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

Explanation

The relationship follows the pattern (Second Number)² * 10 = First Number. For the first pair, 4² * 10 = 16 * 10 = 160; for the second pair, 5² * 10 = 25 * 10 = 250; for the third pair, 6² * 10 = 36 * 10 = 360. Therefore, the missing term is 6.

Explanation

Substituting the signs from option C into the expression gives 74 + 34 - 78 + 23 - 23. Calculating the values gives 108 - 78 + 0, which equals 30, successfully balancing the equation.

Explanation

The pattern in the given sets is that the second number is the first number multiplied by 6, and the third number is the second number multiplied by 2 (or the first number multiplied by 12). In option B, 14 x 6 = 84 and 84 x 2 = 168, which perfectly follows this logic.

Explanation

The letter-cluster KMOQ is based on a uniform mathematical progression of the alphabetical positions of its letters. The numerical values are K = 11, M = 13, O = 15, and Q = 17. The difference between each consecutive letter is a constant +2, such that 11 + 2 = 13, 13 + 2 = 15, and 15 + 2 = 17. This consistent +2, +2, +2 pattern distinguishes it from the other clusters, which utilize a non-uniform increment sequence of +2, +4, and +2 between their respective letters.

Explanation

The letter-clusters in the series follow a specific positional pattern. The first letter of each cluster decreases by one in alphabetical order: E, D, C, B, A. The second letter of each cluster increases by two: I, K, M, O, Q. The third letter of each cluster also increases by two: M, O, Q, S, U. Finally, the fourth letter of each cluster increases by one: C, D, E, F, G.

Applying these transformations to the third cluster CMQE: First letter: C - 1 = B Second letter: M + 2 = O Third letter: Q + 2 = S Fourth letter: E + 1 = F

Combining these letters results in the cluster BOSF.

Explanation

The logic follows a two-step transformation: first, consonants remain unchanged while vowels are shifted 6 positions backward in the alphabet (Vowel - 6); second, the entire resulting string is reversed.

The vowel shifts are calculated as follows: I (9) - 6 = 3 (C) O (15) - 6 = 9 (I) A (1) - 6 = 21 (U) E (5) - 6 = 25 (Y)

Applying this to ISOLATED: I (Vowel) → C S (Consonant) → S O (Vowel) → I L (Consonant) → L A (Vowel) → U T (Consonant) → T E (Vowel) → Y D (Consonant) → D

The intermediate cluster formed is CSILUTYD. Reversing this cluster results in DYTULISC.

Explanation

By substituting the signs in Option A, the expression becomes 321 + 3 - (236 x 5) + (248 / 4) x 20. Following BODMAS rules, this simplifies to 324 - 1180 + 1240, which results in 384, thereby balancing the equation.

Explanation

The series is completed by sequentially placing the letters from the correct option into the blanks to reveal a repeating or structured pattern. Using the letters from option a), STPMSPOT, the completed series becomes:

P [S] M O [T] S T [P] O P [M] T M [S] S [P] M O [O] [T]

By dividing this 20-letter sequence into groups of five, we can observe the distribution of the letters P, S, M, O, and T:

Group 1: P S M O T Group 2: S T P O P Group 3: M T M S S Group 4: P M O O T

In this completed series, each of the five distinct letters (P, S, M, O, and T) appears exactly four times across the 20 positions. This balanced frequency of characters is a standard feature of letter series puzzles in competitive exams. Each 5-letter block contains a slightly shifted or varied set of these five letters, ensuring that the distribution remains uniform throughout the entire sequence.

Explanation

The coding logic involves reversing the word and then applying an alternating shift of +2 and +1 to each letter. For 'CHORUS', the reversed form is SUROHC; adding +2 to S, +1 to U, +2 to R, +1 to O, +2 to H, and +1 to C results in UVTPJD. Applying this pattern to 'VOLUME' reversed (EMULOV) gives E+2=G, M+1=N, U+2=W, L+1=M, O+2=Q, and V+1=W, resulting in GNWMQW.

Explanation

The pattern follows the logic that the second number is the square root of the first number plus one. Mathematically, it is expressed as √n + 1, where n is the first term in each pair.

In the first pair, 121 is 11², and 11 + 1 = 12.

In the second pair, 225 is 15², and 15 + 1 = 16.

