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

Explanation

The pattern follows a two-step logic: first, reverse the letters of the word, and then add consecutive natural numbers (1, 2, 3, ...) to the alphabetical positions of the reversed letters.

Applying this logic to UNREAL: Reverse the letter-cluster: L-A-E-R-N-U. Add consecutive integers starting from 1 to their positional values: L (12) + 1 = 13 → M A (1) + 2 = 3 → C E (5) + 3 = 8 → H R (18) + 4 = 22 → V N (14) + 5 = 19 → S U (21) + 6 = 27 → A (using 27 mod 26 = 1)

This transformation results in the letter-cluster MCHVSA. The same logic is observed in CROWN (reversed N-W-O-R-C + 1, 2, 3, 4, 5 = OYRVH) and TABLE (reversed E-L-B-A-T + 1, 2, 3, 4, 5 = FNEEY).

Explanation

The series is formed by repeating a five-letter pattern where the first two letters (RE) and the last two letters (QT) remain constant, while the middle letter increases alphabetically in each subsequent block.

The pattern follows a sequence of four blocks: Block 1: R E U Q T Block 2: R E V Q T Block 3: R E W Q T Block 4: R E X Q T

In this sequence, the third letter of each block progresses as U → V → W → X.

By filling the blanks to complete these blocks, we obtain the letters: Q (from Block 1), E and V (from Block 2), Q and T (from Block 3), and X and Q (from Block 4). Placing these letters in order yields QEVQTXQ.

Explanation

The relationship between the terms in the given sets follows a linear mathematical logic where the second number is derived from the first by multiplying it by 3 and then adding 7. The general formula for the sequence is y = 3x + 7.

In the first set, 15 : 52, the calculation is: 15 × 3 + 7 = 45 + 7 = 52

In the third set, 22 : 73, the calculation is: 22 × 3 + 7 = 66 + 7 = 73

To find the missing value in the second set, we apply the same rule to the term 33: 33 × 3 + 7 = 99 + 7 = 106

This logical consistency across all pairs confirms that the transformation involves a common multiplier and a constant addition.

Explanation

The relationship can be decoded by breaking down the statement from the end. Gaurav's paternal grandfather's only son refers to Gaurav's father, as the only son of a paternal grandfather must be the father of the person speaking. The statement then says that Suraj is the son of this individual, meaning Suraj is the son of Gaurav's father. Since both Suraj and Gaurav share the same father, Gaurav is the brother of Suraj.

Explanation

The coding logic follows the sum of the numerical positions of each letter in the English alphabet, where A = 1, B = 2, ..., Z = 26.

For the word MARS: M = 13 A = 1 R = 18 S = 19 Total sum = 13 + 1 + 18 + 19 = 51

For the word STARS: S = 19 T = 20 A = 1 R = 18 S = 19 Total sum = 19 + 20 + 1 + 18 + 19 = 77

Following the same logic for MOON: M = 13 O = 15 O = 15 N = 14 Total sum = 13 + 15 + 15 + 14 = 57

Explanation

The relationship between the numbers in the given sets (a, b, c) follows the mathematical pattern (a × c) + 1 = b.

In the first set (4, 25, 6), the product of the first and third numbers is 4 × 6 = 24. Adding 1 to this product results in the middle number: 24 + 1 = 25.

In the second set (3, 28, 9), the product of the first and third numbers is 3 × 9 = 27. Adding 1 to this product results in the middle number: 27 + 1 = 28.

In the set (2, 17, 8), the first and third numbers are multiplied to get 2 × 8 = 16. Adding 1 to this value yields the middle number: 16 + 1 = 17.

Explanation

The relationship between the numbers in the given sets follows the formula c = (a × b) - (a)/(b), where a, b, and c represent the first, second, and third numbers of the set respectively.

