) Third group (9-12): (L) M N L → L M N L (Base block) Fourth group (13): (N) → Start of the next reverse block

The letters filled in the blanks from left to right are M, N, L, L, and N.

Explanation

To determine the relationship, we break down the description provided by Sneha step by step. Sneha's brother's wife's son is Sneha's nephew. The father of this son is Sneha's brother. The mother-in-law of Sneha's brother is the mother of the brother's wife. The only daughter of this mother-in-law must be the brother's wife herself. Therefore, the girl in the photo is Sneha's brother's wife.

Explanation

The pattern follows a two-step transformation. First, the first and third letters of the cluster are swapped. Second, a specific increment is applied to the numerical positions of the letters in the resulting sequence: +2 to the first letter, +3 to the second letter, and +2 to the third letter.

For the first pair, GPK : MSI: Swapping the first and third letters of GPK gives KPG. Applying the increments: K(11) + 2 = M(13), P(16) + 3 = S(19), and G(7) + 2 = I(9). This results in MSI.

For the second pair, RHT : VKT: Swapping the first and third letters of RHT gives THR. Applying the increments: T(20) + 2 = V(22), H(8) + 3 = K(11), and R(18) + 2 = T(20). This results in VKT.

Applying the same logic to IDW: Swapping the first and third letters of IDW gives WDI. Applying the increments: W(23) + 2 = Y(25), D(4) + 3 = G(7), and I(9) + 2 = K(11).

The resulting letter-cluster is YGK.

Explanation

The coding pattern follows the rule where the code is the square of the total number of letters present in the word. In the case of DUST, there are 4 letters, and the square of 4 is 4² = 16. For the word EARTH, there are 5 letters, and the square of 5 is 5² = 25. Applying the same logic to the word MAN, which contains 3 letters, the code is calculated as 3² = 9.

Explanation

Dictionary order is determined by comparing words letter by letter from left to right. All words begin with Di. Comparing the third letters, Diagram (6), Dialect (4), Dialogue (2), Diamond (1), and Diameter (5) start with Dia, while Dictator (3) starts with Dic. Since a comes before c, Dictator (3) is the last word in the sequence. Among the Dia- words, the fourth letters are g, l, l, m, m. Diagram (6) comes first because g precedes l and m. Next, comparing the Dial- words, Dialect (4) has e as its fifth letter, while Dialogue (2) has o. Since e comes before o, Dialect (4) precedes Dialogue (2). Finally, comparing the Diam- words, Diameter (5) has e as its fifth letter, whereas Diamond (1) has o. Since e comes before o, Diameter (5) precedes Diamond (1). This results in the alphabetical sequence 6, 4, 2, 5, 1, 3.

Explanation

The series follows a specific pattern of increasing positional values for each letter in the group. By identifying the numerical position of each letter in the English alphabet (A=1, B=2, …, Z=26), the pattern for each position is as follows:

First letter: The values increase by 2 in each step. A(1) +2 C(3) +2 E(5) +2 G(7) +2 I(9). The missing first letter is G.

Second letter: The values increase by 4 in each step. J(10) +4 N(14) +4 R(18) +4 V(22) +4 Z(26). The missing second letter is V.

Third letter: The values increase by 6 in each step. R(18) +6 X(24) +6 D(30 ≡ 4) +6 J(10) +6 P(16). The missing third letter is J.

Fourth letter: The values increase by 8 in each step. X(24) +8 F(32 ≡ 6) +8 N(14) +8 V(22) +8 D(30 ≡ 4). The missing fourth letter is V.

Combining these letters results in the term GVJV.

Explanation

The numerical value for each word is determined by taking the sum of the reverse positional values of its letters (where A = 26, B = 25, ..., Z = 1) and multiplying that sum by 5.

For BOOK: The reverse positions are B = 25, O = 12, O = 12, and K = 16. Sum = 25 + 12 + 12 + 16 = 65 Code = 65 × 5 = 325

For READ: The reverse positions are R = 9, E = 22, A = 26, and D = 23. Sum = 9 + 22 + 26 + 23 = 80 Code = 80 × 5 = 400

Applying the same logic to ABLE: The reverse positions are A = 26, B = 25, L = 15, and E = 22. Sum = 26 + 25 + 15 + 22 = 88 Code = 88 × 5 = 440

Explanation

The letter-series follows a pattern of repeating five-letter blocks where the third letter of each block increments alphabetically. The base structure of the block is G-L-X-R-E.