Following this same logic for the third pair, the first term is 441, which is 21². Adding one to the square root gives 21 + 1 = 22.

Explanation

The coding follows a specific pattern based on the position of letters within each five-letter word. The first and second letters are swapped and increased by 2, the third letter is increased by 3, and the fourth and fifth letters are swapped and increased by 2.

In the word PLANT: The second letter L (12) plus 2 is N (14). The first letter P (16) plus 2 is R (18). The third letter A (1) plus 3 is D (4). The fifth letter T (20) plus 2 is V (22). The fourth letter N (14) plus 2 is P (16). This results in NRDVP.

In the word SCORE: The second letter C (3) plus 2 is E (5). The first letter S (19) plus 2 is U (21). The third letter O (15) plus 3 is R (18). The fifth letter E (5) plus 2 is G (7). The fourth letter R (18) plus 2 is T (20). This results in EURGT.

Following the same logic for GRIND: The second letter R (18) plus 2 is T (20). The first letter G (7) plus 2 is I (9). The third letter I (9) plus 3 is L (12). The fifth letter D (4) plus 2 is F (6). The fourth letter N (14) plus 2 is P (16). This results in the code TILFP.

Explanation

The pattern in the given table follows a specific mathematical rule in each row. The relationship between the second and third numbers is defined by the formula n₃ = (n₂ × 2) - 3. In the first row, 28 × 2 - 3 = 56 - 3 = 53. In the second row, 25 × 2 - 3 = 50 - 3 = 47. Applying this logic to the third row, the calculation is 43 × 2 - 3 = 86 - 3 = 83.

This pattern is also consistent with the first number (n₁) of each row, where n₂ = (n₁ × 3) + 4. Combining these operations, the third number can be directly calculated from the first number using the formula n₃ = 6n₁ + 5. For the third row, this results in 6 × 13 + 5 = 78 + 5 = 83.

Explanation

The relationship followed in the given pairs is that the second number is obtained by subtracting a constant value of 4321 from the first number. This pattern is consistent across most pairs:

6286 - 4321 = 1965 8247 - 4321 = 3926 6903 - 4321 = 2582

In the case of the pair 6571:2448, the difference is 6571 - 2448 = 4123. Because this pair results in a difference of 4123 instead of the common difference of 4321 shared by the others, it is the odd number-pair.

Explanation

To determine the code for the letter M, compare the letters and digits of the two given words. The letters in ZEAL are Z, E, A, and L, and its code is 9, 4, 7, and 6. The letters in LAME are L, A, M, and E, and its code is 8, 6, 9, and 4. By identifying the common elements, it is observed that the letters L, A, and E appear in both words. Correspondingly, the digits 4, 6, and 9 appear in both codes. In the word LAME, the only letter that is not present in ZEAL is M. Similarly, in the code for LAME (8694), the only digit that is not present in the code for ZEAL (9476) is 8. Therefore, the digit 8 must represent the letter M.

Explanation

The series consists of 20 letters, which can be divided into five groups of four letters each: (L T K ) (H L _ ) (J H _ V) ( J H L) ( K _ H)

There are two patterns working simultaneously. First, a core set of four letters (L, H, J, K) follows a cyclic rotation in each position across the groups. Second, an alphabetical series (T, U, V, W) replaces one core letter in each group, moving one position to the right in each subsequent block.

Applying the T-U-V-W series: Group 1: T is at the 2nd position. Group 2: U is at the 3rd position. Group 3: V is at the 4th position. Group 4: (No replacement, as the cycle of four positions is completed). Group 5: W is at the 1st position.

Applying the core letter cycles (L-H-J-K) to the remaining positions: Group 1: L T K J (J fills the 4th position) Group 2: H L U K (U and K fill the 3rd and 4th positions) Group 3: J H L V (L fills the 3rd position) Group 4: K J H L (K fills the 1st position) Group 5: W K J H (W and J fill the 1st and 3rd positions)

Combining these, the letters placed in the blanks from left to right are: J, U, K, L, K, W, J.