For the first set (100, 2, 150): (100 × 2) - ¹⁰⁰⁄₂ = 200 - 50 = 150

For the second set (50, 5, 240): (50 × 5) - ⁵⁰⁄₅ = 250 - 10 = 240

Applying this same mathematical logic to the numbers in the set (16, 8, 126): (16 × 8) - ¹⁶⁄₈ = 128 - 2 = 126

Explanation

The given series follows a multiplication pattern where each subsequent term is the product of the previous term and an increasing consecutive integer starting from 2.

First term to second term: 2 × 2 = 4 Second term to third term: 4 × 3 = 12 Third term to fourth term: 12 × 4 = 48 Fourth term to fifth term: 48 × 5 = 240

The multipliers used in the sequence are 2, 3, 4, and 5. Following this logic, the next multiplier must be 6. To find the missing number that replaces the question mark, the fifth term is multiplied by 6:

240 × 6 = 1440

Explanation

The expression L + M + N - O ÷ P × Q provides a set of coded family relations. The symbol + represents that the first person is the sister of the second. Therefore, L + M means L is the sister of M, and M + N means M is the sister of N. This indicates that L, M, and N are siblings from the same generation. Furthermore, N - O indicates that N is the wife of O. Because L and N are sisters, the statement that L is the daughter of N is incorrect.

Explanation

The coding logic follows the mathematical pattern of n³, where n represents the total number of letters in the given word.

For the word DEN, the number of letters is n = 3. Calculating the cube of the number of letters gives 3 × 3 × 3 = 27.

For the word SNAKE, the number of letters is n = 5. Calculating the cube of the number of letters gives 5 × 5 × 5 = 125.

Applying the same logic to the word CAVE, the number of letters is n = 4. The code for CAVE is calculated as 4³ = 4 × 4 × 4 = 64.

Explanation

The pattern follows the logic that the third number is obtained by subtracting three times the second number from the first number.

The formula for the pattern is: First Number - (3 × Second Number) = Third Number

Applying this logic to the given sets:

For the first set (16, 4, 4): 16 - (3 × 4) = 16 - 12 = 4

For the second set (30, 5, 15): 30 - (3 × 5) = 30 - 15 = 15

For the third set (8, 2, ?): 8 - (3 × 2) = 8 - 6 = 2

Following the same logic, the number that replaces the question mark is 2.

Explanation

The logic applied to the letter-clusters is the subtraction of 6 from the numerical position of each letter in the English alphabet. In the first pair PIG : JCA, the operations are P (16) - 6 = 10 (J), I (9) - 6 = 3 (C), and G (7) - 6 = 1 (A). Similarly, for the second pair SUN : MOH, the operations are S (19) - 6 = 13 (M), U (21) - 6 = 15 (O), and N (14) - 6 = 8 (H). Applying this consistent rule to the fifth cluster TEK, we subtract 6 from each letter position. For the first letter T (20), 20 - 6 = 14 (N). For the second letter E (5), we subtract 6 in a cyclic alphabetical order, resulting in 5 - 6 = -1, which corresponds to Y (25). For the third letter K (11), 11 - 6 = 5 (E). Combining these results gives the letter-cluster NYE.

Explanation

The letter series is based on a repeating structure of five-letter groups with a shifting internal pattern. Dividing the series into these groups reveals the logic:

Group 1: L K (A) J I Group 2: L (K) C J (I) Group 3: L (K) E J I Group 4: L K (J) G I

The pattern follows these rules: The first two letters of each group are consistently L and K. The fifth (last) letter of each group is consistently I. The third and fourth letters involve a variable (A, C, E, G) and the letter J. In the first three groups, the variable letter occupies the third position and progresses by skipping one letter in the alphabet: A to C (+2), and C to E (+2). The fourth position remains J. In the fourth group, the positions of J and the variable letter are swapped. J moves to the third position, and the next letter in the progression, G (E+2), moves to the fourth position.

By placing the letters from option a (A, K, I, K, J) into the blanks in order: Blank 1: A (completes L K A J I) Blank 2: K (completes the start of the second group L K C J I) Blank 3: I (completes the end of the second group L K C J I) Blank 4: K (completes the start of the third group L K E J I) Blank 5: J (completes the third position of the fourth group L K J G I)

This substitution maintains the structural integrity and the alphabetical progression of the series.

