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

Explanation

The words arranged in alphabetical order are Warcraft (3), Wardrobe (5), Wardship (6), Warehouse (2), Warranty (4), and Warriors (1). This sequence matches Option C because 'r' in Wardrobe precedes 's' in Wardship, and 'a' in Warranty precedes 'i' in Warriors.

Explanation

The logical validity of the conclusions is determined by the rules of syllogism and immediate inference. The third statement provided is "Some plates are desks", which is a particular affirmative (I-type) proposition. According to the rule of conversion, an I-type proposition "Some A are B" can be converted into "Some B are A". Therefore, from the statement "Some plates are desks", it logically follows that "Some desks are plates", which corresponds to Conclusion III.

Regarding Conclusion IV, which states "All trays are desks", it is logically invalid because universal conclusions (A-type: All) cannot be derived from particular premises (I-type: Some). Since the statements only establish that there is a partial overlap between desks and trays, one cannot definitively conclude that every single tray is a desk. In a syllogism where all premises are of the "Some" type, no universal conclusion can be drawn, and only the direct conversions of the given statements remain valid. Therefore, only Conclusion III follows.

Explanation

The relationship established in the first pair is between a sensory organ and its primary function. The skin is the human body's organ for the sense of touch. Similarly, the nose is the primary organ for the sense of olfaction, which is the sense of smell. This process involves the detection of airborne chemical molecules by olfactory receptors located in the nasal cavity, which the brain then interprets as distinct scents.

Explanation

To determine the relationship, break down the description from the perspective of Ganesh. Ganesh's mother's brother is his maternal uncle. His maternal uncle's father is his maternal grandfather. The granddaughter of his maternal grandfather is the daughter of his maternal grandfather's children. These children include Ganesh's mother and his maternal uncle. Therefore, the granddaughter could be either Ganesh's sister or his maternal uncle's daughter. A maternal uncle's daughter is defined as a cousin. Given the available options, cousin is the correct relationship described by the sequence.

Explanation

The first letter of each cluster follows the sequence of the five English vowels in reverse alphabetical order: U, O, I, E, and finally A. The second letter of each cluster follows a consistent addition pattern where each subsequent letter is three positions ahead in the alphabet. Starting from V, the progression is V + 3 = Y, Y + 3 = B (by cycling from Z back to A), B + 3 = E, and E + 3 = H. Combining the first letter A with the second letter H results in the cluster AH.

Explanation

The relationship followed in the number-pairs is y = ˣ⁄₂ + 1, where x is the first number and y is the second. Applying this operation to the first number 15 results in ¹⁵⁄₂ + 1 = 7.5 + 1 = 8.5. Since this calculation produces 8.5 rather than the second number 4, this pair does not adhere to the established pattern.

Explanation

The logic followed in the given sets is: (First Number ÷ Second Number)² = Third Number.

In the first set (55, 11, 25), dividing the first number by the second gives 55 ÷ 11 = 5. Squaring this result yields the third number: 5² = 25.

In the second set (64, 16, 16), dividing the first number by the second gives 64 ÷ 16 = 4. Squaring this result yields the third number: 4² = 16.

Applying the same mathematical relationship to option a (33, 11, 9), dividing the first number by the second gives 33 ÷ 11 = 3. Squaring this result yields the third number: 3² = 9.

Explanation

The relationship between the letter-clusters follows a specific addition pattern based on the alphabetical positions of the letters. For the first pair HMD : KOE, the transformations are H + 3 = K, M + 2 = O, and D + 1 = E. Similarly, for the second pair BNQ : EPR, the transformations are B + 3 = E, N + 2 = P, and Q + 1 = R.

To find the sixth letter-cluster that results in FLV, we apply the inverse of this pattern to the target cluster: subtract 3 from the first letter, 2 from the second letter, and 1 from the third letter. Calculating for FLV: F(6) - 3 = 3, which corresponds to C; L(12) - 2 = 10, which corresponds to J; and V(22) - 1 = 21, which corresponds to U. This yields the cluster CJU.

Explanation

The letter-clusters in this set generally follow a pattern where each subsequent letter is 4 positions ahead of the previous one in the English alphabet. The cluster HJKP is the odd one because it breaks this rule. Using the numerical positions of the letters where A = 1 and Z = 26, the values for HJKP are H = 8, J = 10, K = 11, and P = 16. The increments between these letters are 10 - 8 = 2, 11 - 10 = 1, and 16 - 11 = 5. This deviation from the consistent +4 sequence identifies it as the cluster that does not belong.

Explanation

The relationship between the numbers in each pair follows the mathematical pattern x : x × (x - 2)².

For the first pair 5:45, substituting x = 5 into the formula: 5 × (5 - 2)² = 5 × 3² = 5 × 9 = 45

For the second pair 3:3, substituting x = 3 into the formula: 3 × (3 - 2)² = 3 × 1² = 3 × 1 = 3

Applying the same logic to the third pair where x = 6: 6 × (6 - 2)² = 6 × 4² = 6 × 16 = 96

Explanation

The series follows a pattern where consecutive prime numbers starting from 7 are added to each term to obtain the next term. The differences between the given numbers are: 15 - 8 = 7 26 - 15 = 11 Following the sequence of prime numbers (7, 11, 13, 17, 19, ...), the next difference should be 13. Adding 13 to the third term results in: 26 + 13 = 39 To verify this, the next prime number after 13 is 17. Adding 17 to 39 gives: 39 + 17 = 56 The subsequent prime number is 19, and adding it to 56 confirms the final term: 56 + 19 = 75 The sequence of differences is 7, 11, 13, 17, 19, which are consecutive prime numbers.