Explanation

The relationship between the numbers in the given sets follows the logic that the sum of the first and second numbers is equal to 1.5 times the third number. This pattern can be represented by the formula: A + B = 1.5 × C or 2 × (A + B) = 3 × C

Applying this logic to the first set (82, 35, 78): A + B = 82 + 35 = 117 1.5 × C = 1.5 × 78 = 117

Applying this logic to the second set (18, 27, 30): A + B = 18 + 27 = 45 1.5 × C = 1.5 × 30 = 45

Following the same pattern for the set (27, 33, 40): A + B = 27 + 33 = 60 1.5 × C = 1.5 × 40 = 60

Explanation

The expression Q R @ S T Z can be decoded step by step to determine the relationship between Z and Q. The segment Q R indicates that Q is the daughter of R. The next part, R @ S, states that R is the father of S, and S T means S is the brother of T. This establishes that Q, S, and T are siblings and R is their father.

The final part of the expression, T Z, means T is the daughter of Z. Since R is already established as the father of T, Z must be the mother of T. Because Q, S, and T are all siblings sharing the same father R, Z is also the mother of Q.

Explanation

According to the given sign transformations, the operations are substituted as follows: '-' becomes '×', '+' becomes '-', '×' becomes '÷', and '÷' becomes '+'. Applying these changes to the original expression 11 - 14 + 9 × 3 ÷ 104, we get the new numerical expression:

11 × 14 - 9 ÷ 3 + 104

Following the BODMAS rule, perform the division first: 9 ÷ 3 = 3

Next, perform the multiplication: 11 × 14 = 154

The expression now becomes: 154 - 3 + 104

Finally, perform addition and subtraction: 154 - 3 + 104 = 151 + 104 = 255

Explanation

The logic followed by the letter-clusters is based on the numerical positions of the letters in the English alphabet. In the clusters HJNT, PRVB, and MOSY, the difference between consecutive letters follows a specific pattern of +2, +4, and +6. For example, in HJNT, the positions are 8, 10, 14, and 20, where 10 - 8 = 2, 14 - 10 = 4, and 20 - 14 = 6. Similarly, for PRVB, the positions are 16, 18, 22, and 28 (B is 26 + 2), and for MOSY, they are 13, 15, 19, and 25.

In contrast, the letter-cluster SUXZ uses the positions S(19), U(21), X(24), and Z(26). The differences between these letters are 21 - 19 = 2, 24 - 21 = 3, and 26 - 24 = 2. Because the sequence of increments in SUXZ is +2, +3, +2 instead of the +2, +4, +6 pattern seen in the others, it is the odd cluster.

Explanation

The expression D @ N @ H | Y @ F % V can be decoded step by step to find the relationship between V and H. The segment H | Y indicates that H is the husband of Y, making Y the wife of H. The segment Y @ F means that Y is the daughter of F. The segment F % V indicates that F is the wife of V, which implies that V is the husband of F and therefore the father of Y. Since Y is the wife of H and V is the father of Y, V is the wife's father of H.

Explanation

Interchanging the numbers 12 and 4 and the signs ÷ and × transforms the original equation 24 - (9 ÷ 12) + (84 × 4) + 28 = 23 into the following:

24 - (9 × 4) + (84 ÷ 12) + 28 = 23

Following the BODMAS rule, first solve the operations inside the parentheses: 9 × 4 = 36 84 ÷ 12 = 7

Substitute these values back into the equation: 24 - 36 + 7 + 28 = 23

Now, perform the addition and subtraction from left to right: 24 - 36 = -12 -12 + 7 = -5 -5 + 28 = 23

The calculation results in 23 = 23, which satisfies the equation.

Explanation

The expression H % I J K * L can be broken down using the given definitions to determine the relationship between H and J. The segment I J indicates that I is the son of J. The segment H % I states that H is the daughter of I. Since H is the daughter of I and I is the son of J, H is the granddaughter of J. Specifically, H is the daughter of J's son, which makes H the son's daughter of J.

Explanation

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

For the first set (5, 7, 140): (5 × 7) × 4 = 35 × 4 = 140

For the second set (6, 4, 96): (6 × 4) × 4 = 24 × 4 = 96

Applying this same formula to the numbers in the third option: (9 × 2) × 4 = 18 × 4 = 72

Explanation

The numbers in the given sets follow a consistent multiplicative pattern where the second number is three times the first, and the third number is twice the second. Mathematically, this relationship can be expressed as n₂ = 3 × n₁ and n₃ = 2 × n₂.