Explanation

The series follows a pattern where the differences between consecutive terms increase by a constant value of 6. By examining the later part of the series, the difference between 107 and 77 is 30, the difference between 77 and 53 is 24, and the difference between 53 and 35 is 18. These differences (18, 24, 30) form an arithmetic progression with a common difference of 6.

Following this logic in reverse, the difference between the second term and the third term (35) must be 18 - 6 = 12. Consequently, the difference between the first term (17) and the missing second term must be 12 - 6 = 6. Adding this value to the first term yields 17 + 6 = 23. This is confirmed by checking the next step: 23 + 12 = 35, which correctly matches the third term of the series. The full sequence of differences is 6, 12, 18, 24, 30.

Explanation

The expression D @ N @ H | Y @ F % V defines the family relationships as follows. N @ H indicates that N is the daughter of H. H | Y signifies that H is the husband of Y, which identifies Y as the mother of N. Y @ F states that Y is the daughter of F. F % V identifies F as the wife of V. By combining these relations, N is the daughter of Y, and Y is the daughter of F. Consequently, N is the daughter's daughter of F.

Explanation

The series follows a mathematical pattern based on the alphabetical positions of the letters, where each corresponding letter in the clusters undergoes a constant shift of 3.

For the first letter, the pattern is an addition of 3 positions in the alphabet: W(23) → Z(26) → C(3) → F(6). Adding 3 to F results in the letter I (9).

For the second letter, the pattern is a subtraction of 3 positions: G(7) → D(4) → A(1) → X(24). Subtracting 3 from X results in the letter U (21).

For the third letter, the pattern is an addition of 3 positions: N(14) → Q(17) → T(20) → W(23). Adding 3 to W results in the letter Z (26).

For the fourth letter, the pattern is a subtraction of 3 positions: Y(25) → V(22) → S(19) → P(16). Subtracting 3 from P results in the letter M (13).

By combining these results, the next cluster in the series is determined to be IUZM.

Explanation

The given expression M > N = O : P : Q can be decoded using the provided symbols. M > N establishes that M is the mother of N. N = O establishes that N is the father of O. The symbol : represents the sister relationship (as defined by ! in the prefix), which implies that O, P, and Q are siblings. Since N is the father of O, and O is the sibling of P and Q, N is also the father of Q. Because M is the mother of Q's father N, M is the paternal grandmother or the father's mother of Q.

Explanation

The pattern follows the logic n : n × (n + 3). In the first pair, 15 × (15 + 3) = 15 × 18 = 270. Similarly, in the third pair, 18 × (18 + 3) = 18 × 21 = 378. Applying this rule to the second pair where n = 21, we calculate 21 × (21 + 3) = 21 × 24 = 504.

Explanation

The series follows a pattern where each letter in a term moves forward by 6 positions to reach the corresponding letter in the next term. By assigning numerical values to the letters where A=1, B=2, …, Z=26, the transformation for each position is as follows.

For the first letter: E(5) +6 K(11) +6 Q(17) +6 W(23). For the second letter: G(7) +6 M(13) +6 S(19) +6 Y(25). For the third letter: I(9) +6 O(15) +6 U(21) +6 A(27 ≡ 1).

In the third sequence, 21 + 6 = 27, and since there are 26 letters in the alphabet, 27 cycles back to 1, which represents A. Combining these results, the next term in the series is WYA.

Explanation

The logical validity of the conclusions is determined by the specific overlaps defined in the statements. The statement All rice are wheat establishes that the set of rice is a subset of wheat. The second statement, Some wheats are pulses, indicates an intersection between the wheat and pulse sets, but it does not provide any information that necessitates an overlap between rice and pulses. Therefore, conclusion II does not follow.

The third statement, No pulse is a vegetable, means the pulse and vegetable sets are completely disjoint. However, this does not create a definitive relationship between vegetables and rice or vegetables and wheat. There is no premise linking rice to vegetables, making conclusion I unsupported. Similarly, while vegetables cannot be pulses, they can still be entirely separate from the wheat set, meaning conclusion III does not logically follow from the given information. Since no conclusion is certain, none of them follow.