The series is divided as follows: Block 1: G (L) A R E (where X = A) Block 2: G L (B) R (E) (where X = B) Block 3: G (L) C (R) E (where X = C) Block 4: G L (D) (R) E (where X = D)

By filling the blanks sequentially from left to right, we use the letters: 1st blank: L 2nd blank: B 3rd blank: E 4th blank: L 5th blank: R 6th blank: D 7th blank: R

This results in the combined sequence L-B-E-L-R-D-R, which completes the series as GLAREGLBREGLCREGLDRE.

Explanation

The letter-clusters are organized based on a specific positional logic where the second letter is four positions ahead of the first letter in the alphabet, and the first and third letters are alphabetical opposites. This pattern can be expressed as P₂ = P₁ + 4 and P₁ + P₃ = 27, where P represents the numerical position of the letter.

In the cluster KNP, the positions are K=11, N=14, and P=16. While the first and third letters are opposites (11 + 16 = 27), the gap between the first and second letter is only 3 (14 - 11 = 3). This deviates from the consistent +4 increment seen in the other clusters, such as FJU (6+4=10), CGX (3+4=7), and IMR (9+4=13), making it the odd one out.

Explanation

The numbers in each set follow a specific logic where the third number is derived from the first and second numbers using the formula: (First Number ÷ Second Number) × 3 = Third Number.

In the first set (4, 2, 6), dividing 4 by 2 gives 2, and multiplying by 3 results in 6, which is (4 ÷ 2) × 3 = 6. In the second set (9, 3, 9), dividing 9 by 3 gives 3, and multiplying by 3 results in 9, which is (9 ÷ 3) × 3 = 9. Applying this same operation to the third set (24, 6, ?), we divide 24 by 6 to get 4, and then multiply by 3 to find the missing value: (24 ÷ 6) × 3 = 4 × 3 = 12.

Explanation

The numbers in the given sets follow a pattern where each term is the square of a consecutive integer modified by a constant value k. The general form of the set is (n² + k, (n+1)² + k, (n+2)² + k). For the first set (17, 26, 37), the integers are 4, 5, 6 and k = 1, as 4² + 1 = 17, 5² + 1 = 26, and 6² + 1 = 37. For the second set (170, 197, 226), the integers are 13, 14, 15 and k = 1, as 13² + 1 = 170, 14² + 1 = 197, and 15² + 1 = 226. In option a, the numbers (48, 63, 80) follow the same logic using consecutive integers 7, 8, 9 and k = -1, since 7² - 1 = 48, 8² - 1 = 63, and 9² - 1 = 80.

Alternatively, for any sequence where terms are squares of consecutive integers plus a constant, the difference between the terms increases by exactly 2. In the first set, the differences are 26 - 17 = 9 and 37 - 26 = 11, where the difference between these is 11 - 9 = 2. In the second set, the differences are 197 - 170 = 27 and 226 - 197 = 29, where the difference between these is 29 - 27 = 2. Similarly, for the set in option a, the differences are 63 - 48 = 15 and 80 - 63 = 17, where the difference between these is 17 - 15 = 2.

Explanation

The relationship followed in the given sets is that the sum of the first two numbers equals the third number. This can be expressed by the formula n₁ + n₂ = n₃.

In the first set (38, 29, 67): 38 + 29 = 67

In the second set (43, 36, 79): 43 + 36 = 79

Applying this same operation to the set (47, 35, 82): 47 + 35 = 82

The numbers in this set satisfy the addition pattern established by the example sets, where the third element is the direct sum of the whole numbers of the first and second elements.

Explanation

The mathematical operation governing the number-pairs is a constant difference where the first number minus 479 equals the second number. This rule is consistent for the pairs (1984, 1505), (1805, 1326), and (2136, 1657), as 1984 - 1505 = 479, 1805 - 1326 = 479, and 2136 - 1657 = 479. In contrast, the pair (1826, 1472) deviates from this pattern because 1826 - 1472 = 354, rather than 479.

Explanation

The numbers in the given sets follow a constant ratio of 3:5. For the first set (39, 65), the relation is 39 × ⁵⁄₃ = 13 × 5 = 65. Similarly, for the second set (63, 105), the relation is 63 × ⁵⁄₃ = 21 × 5 = 105.