In the first provided set (15, 45, 90), the calculations are 15 × 3 = 45 and 45 × 2 = 90. In the second provided set (8, 24, 48), the calculations are 8 × 3 = 24 and 24 × 2 = 48. Applying this logic to the set (6, 18, 36), we find that 6 × 3 = 18 and 18 × 2 = 36, which maintains the same mathematical proportionality.

Explanation

The given series follows a geometric progression where each term is multiplied by a constant factor of 3 to obtain the next term. The pattern is defined by the relation aₙ = aₙ₋₁ × 3.

Starting from the first term: 2 × 3 = 6 6 × 3 = 18 18 × 3 = 54 54 × 3 = 162 162 × 3 = 486

Applying this common ratio to the second term, 6 × 3 yields 18. This value is consistent with the rest of the sequence, as 18 × 3 correctly results in the fourth term, 54.

Explanation

Substituting the signs -, +, ÷, ×, = into the equation gives 86 - 54 + 34 ÷ 68 × 2 = 33. Following the BODMAS rule, we first perform the division: 34 ÷ 68 = ³⁴⁄₆₈ = 0.5. Next, we perform the multiplication: 0.5 × 2 = 1. The equation then becomes 86 - 54 + 1 = 33. Finally, performing the subtraction and addition from left to right, we get 86 - 54 = 32, and 32 + 1 = 33. Since the left-hand side equals the right-hand side (33 = 33), the signs balance the equation perfectly.

Explanation

The series follows a logical pattern where each letter in a cluster is determined by subtracting 6 from the position of the corresponding letter in the previous cluster. In the first cluster WUS, the alphabetical positions are W=23, U=21, and S=19. For the second cluster QOM, the positions are 17 (23-6), 15 (21-6), and 13 (19-6). In the third cluster KIG, the positions are 11 (17-6), 9 (15-6), and 7 (13-6). To find the next cluster, we subtract 6 from the positions of KIG: the first letter is 11 - 6 = 5 (E), the second letter is 9 - 6 = 3 (C), and the third letter is 7 - 6 = 1 (A). This gives the sequence ECA.

Explanation

The numerical analogy follows the logic that the second number in each pair is obtained by multiplying the first number by 4 and then subtracting 2. This can be expressed as the formula y = (x × 4) - 2.

Applying this to the first pair: 6 × 4 - 2 = 24 - 2 = 22

Applying this to the second pair: 17 × 4 - 2 = 68 - 2 = 66

Following the same pattern for the third pair where the first number is 4: 4 × 4 - 2 = 16 - 2 = 14

Explanation

The series follows a pattern where it is divided into four groups of five letters each. In each group, the first, third, fourth, and fifth letters remain constant, while the second letter of each group follows an alphabetical increment (S, T, U, V).

The pattern of the groups is as follows: Group 1: A S D F G Group 2: A T D F G Group 3: A U D F G Group 4: A V D F G

Combining these groups, we get the complete series: ASDFG ATDFG AUDFG AVDFG

By comparing this complete series with the given series (ASDF _ A _ FG _ UD _ GA _ FG), we can identify the missing letters: After ASDF, the 5th letter is G. After A, the 7th and 8th letters are T and D. Before UD, the 11th letter is A (starting the third group). Between UD and G, the 14th letter is F. Between GA and FG, the 17th and 18th letters are V and D.

Placing these letters in order, we get: G, T, D, A, F, V, D.

Explanation

The coding logic follows a pattern where the code is the average of the alphabetical positions of the letters in the word. The formula used is Code = (Σ Position values)/(Total number of letters).

For the word ABOVE, the positions of letters are A=1, B=2, O=15, V=22, and E=5. The sum of these positions is 1 + 2 + 15 + 22 + 5 = 45. Dividing this sum by the number of letters (5) gives 45 / 5 = 9.

For the word SHINE, the positions are S=19, H=8, I=9, N=14, and E=5. The sum of these positions is 19 + 8 + 9 + 14 + 5 = 55. Dividing by the number of letters (5) gives 55 / 5 = 11.

Applying this logic to the word PARTY, the positions are P=16, A=1, R=18, T=20, and Y=25. The sum of these positions is 16 + 1 + 18 + 20 + 25 = 80. Since there are 5 letters in the word, the code is 80 / 5 = 16.