Explanation

Statement 1 is a universal affirmative proposition of the form All M are F. According to the logical rule of conversion, if a statement All A are B is true, then its converse Some B are A is always logically valid. Since all machines are contained within the set of factories, it necessarily follows that some of the entities within the factory set are machines. Therefore, conclusion III follows directly from the first statement.

Conclusions I and II do not follow because the connection between factories and houses, or machines and houses, is mediated by two particular affirmative (Some) statements. In syllogistic logic, no definite conclusion can be drawn between the subject of the first statement and the predicate of the last statement when the middle terms are linked only by Some, as there is no guarantee of an overlap that spans the entire chain. Conclusion III is the only certain inference based on the given premises.

Explanation

The relationship established in the first pair is that of antonyms. Attack represents an offensive action or the onset of a struggle, while Defence represents the act of resisting an attack or protecting oneself. To follow the same logic for the second pair, one must find the antonym of Accept. Accept means to consent to receive or undertake something offered. Refuse is the direct opposite, meaning to indicate that one is not willing to accept or grant something.

Explanation

The letter clusters follow an alternating pattern of +1 and -1 applied to the alphabetical positions of the letters. In the first pair, FRENCH becomes GQFMDG through the operations: F + 1 = G, R - 1 = Q, E + 1 = F, N - 1 = M, C + 1 = D, and H - 1 = G. Similarly, in the second pair, GERMAN becomes HDSLBM through the operations: G + 1 = H, E - 1 = D, R + 1 = S, M - 1 = L, A + 1 = B, and N - 1 = M. Applying this consistent pattern to the fifth letter-cluster ARABIC, we calculate the transformations as: A + 1 = B, R - 1 = Q, A + 1 = B, B - 1 = A, I + 1 = J, and C - 1 = B. This sequence of operations results in the cluster BQBAJB.

Explanation

The series is composed of four groups of five letters each. By dividing the series, we observe the following blocks: (A B _ K P), (C _ H K P), (E B H _ P), and (G B H K _). Within these blocks, the letters in the second, third, fourth, and fifth positions remain constant as B, H, K, and P respectively. The first letter of each block follows an incremental pattern of +2 in the alphabetical order: A +2 C +2 E +2 G. Sequentially placing the letters H, B, K, and P into the blanks completes the repeating pattern of letters B, H, K, and P preceded by the advancing first letter.

Explanation

The given sequence is an arithmetic progression where each subsequent term is found by adding a constant difference. By calculating the difference between the consecutive terms provided at the end of the series, we find: 249 - 212 = 37 212 - 175 = 37 175 - 138 = 37 138 - 101 = 37

The constant difference is 37. To find the missing second term, add this difference to the first term: 27 + 37 = 64

We can verify this by checking the transition to the third term: 64 + 37 = 101

Since the calculation aligns with the rest of the series, the missing number is 64.

Explanation

The logic governing the given sets is that the third number is the difference between the cubes of the first two numbers. The formula is a³ - b³ = c.

In the first set (12, 7, 1385): 12³ - 7³ = 1728 - 343 = 1385

In the second set (19, 15, 3484): 19³ - 15³ = 6859 - 3375 = 3484

Following this pattern for the set in option c (21, 16, 5165): 21³ - 16³ = 9261 - 4096 = 5165

Explanation

The logic followed in the given sets is based on the relation: Second number = (2 × First number) + (3 × Third number).

In the first set (9, 69, 17), the operation is 2 × 9 + 3 × 17 = 18 + 51 = 69. In the second set (13, 47, 7), the operation is 2 × 13 + 3 × 7 = 26 + 21 = 47.

Applying this same logic to the set (19, 50, 4) in option d, the calculation is 2 × 19 + 3 × 4 = 38 + 12 = 50. This matches the middle number provided in the set.