In the set (96, 160), the same mathematical pattern is applied. Dividing the first number by 3 gives 96 ÷ 3 = 32, and multiplying this result by 5 yields 32 × 5 = 160. Thus, the numbers 96 and 160 are related by the same ratio of 3:5 observed in the original sets.

Explanation

To make the equation 110 ÷ 20 + 5 × 13 - 9 = 153 correct, the signs for division (÷) and addition (+) are interchanged. Applying this change, the new equation becomes 110 + 20 ÷ 5 × 13 - 9 = 153. Following the BODMAS rule, the division is performed first: 20 ÷ 5 = 4. Next, the multiplication is carried out: 4 × 13 = 52. Finally, the addition and subtraction are performed: 110 + 52 - 9 = 162 - 9 = 153. Since the left-hand side equals the right-hand side, the interchange of ÷ and + makes the equation correct.

Explanation

The analogy follows the relationship of an infection or parasite and the specific organ or part of the body it primarily affects. Ringworm is a fungal infection that grows on the surface of the skin, causing a red, circular rash. Similarly, a tapeworm is a type of parasitic flatworm that lives in the human digestive tract, specifically attaching itself to the wall of the intestine to absorb nutrients. Therefore, the intestine is the primary site of infection for a tapeworm in the same way the skin is the site for ringworm.

Explanation

The given sequence follows a geometric progression where each term is obtained by multiplying the previous term by a common ratio r. Calculating the ratio between the first two terms:

r = (1)/(88){¹⁄₁₇₆} = ¹⁷⁶⁄₈₈ = 2

Verifying this ratio with the last two terms of the series:

r = (1)/(11){¹⁄₂₂} = ²²⁄₁₁ = 2

Since the common ratio r = 2 is consistent throughout the series, the missing third term is found by multiplying the second term by 2:

Third term = ¹⁄₈₈ × 2 = ¹⁄₄₄

This is also consistent with the relationship between the third and fourth terms, as ¹⁄₄₄ × 2 = ¹⁄₂₂. The pattern shows that the denominator is being halved at each step, which effectively doubles the value of the fraction.

Explanation

Based on the instructions provided, the operators in the expression are replaced as follows: + is replaced by ÷, ÷ is replaced by -, - is replaced by ×, and × is replaced by +.

The original expression is 805 + 23 ÷ 4 - 6 × 2.

After replacing the signs according to the rules, the expression becomes: 805 ÷ 23 - 4 × 6 + 2

To find the value, follow the BODMAS rule (Division, Multiplication, Addition, Subtraction). First, perform the division: 805 ÷ 23 = 35. Next, perform the multiplication: 4 × 6 = 24. Substituting these results back into the expression gives 35 - 24 + 2. Finally, perform the addition and subtraction: 11 + 2 = 13.

Explanation

The relation follows the formula n₁ × n₂ × 3 = n₃. In the set (3, 6, 54), the calculation is 3 × 6 × 3 = 54. In the set (4, 2, 24), the calculation is 4 × 2 × 3 = 24. For the set (3, 4, 36), applying the same logic gives 3 × 4 × 3 = 36.

Explanation

To determine the relationship, analyze the description from the end of the statement. The phrase daughter of my daughter-in-law refers to Rocky's granddaughter, because his daughter-in-law is the wife of his son, and their daughter is Rocky's grandchild. The man in the description is the father of this granddaughter. Since the father of Rocky's son's daughter is the son himself, the man Rocky is pointing to is his own son. Therefore, Rocky is the father of that man.

Explanation

The letter series can be completed by dividing the sequence into four groups of four letters each. The pattern is as follows:

TM_P / T_R_ / MRP_ / R___

By substituting the letters from option b) PRMPTTM into the blanks, the sequence becomes:

TM[P]P / T[R]R[M] / MRP[P] / R[T][T][M]

The resulting series is TMPP / TRRM / MRPP / RTTM. The underlying logic is based on an alternating repetition pattern within each group of four letters. In the first and third groups (odd-numbered groups), the third letter is repeated in the fourth position (3ʳᵈ = 4ᵗʰ). In the second and fourth groups (even-numbered groups), the second letter is repeated in the third position (2ⁿᵈ = 3ʳᵈ).