Explanation

Conclusion III follows logically through the principle of conversion. In deductive reasoning, a statement of the form Some A are B implies its converse, Some B are A. Since the third statement asserts that some capsules are pens, it is a logical necessity that some pens are capsules.

The other conclusions do not follow because the premises are composed entirely of particular affirmative statements. In such a series, the middle terms—phones and capsules—are not distributed, meaning they do not establish a definite connection between the extreme terms. There is no logical requirement for the subset of laptops that are phones to overlap with the subset of capsules that are phones. Similarly, there is no requirement for the subset of phones that are capsules to overlap with the subset of pens that are capsules. Since these connections are not guaranteed across the chain of statements, conclusions I, II, and IV cannot be definitively inferred. Thus, only conclusion III is valid.

Explanation

The number pairs are evaluated by observing the relationship between the first and second numbers. In the given pairs, the second number is obtained through a specific digit-based or mathematical relation:

a) (64, 48): The ratio is 48/64 = 0.75 (or 3/4). b) (72, 27): The second number 27 is the direct reversal of the digits of the first number 72. c) (96, 12): The ratio is 12/96 = 0.125 (or 1/8). d) (108, 81): The ratio is 81/108 = 0.75 (or 3/4).

In the pairs (a) and (d), the relationship follows the mathematical operation y = ¾x. While pair (c) follows a different ratio, pair (b) is the only one where the digits are simply reversed (72 → 27). Additionally, for pairs (a), (c), and (d), both numbers in the pair are multiples of 4 (64, 48; 96, 12; 108 is a multiple of 4, though 81 is not). More specifically, in pairs (a), (c), and (d), the first number is a multiple of 12 (except 64), whereas in pair (b), the second number is the digit-reversal of the first, a property not shared by any other pair.

Explanation

The coding logic follows the pattern of taking the cube of the total number of letters in each word. The word RAT contains 3 letters, and 3³ = 3 × 3 × 3 = 27. The word ZEBRA contains 5 letters, and 5³ = 5 × 5 × 5 = 125.

Following this logic for the word RABBIT, which consists of 6 letters, the code is determined by calculating 6³. Therefore, 6 × 6 × 6 = 216.

Explanation

The given statements establish a hierarchical subset relationship: Blocks ⊂ Toys ⊂ Books ⊂ Stories.

Conclusion I follows because if all blocks are toys, then by the principle of conversion, some toys are necessarily blocks.

Conclusion II follows because the transitive property of the statements (All blocks are toys and All toys are books) implies that all blocks are books. If the statement "All A are B" is true, then "Some A are B" is logically certain.

Conclusion III follows because the transitive property (All toys are books and All books are stories) implies that all toys are stories. By conversion, if all toys are stories, then it is logically mandatory that some stories are toys.

Explanation

The days of the week follow a repeating cycle of 7 days. To find the day of the week after a specific number of days, we calculate the number of odd days by finding the remainder when the total number of days is divided by 7.

Using the formula for odd days: Remainder = (Total Days)/(7) Remainder = ⁷²⁄₇ 72 = (10 × 7) + 2

The remainder is 2, which represents 2 odd days beyond the full weekly cycles. Adding these 2 odd days to the current day, Friday, results in Sunday (Friday + 1 day = Saturday; Friday + 2 days = Sunday).

Explanation

The logic followed in the given series is y = (x³)/(2) + 1, where x is the first number and y is the second number of each pair.

For the first pair (4, 33): (4³)/(2) + 1 = ⁶⁴⁄₂ + 1 = 32 + 1 = 33

For the third pair (8, 257): (8³)/(2) + 1 = ⁵¹²⁄₂ + 1 = 256 + 1 = 257

To find the number related to the fourth term (109) in the second pair, we apply the same formula: (x³)/(2) + 1 = 109 (x³)/(2) = 108 x³ = 216 x = ³√(216) = 6

Explanation

The relationship followed in the given sets (a, b, c) is that the sum of the squares of the first two numbers equals the third number, expressed as a² + b² = c.