Explanation

The relationship between the numbers in the pairs is defined by the formula y = 2x³, where the second number is twice the cube of the first number. For the pair 5:685, substituting the first number into the formula gives 2 × 5³ = 2 × 125 = 250. Since the resulting value of 250 does not match the provided second number of 685, this pair is the odd one out as it deviates from the cubic pattern.

Explanation

The coding logic follows a linear shift where each letter of the word is replaced by the letter immediately preceding it in the English alphabetical sequence (Position - 1). In the word ENVOY, E becomes D, N becomes M, V becomes U, O becomes N, and Y becomes X. Similarly, in the word CHECK, C becomes B, H becomes G, E becomes D, C becomes B, and K becomes J.

Applying this -1 positional shift to the word ANGLE: A shifts back to Z (cyclic shift) N shifts back to M G shifts back to F L shifts back to K E shifts back to D

By combining these results, the word ANGLE is coded as ZMFKD.

Explanation

The numbers in the given sets follow a logic where the first number is obtained by squaring the second number and subtracting 2. The third number in each set acts as a distractor and does not impact the primary mathematical relationship.

The relationship can be expressed by the formula: First Number = (Second Number)² - 2

Applying this formula to the given sets: Set 1: (194, 14, 4) 14² - 2 = 196 - 2 = 194

Set 2: (527, 23, 5) 23² - 2 = 529 - 2 = 527

Now, applying the same logic to the options: Option b: (2, 2, 2) 2² - 2 = 4 - 2 = 2

This matches the first number of the set in option b. Checking the other options confirms that they do not satisfy this relationship: a) 8² - 2 = 62 ≠ 63 c) 3² - 2 = 7 ≠ 8 d) 6² - 2 = 34 ≠ 10

Explanation

The relationship established in the first pair is between a professional and their primary place of practice. A doctor is a professional who carries out their medical duties and treats patients within a hospital. Applying the same logic to the second pair, a lawyer is a professional whose primary workplace for practicing law, representing clients, and engaging in legal proceedings is a court.

Explanation

The coding logic follows a two-step process: reversing the word and then adding a decreasing sequence of integers starting from +6 to +1 to the positional values of the letters.

For the word TURNIP: Step 1: Reverse the word to get PINRUT. Step 2: Apply the shifts to the alphabetical positions: P(16) + 6 = 22 → V I(9) + 5 = 14 → N N(14) + 4 = 18 → R R(18) + 3 = 21 → U U(21) + 2 = 23 → W T(20) + 1 = 21 → U The result is VNRUWU.

For the word DAIKON: Step 1: Reverse the word to get NOKIAD. Step 2: Apply the shifts: N(14) + 6 = 20 → T O(15) + 5 = 20 → T K(11) + 4 = 15 → O I(9) + 3 = 12 → L A(1) + 2 = 3 → C D(4) + 1 = 5 → E The result is TTOLCE.

Applying this logic to RADISH: Step 1: Reverse the word to get HSIDAR. Step 2: Apply the shifts: H(8) + 6 = 14 → N S(19) + 5 = 24 → X I(9) + 4 = 13 → M D(4) + 3 = 7 → G A(1) + 2 = 3 → C R(18) + 1 = 19 → S The resulting code is NXMGCs.

Explanation

The second number in the pairs follows the pattern of centered hexagonal numbers, which are defined by the formula y = 3n² + 3n + 1. This formula also represents the difference between two consecutive cubes, (n+1)³ - n³. For the pair (8, 20), the first number 8 is 2³, suggesting n = 2. Applying the formula, the second number should be 3(2)² + 3(2) + 1 = 12 + 6 + 1 = 19, or 3³ - 2³ = 27 - 8 = 19. Because the given second number is 20 rather than 19, this pair does not follow the mathematical operation. Additionally, 20 is the only second number in the set that is not a centered hexagonal number.