Specifically: Group 1: T, M, P, P (The letter P at the 3rd position is repeated) Group 2: T, R, R, M (The letter R at the 2nd position is repeated) Group 3: M, R, P, P (The letter P at the 3rd position is repeated) Group 4: R, T, T, M (The letter T at the 2nd position is repeated)

This consistent alternating structure confirms that the sequence is formed by the letters P, R, M, P, T, T, M.

Explanation

The relationship between the sets can be understood through subset logic. Since some teachers are scientists and all scientists are doctors, the intersection between teachers and scientists is contained within the set of doctors, confirming that some doctors are teachers (Conclusion I). Furthermore, because all doctors are engineers, the entire set of doctors is a subset of the engineers; thus, the individuals who are both teachers and doctors are also engineers, which proves that some engineers are teachers (Conclusion II). Regarding Conclusion III, the premise that all scientists are doctors implies that every element in the scientist set is also in the doctor set. In logical deduction, the universal affirmative statement All S are D implies the particular affirmative statement Some D are S, provided the sets are non-empty. Therefore, all three conclusions are logically sound based on the given statements.

Explanation

The given series follows a descending pattern where each subsequent term is obtained by subtracting consecutive multiples of 11 from the preceding term.

The difference between the first two terms is 232 - 221 = 11, which is 11 × 1. The difference between the second and third terms is 221 - 199 = 22, which is 11 × 2. According to this logic, the next difference in the sequence must be 11 × 3 = 33. Applying this to the third term, we get 199 - 33 = 166.

We can verify this pattern by continuing the subtractions for the remaining terms. The next multiple of 11 is 11 × 4 = 44. Subtracting this from our calculated value gives 166 - 44 = 122, which matches the fifth term. The final difference is 122 - 67 = 55, which is 11 × 5, confirming that the pattern of subtracting 11n is consistent throughout the series.

Explanation

The expression is evaluated by substituting the given characters with their corresponding mathematical operators: > represents +, S represents ÷, f represents ×, and c represents -. When these substitutions are applied, the expression 205 > 210 S 15 f 2 c 19 becomes the numerical expression 205 + 210 ÷ 15 × 2 - 19. Following the BODMAS rule, the operations are performed in the order of Division, Multiplication, Addition, and then Subtraction.

First, perform the division: 210 ÷ 15 = 14. The expression now is: 205 + 14 × 2 - 19. Next, perform the multiplication: 14 × 2 = 28. The expression now is: 205 + 28 - 19. Then, perform the addition: 205 + 28 = 233. Finally, perform the subtraction: 233 - 19 = 214.

Explanation

The coding logic follows a two-step process: first, reverse the letters of the given word, and then subtract numerical values in descending order from 6 to 1 from the positional values of the reversed letters.

For the word PLIERS, the positions are P(16), L(12), I(9), E(5), R(18), S(19). Reversing these gives S(19), R(18), E(5), I(9), L(12), P(16). Applying the subtraction: 19 - 6 = 13 (M) 18 - 5 = 13 (M) 5 - 4 = 1 (A) 9 - 3 = 6 (F) 12 - 2 = 10 (J) 16 - 1 = 15 (O) This results in the code MMAFJO.

For the word SHOVEL, the positions are S(19), H(8), O(15), V(22), E(5), L(12). Reversing these gives L(12), E(5), V(22), O(15), H(8), S(19). Applying the subtraction: 12 - 6 = 6 (F) 5 - 5 = 0 ≡ 26 (Z) 22 - 4 = 18 (R) 15 - 3 = 12 (L) 8 - 2 = 6 (F) 19 - 1 = 18 (R) This results in the code FZRLFR.

Applying the same logic to WRENCH: The positions are W(23), R(18), E(5), N(14), C(3), H(8). Reversing the order gives H(8), C(3), N(14), E(5), R(18), W(23). Applying the subtraction (6, 5, 4, 3, 2, 1): 8 - 6 = 2 (B) 3 - 5 = -2 ≡ 24 (X) 14 - 4 = 10 (J) 5 - 3 = 2 (B) 18 - 2 = 16 (P) 23 - 1 = 22 (V) The resulting code is BXJBPV.