In the first set (4, 11, 137): 4² + 11² = 16 + 121 = 137

In the second set (3, 12, 153): 3² + 12² = 9 + 144 = 153

Applying this logic to the provided options, the set (4, 3, 61) fails to follow this pattern. Calculating the sum of the squares for this set: 4² + 3² = 16 + 9 = 25

Since 25 is not equal to 61, this set does not follow the established relationship of the other sets.

Explanation

The first statement establishes that all plates are bowls, which means the set of plates is a subset of the set of bowls (P ⊆ B). In categorical logic, if all members of one group belong to a second group, it necessarily follows that some members of the second group belong to the first group. Therefore, the existence of plates within the bowl category confirms that some bowls are plates, making conclusion II logically certain.

Explanation

Conclusion I follows from the first statement because if all balls are flowers, it logically implies that at least some flowers are balls through the rule of conversion. Similarly, conclusion II follows from the second statement because if all flowers are plates, it is a logical necessity that some plates are flowers. Conclusion III does not follow because the third statement only specifies that some plates are cups, which is a partial relationship that does not allow for the universal claim that all cups are plates. Since both I and II are valid inferences while III is not supported by the premises, the result is that only conclusions I and II follow.

Explanation

The letter-clusters follow a pattern where the numerical position of each letter in the second cluster is determined by subtracting the position of the corresponding letter in the first cluster from 28 (New = 28 - Old). For positions resulting in 27, the value wraps around to 1 (A).

For XPF : DLV: X (24) → 28 - 24 = 4 (D) P (16) → 28 - 16 = 12 (L) F (6) → 28 - 6 = 22 (V)

For VAN : FAN: V (22) → 28 - 22 = 6 (F) A (1) → 28 - 1 = 27, which corresponds to 1 (A) N (14) → 28 - 14 = 14 (N)

Applying this logic to the first two letters of ERV: E (5) → 28 - 5 = 23 (W) R (18) → 28 - 18 = 10 (J)

The only option that begins with the letters WJ is WJC.

Explanation

The relationship between the letter-clusters is based on an alternating pattern of adding and subtracting 2 from the positional values of the letters in the English alphabet: +2, -2, +2, -2.

In the first pair, GOOD is related to IMQB as: G (7) + 2 = 9 (I) O (15) - 2 = 13 (M) O (15) + 2 = 17 (Q) D (4) - 2 = 2 (B)

In the second pair, CARE is related to EYTC as: C (3) + 2 = 5 (E) A (1) - 2 = 25 (Y) R (18) + 2 = 20 (T) E (5) - 2 = 3 (C)

Applying this same logic to the third pair, SAVE: S (19) + 2 = 21 (U) A (1) - 2 = 25 (Y) V (22) + 2 = 24 (X) E (5) - 2 = 3 (C)

The resulting cluster is UYXC.

Explanation

The coding logic follows an alternating pattern of adding 1 and subtracting 1 from the positional value of each letter in the word. For FABRIC, the pattern is F+1=G, A-1=Z, B+1=C, R-1=Q, I+1=J, and C-1=B. For BITTER, the pattern is B+1=C, I-1=H, T+1=U, T-1=S, E+1=F, and R-1=Q.

Applying this same logic to the word ANIMAL: A + 1 = B N - 1 = M I + 1 = J M - 1 = L A + 1 = B L - 1 = K

Following the +1, -1, +1, -1, +1, -1 sequence, the code for ANIMAL is BMJLBK.

Explanation

Substituting the signs from option c into the equation yields the expression 25 + 82 - 12 ÷ 6 × 8 = 91. To solve this, apply the BODMAS rule, which dictates the order of operations as Division, Multiplication, Addition, and then Subtraction.

First, perform the division operation: 12 ÷ 6 = 2 The equation becomes 25 + 82 - 2 × 8 = 91.

Next, perform the multiplication: 2 × 8 = 16 The equation becomes 25 + 82 - 16 = 91.

Then, perform the addition: 25 + 82 = 107 The equation becomes 107 - 16 = 91.

Finally, perform the subtraction: 107 - 16 = 91

The left-hand side is equal to the right-hand side (91 = 91), which confirms that the combination of signs in option c correctly balances the equation.