Explanation

The series follows a pattern where the differences between consecutive terms form an arithmetic progression with a common difference of 4. We can determine this by calculating the differences between the known numbers in the latter half of the series: 47 - 33 = 14 65 - 47 = 18

The difference between these two results (18 - 14) is 4. Applying this common difference to the beginning of the series, the first difference is 17 - 15 = 2. Following the logic, the subsequent differences should increase by 4 each time, resulting in a sequence of differences: 2, 6, 10, 14, and 18.

To find the missing number, we add the next difference in the sequence to the second term: 17 + 6 = 23

We can verify this by adding the next difference in the sequence (10) to our result: 23 + 10 = 33

As 33 matches the next term provided in the series, the pattern is confirmed.

Explanation

To determine the relationship, trace the lineage step by step from Rahul's perspective. Rahul's mother's paternal grandfather is his maternal great-grandfather. The only son of this maternal great-grandfather is Rahul's maternal grandfather. The granddaughter of Rahul's maternal grandfather must be the daughter of his child. Since Rahul's mother is the daughter of this grandfather, her daughter is the person in the competition. Consequently, the daughter of Rahul's mother is Rahul's sister.

Explanation

To make the equation 24× 9 + 6 ÷ 24 - 18 = 22 correct, the numbers 6 and 9 are interchanged, and the signs ÷ and + are swapped. Following these modifications, the expression on the left-hand side is rewritten as 24 × 6 ÷ 9 + 24 - 18. According to the BODMAS rule, operations must be performed in the order of Division, Multiplication, Addition, and then Subtraction. First, the multiplication and division segment is evaluated: 24 × 6 ÷ 9 can be calculated as 144 ÷ 9, which equals 16. Substituting this value back into the equation yields 16 + 24 - 18. Next, the addition is performed, where 16 + 24 results in 40. Finally, the subtraction is carried out as 40 - 18, which equals 22. This result matches the value on the right-hand side of the equation.

Explanation

The series follows a specific addition and subtraction pattern for each letter position in the triplets. For the first letter of each term, there is a constant increment of 6: A (1) + 6 = G (7), G (7) + 6 = M (13), M (13) + 6 = S (19), S (19) + 6 = Y (25). Continuing this, Y (25) + 6 = 31, which corresponds to E (5) in the alphabetical cycle (31 - 26 = 5).

For the second letter, there is a constant decrement of 7: L (12) - 7 = E (5), E (5) - 7 = -2, which corresponds to X (24) in the reverse alphabetical cycle (26 - 2 = 24), X (24) - 7 = Q (17), Q (17) - 7 = J (10). Continuing this, J (10) - 7 = 3, which corresponds to the letter C.

For the third letter, there is a constant increment of 2: W (23) + 2 = Y (25), Y (25) + 2 = 27, which is A (1), A (1) + 2 = C (3), C (3) + 2 = E (5). Continuing this, E (5) + 2 = 7, which corresponds to the letter G. Combining these results, the next term is ECG.

Explanation

The coding logic follows a two-step process: first, the word is reversed, and second, decreasing integers from 6 to 1 are subtracted from the positional values of the letters in the reversed string.

For GINGER, the reversal is REGNIG. Applying the subtraction pattern: R (18) - 6 = 12 (L) E (5) - 5 = 26 (Z) G (7) - 4 = 3 (C) N (14) - 3 = 11 (K) I (9) - 2 = 7 (G) G (7) - 1 = 6 (F) The resulting code is LZCKGF.

For GARLIC, the reversal is CILRAG. Applying the subtraction pattern: C (3) - 6 = 23 (W) I (9) - 5 = 4 (D) L (12) - 4 = 8 (H) R (18) - 3 = 15 (O) A (1) - 2 = 25 (Y) G (7) - 1 = 6 (F) The resulting code is WDHOYF.

Applying this logic to CLOVES, the reversal is SEVOLC. Subtracting the integers: S (19) - 6 = 13 (M) E (5) - 5 = 26 (Z) V (22) - 4 = 18 (R) O (15) - 3 = 12 (L) L (12) - 2 = 10 (J) C (3) - 1 = 2 (B) The resulting code is MZRLJB.