Explanation

The coding logic follows an alternating addition pattern of +2 and +3 to the alphabetical positions of the letters in the given words. For the word SPIT, the transformation is S + 2 = U, P + 3 = S, I + 2 = K, and T + 3 = W. Similarly, for the word COPY, the transformation is C + 2 = E, O + 3 = R, P + 2 = R, and Y + 3 = B (advancing 3 positions from Y leads to Z, A, then B).

Applying this identical +2, +3, +2, +3 pattern to the word MOCK: M + 2 = O (13 + 2 = 15) O + 3 = R (15 + 3 = 18) C + 2 = E (3 + 2 = 5) K + 3 = N (11 + 3 = 14)

Following these steps, the word MOCK is coded as OREN.

Explanation

The letter-cluster ADZV is the odd one out because it fails the pattern where the first and third letters, as well as the second and fourth letters, are alphabetical opposites. Letters are considered opposites if the sum of their numerical positions in the alphabet is 27. In ADZV, the first and third letters A (1) and Z (26) satisfy 1 + 26 = 27. However, the second and fourth letters D (4) and V (22) have a positional sum of 4 + 22 = 26. For the cluster to follow the consistent logic of the set, the fourth letter would need to be W (23) to satisfy the 4 + 23 = 27 requirement.

Explanation

The relationship between the numbers in the given sets is based on the formula: 3 × First Number - 2 × Second Number = Third Number.

Applying this logic to the first set (12, 8, 20): 3 × 12 = 36 2 × 8 = 16 36 - 16 = 20

Applying this logic to the second set (7, 3, 15): 3 × 7 = 21 2 × 3 = 6 21 - 6 = 15

Following the same pattern in option a), which is (9, 4, 19): 3 × 9 = 27 2 × 4 = 8 27 - 8 = 19

Explanation

The mathematical rule followed by the number pairs is y = x²(x - 3), where x is the first number and y is the second number. Applying this operation to the first numbers 8, 11, and 6 results in 8² × 5 = 320, 11² × 8 = 968, and 6² × 3 = 108. The pair (5, 100) is the odd one out because the same logic results in 5² × (5 - 3) = 25 × 2 = 50, which is different from the provided second number 100.

Explanation

By interchanging the signs ÷ and -, the equation becomes 312 ÷ 13 × 14 + 207 - 4 = 539. Applying the BODMAS rule, we first perform the division: 312 ÷ 13 = 24. Next, we multiply the result by 14: 24 × 14 = 336. Then, we perform the addition: 336 + 207 = 543. Finally, we perform the subtraction: 543 - 4 = 539. Since the left-hand side equals the right-hand side, the equation is correct.

Explanation

To determine the dictionary order, words are compared letter by letter from left to right. All five words begin with the prefix App. Examining the fourth letters, Apparel (5) and Apparition (4) have a, Appear (1) has e, and Approach (2) and Approximate (3) have r. In the alphabet, a comes before e, which comes before r.

To order Apparel (5) and Apparition (4), we look at the sixth letter because the first five letters Appar are the same. Apparel has e and Apparition has i. Since e precedes i, word 5 comes before word 4. Next is Appear (1) as its fourth letter e precedes r. For the final two words, the first five letters Appro are identical. Comparing the sixth letters, Approach (2) has a and Approximate (3) has x. Since a precedes x, word 2 comes before word 3. The resulting sequence is 5, 4, 1, 2, 3.

Explanation

The series follows a logical repeating pattern based on the five-letter word MONKS. By dividing the entire sequence into groups of five letters each, we can identify the missing characters in each segment:

Group 1: M _ _ K S Group 2: _ O N _ S Group 3: M O _ K _ Group 4: _ _ N K S

By applying the word MONKS to each group: In Group 1, the missing letters are O and N to complete MONKS. In Group 2, the missing letters are M and K to complete MONKS. In Group 3, the missing letters are N and S to complete MONKS. In Group 4, the missing letters are M and O to complete MONKS.

When the letters from the blanks are placed sequentially from left to right, they form the string ONMKNSMO. This sequence completes the series as MONKS | MONKS | MONKS | MONKS.

Explanation

The first pair of words, Vacant and Empty, are synonyms because they both describe something that is unoccupied or contains nothing. Following this same relationship of synonymy, the word that corresponds to Enormous is Huge, as both terms are used to describe something that is exceptionally large in size, extent, or amount.