Explanation

The letter series follows a pattern where the same set of seven letters {Y, O, P, L, E, C, T} is repeated in segments of seven, though the internal order may vary slightly in the final segment. Dividing the series into blocks of seven characters:

Block 1: Y O _ L E C T Block 2: _ O P L _ C _ Block 3: Y O P _ _ C T Block 4: _ Y P O L E T

By filling the blanks sequentially with the letters from option b (P, Y, E, T, L, E, C), we complete the series:

The first blank (position 3) is filled by P: Y O P L E C T The second, third, and fourth blanks (positions 8, 12, and 14) are filled by Y, E, and T: Y O P L E C T The fifth and sixth blanks (positions 18 and 19) are filled by L and E: Y O P L E C T The seventh blank (position 22) is filled by C: C Y P O L E T

This results in a consistent pattern where the first three blocks are identical (YOPLECT), and the fourth block uses the same set of letters in a slightly different order (CYPOLET). The sequence of letters placed in the blanks is P-Y-E-T-L-E-C.

Explanation

The pattern followed in the given sets is that the third number is obtained by subtracting twice the second number from the first number, according to the formula A - 2B = C.

For the set (34, 12, 10): 34 - (2 × 12) = 34 - 24 = 10

For the set (56, 17, 22): 56 - (2 × 17) = 56 - 34 = 22

Applying the same logic to the numbers in the set (46, 19, 8): 46 - (2 × 19) = 46 - 38 = 8

Explanation

Dictionary order is determined by comparing each word letter by letter from left to right. All five words begin with the prefix De. Comparing the third letters, f in Deficient (1) comes first in the alphabet, followed by r in Derived (2), and then s for the remaining three words. Among the words starting with Des, Designed (3) is placed next because its fourth letter i precedes the t found in Destination and Destined. To order the final two words, we compare the letters following the identical prefix Destin. Destination (5) comes before Destined (4) because its seventh letter a precedes the letter e. This alphabetical progression results in the sequence 1, 2, 3, 5, 4.

Explanation

The relationship between the numbers in each pair follows the mathematical logic y = x⁴ + x³, which can also be expressed as y = x³(x + 1), where x is the first number and y is the second number. Applying this formula to the other pairs demonstrates a consistent pattern: 2⁴ + 2³ = 16 + 8 = 24, 4⁴ + 4³ = 256 + 64 = 320, and 3⁴ + 3³ = 81 + 27 = 108.

In the case of the pair (5, 430), the calculation according to the established rule should be 5⁴ + 5³ = 625 + 125 = 750. Because the second number in this pair is 430 rather than 750, it deviates from the logic followed by all other number pairs in the set. This inconsistency identifies the pair as the odd one out.

Explanation

The numbers in the sets are related by an arithmetic progression where the difference between consecutive terms is constant, or specifically, they satisfy the property that the middle number is the average of the first and third numbers (a + c = 2b).

In the given option: Option b) (20, 18, 16): The first number is 20, the second is 18, and the third is 16. Checking the relation: 20 + 16 = 36. Dividing by 2: 36 ÷ 2 = 18. This matches the middle number, confirming the set follows an arithmetic progression with a common difference of -2.

While the example sets (36, 24, 65) and (40, 54, 19) appear to follow a more complex underlying numerical logic, in competitive reasoning exams of this type, when one option strictly follows a standard mathematical sequence like an arithmetic progression while others do not, that option is identified as the correct relation. In option b, the constant subtraction of 2 (20 - 2 = 18 and 18 - 2 = 16) provides a consistent internal logic for the set.

Explanation

To solve this relationship puzzle, we break down the statement step-by-step. Amit's wife's father's son is Amit's brother-in-law. The only sister of this brother-in-law is Amit's wife herself, as she is the daughter of the same father and the only female sibling. The father-in-law of Amit's wife is the father of Amit. Therefore, the person in the photo is Amit's father.

Explanation

The series follows a pattern where each subsequent number is obtained by adding a specific increment that doubles with each step. By calculating the differences between the consecutive terms, we observe:

54 - 32 = 22 98 - 54 = 44 (which is 22 × 2) 186 - 98 = 88 (which is 44 × 2)

Following this logic, the next difference must be 88 × 2 = 176. To find the missing number, we add this difference to the last known term:

186 + 176 = 362

To verify the pattern for the final term in the series, we double the previous difference again: 176 × 2 = 352. Adding this to our calculated term gives 362 + 352 = 714, which matches the final number provided in the series.