Explanation

The numbers in the given sets follow the mathematical relationship n₁ = 5 × (n₂ + n₃) - 3, where n₁, n₂, and n₃ represent the first, second, and third numbers of the set respectively.

In the first set (62, 5, 8), the relation is applied as 5 × (5 + 8) - 3 = 5 × 13 - 3 = 65 - 3 = 62.

In the second set (87, 7, 11), the same logic applies as 5 × (7 + 11) - 3 = 5 × 18 - 3 = 90 - 3 = 87.

For the set in option (c) (112, 8, 15), substituting the values into the formula yields 5 × (8 + 15) - 3 = 5 × 23 - 3 = 115 - 3 = 112. This confirms that the numbers are related in the same way as the numbers in the provided sets.

Explanation

The logic followed in the given sets is 2(a² + b²) = c, where a and b are the first two numbers and c is the third number. In the first set, 2(4² + 5²) = 2(16 + 25) = 2(41) = 82. In the second set, 2(6² + 11²) = 2(36 + 121) = 2(157) = 314.

Applying this logic to the set (11, 9, 560), we calculate 2(11² + 9²) = 2(121 + 81) = 2(202) = 404. Since 404 is not equal to 560, this set does not follow the established mathematical relationship.

Explanation

The logic followed in the given sets is: a² - b² - 8 = c.

In the first set (7, 5, 16): 7² - 5² - 8 = 49 - 25 - 8 = 16

In the second set (12, 10, 36): 12² - 10² - 8 = 144 - 100 - 8 = 36

Applying the same logic to the set in option d) (8, 7, 7): 8² - 7² - 8 = 64 - 49 - 8 = 15 - 8 = 7

Explanation

To arrange words in dictionary order, we compare the letters of each word from left to right. All six words begin with the prefix Mis. Comparing the fourth letter, Missing (2) and Mission (5) contain the letter s, which precedes the letter t found in the other four words. Between Missing (2) and Mission (5), the first five letters Missi are identical; the sixth letter n in Missing precedes the letter o in Mission, placing 2 before 5.

For the remaining words starting with Mist, we compare the fifth letter. Mistaken (1) has a, Mistyped (3) has y, and Mistrust (4) and Mistress (6) both have r. Since a comes first alphabetically, Mistaken (1) is next in the sequence. Between Mistress (6) and Mistrust (4), we look at the sixth letter after the common prefix Mistr. The letter e in Mistress precedes the letter u in Mistrust, so 6 comes before 4. Finally, Mistyped (3) is placed last because its fifth letter y comes after a and r. This results in the order 2, 5, 1, 6, 4, 3.

Explanation

The letter series follows a repeating pattern of five-letter groups where the first three letters (N, O, P) and the fifth letter (Q) remain constant, while the fourth letter decreases by one position in reverse alphabetical order.

The sequence of the variable fourth letter is: J → I → H → G

Applying this pattern, we can divide the series into the following groups: Group 1: N O P J Q Group 2: N O P I Q Group 3: N O P H Q Group 4: N O P G Q

By placing the letters from option b in the blanks of the provided string NOP_QNO_IQN_PHQ_OPG: The first blank (NOP_Q) is filled by J to complete the first group: NOPJQ. The second blank (NO_IQ) is filled by P to complete the constant NOP prefix of the second group: NOPIQ. The third blank (N_PHQ) is filled by O to complete the constant NOP prefix of the third group: NOPHQ. The fourth blank (placed at the end or as the delimiter) is filled by Q to complete the constant fifth position of the pattern.

The letters that complete the series are J, P, O, and Q.

Explanation

By mapping the letters to their numerical positions in the alphabet where A=1, B=2, …, Z=26, the clusters generally follow a specific increment pattern of +5, +3, and +2 between consecutive letters. In the cluster CHLP, the letter positions are C=3, H=8, L=12, and P=16. The differences between these positions are 3+5=8, 8+4=12, and 12+4=16. This results in an increment sequence of +5, +4, +4, which deviates from the +5, +3, +2 logic shared by the other three clusters, making it the odd one out.

Explanation

By interchanging the signs × and - and the numbers 15 and 10 in the original equation 25 - 10 ÷ 5 + 15 × 30 = 55, the new expression becomes:

25 × 15 ÷ 5 + 10 - 30

Following the BODMAS rule, first perform the division: 15 ÷ 5 = 3

The expression now reads: 25 × 3 + 10 - 30

Next, perform the multiplication: 25 × 3 = 75

The expression now reads: 75 + 10 - 30

Perform the addition: 75 + 10 = 85

Finally, perform the subtraction: 85 - 30 = 55

The result matches the target value of 55, confirming that these interchanges make the equation correct.

Explanation

The series follows a pattern where consecutive prime numbers are added to each preceding term, starting from the prime number 5. The differences between consecutive terms are as follows:

23 - 18 = 5 (the first prime number in the sequence) ? - 23 = 7 (the next prime number is 7) 41 - ? = 11 (the next prime number is 11) 54 - 41 = 13 (the next prime number is 13) 71 - 54 = 17 (the next prime number is 17)

By applying the addition of the prime number 7 to the second term, we calculate 23 + 7 = 30. To verify, we add the next prime number, 11, to 30, which results in 30 + 11 = 41. This matches the subsequent term in the given series, confirming that 30 is the correct missing number.

Explanation

The logic followed in the letter-clusters is based on the concept of opposite letters in the English alphabet, where the sum of the numerical positions of two opposite letters is always 27.

In the first pair RAT and IZG, the letter R (18) is replaced by I (9) because 18 + 9 = 27. The letter A (1) is replaced by Z (26) because 1 + 26 = 27. The letter T (20) is replaced by G (7) because 20 + 7 = 27.

In the second pair YUM and BFN, the letter Y (25) is replaced by B (2) because 25 + 2 = 27. The letter U (21) is replaced by F (6) because 21 + 6 = 27. The letter M (13) is replaced by N (14) because 13 + 14 = 27.

Following the same logic for the fifth letter-cluster SIP, the letter S (19) is replaced by H (8) since 19 + 8 = 27. The letter I (9) is replaced by R (18) since 9 + 18 = 27. The letter P (16) is replaced by K (11) since 16 + 11 = 27.

Explanation

The coding logic is based on the sum of the positional values of the letters in the English alphabet (A=1, B=2, …, Z=26) multiplied by the total number of letters in the word. For the word BARBIE, the positional values are B=2, A=1, R=18, B=2, I=9, and E=5. The sum of these values is 2 + 1 + 18 + 2 + 9 + 5 = 37. Multiplying this sum by the 6 letters in the word results in 37 × 6 = 222. For the word ELSA, the positional values are E=5, L=12, S=19, and A=1. The sum is 5 + 12 + 19 + 1 = 37. Multiplying this sum by the 4 letters in the word results in 37 × 4 = 148. To find the value for ARIEL, the sum of the positional values is calculated as A=1, R=18, I=9, E=5, and L=12, which equals 1 + 18 + 9 + 5 + 12 = 45. Multiplying this sum by the 5 letters in the word yields 45 × 5 = 225.

Explanation

By interchanging the division (÷) and addition (+) signs, the equation becomes 173 + 169 ÷ 13 × 5 - 13 = 225. Following the BODMAS rule, the division is performed first: 169 ÷ 13 = 13. The expression simplifies to 173 + 13 × 5 - 13. Next, multiplication is carried out: 13 × 5 = 65. The expression then becomes 173 + 65 - 13. Adding 173 and 65 gives 238, and finally, 238 - 13 = 225. This verifies that the left-hand side is equal to the right-hand side.

Explanation

In the given number-pairs, the logic follows the formula x = y² - 2, where x represents the first number and y represents the second number. Applying this to the pairs, we find that 12² - 2 = 144 - 2 = 142, 5² - 2 = 25 - 2 = 23, and 3² - 2 = 9 - 2 = 7. The pair 80:9 is the odd one out because it follows a different operation, 9² - 1 = 81 - 1 = 80, instead of subtracting two from the square of the second number.