Explanation

The relationship between the terms in each pair follows a constant subtraction pattern. In the first pair, the difference between the numbers is 7183 - 3850 = 3333. In the third pair, the difference is 8972 - 5639 = 3333. Applying the same logic to the second pair, subtracting 3333 from the third term gives 6957 - 3333 = 3624.

Explanation

The relationship between the numbers in each pair follows the pattern y = 5x³, where y is the first number and x is the second number.

In the first pair 625:5, the calculation is 5 × 5³ = 5 × 125 = 625.

In the second pair 2560:8, the calculation is 5 × 8³ = 5 × 512 = 2560.

Applying this same logic to the third pair 5000:?, let the missing number be x. 5x³ = 5000 x³ = ⁵⁰⁰⁰⁄₅ x³ = 1000 x = ³√(1000) x = 10

Explanation

The coding logic follows the pattern where the sum of the positional values of the letters in the English alphabet is multiplied by 2. For the word ASK, the positional values are A = 1, S = 19, and K = 11. The sum is 1 + 19 + 11 = 31, and multiplying by 2 gives 31 × 2 = 62. Similarly, for the word BYE, the positional values are B = 2, Y = 25, and E = 5. The sum is 2 + 25 + 5 = 32, and multiplying by 2 gives 32 × 2 = 64.

Following this same logic for the word CRY, the positional values are C = 3, R = 18, and Y = 25. The sum of these values is 3 + 18 + 25 = 46. Multiplying this sum by 2 results in 46 × 2 = 92.

Explanation

Applying the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction) to the sequence of signs in option d, the equation is solved as follows:

256 ÷ 4 - 9 × 3 + 14 = 51

First, perform the division: 256 ÷ 4 = 64

Next, perform the multiplication: 9 × 3 = 27

Substitute these values back into the equation: 64 - 27 + 14 = 51

Perform the addition and subtraction from left to right: 64 - 27 = 37 37 + 14 = 51

The left-hand side equals the right-hand side, balancing the equation.

Explanation

The letter-series is based on the repetition of a five-letter core, CLO_E, where the fourth letter increments by one position in the English alphabet with each iteration. The sequence progresses through four stages: CLOVE, then CLOWE, followed by CLOXE, and finally CLOYE.

When the letters from the correct option (O, L, O, X, E, L, Y) are inserted into the seven blanks of the provided series, the resulting sequence is CLOVECLOWECLOXECLOYE. This complete string follows the identified pattern perfectly: the first block is CLOVE (letters 1-5), the second is CLOWE (letters 6-10), the third is CLOXE (letters 11-15), and the fourth is CLOYE (letters 16-20). The fourth letters follow the alphabetical sequence V to W to X to Y, maintaining the structural logic of the series.

Explanation

The coding logic follows two steps: reversing the order of the letters in the word and then shifting the central letter forward by three positions in the alphabetical sequence.

In the word TABLE, the letters are at positions T(1), A(2), B(3), L(4), and E(5). Reversing the sequence gives E(5), L(4), B(3), A(2), and T(1). The central letter at position 3 is B. Applying a +3 shift to B (2 + 3 = 5) results in the letter E. Replacing the central letter with E gives the code ELEAT.

Similarly, for the word SWING, the reversed order is G(5), N(4), I(3), W(2), and S(1). The central letter I is shifted forward by three places (9 + 3 = 12), which is the letter L. Replacing the middle letter results in GNLWS.

Applying this logic to FRAME, the letters are F(1), R(2), A(3), M(4), and E(5). Reversing the letters yields the sequence E, M, A, R, F. The central letter A is shifted forward by three positions (1 + 3 = 4), which corresponds to the letter D. Replacing A with D results in the final code EMDRF.

Explanation

By interchanging the signs - and +, the given equation becomes: 588 ÷ 28 × 32 - 72 + 160 = 760

Applying the BODMAS rule: First, perform the division: 588 ÷ 28 = 21. The equation now is: 21 × 32 - 72 + 160 = 760.

Next, perform the multiplication: 21 × 32 = 672. The equation now is: 672 - 72 + 160 = 760.

Then, perform addition and subtraction from left to right: 672 - 72 = 600 600 + 160 = 760

Since the Left Hand Side (760) equals the Right Hand Side (760), interchanging these signs makes the equation correct.

Explanation

The relationship follows a logic where the second number in each pair is obtained by squaring the first number and then subtracting 100 from the result.

Logic: Second Number = (First Number)² - 100

For the first pair, 17² - 100 = 289 - 100 = 189. For the second pair, 13² - 100 = 169 - 100 = 69. Applying this same pattern to the third pair with the number 18, we calculate 18² - 100 = 324 - 100 = 224.

Explanation

Conclusion I follows from the first statement: All males are boys. In syllogistic logic, the universal affirmative statement All A are B implies the particular affirmative Some B are A. Therefore, if all males are boys, it is necessarily true that some boys are males.

Conclusion II follows from the third statement: All students are teachers. Using the same logic of immediate conversion, if the entire set of students is contained within the set of teachers, then a part of the teacher population consists of students. Thus, some teachers are students.

Conclusion III does not follow because there is no direct or transitive relationship established between males and students. Males are defined as a subset of boys, and students are a subset of teachers. While the statements mention that some teachers are boys, this partial overlap does not provide enough information to link the specific subset of males to the subset of students.

Explanation

The logic followed in the given sets is that the middle number is the sum of the first number and twice the third number. The relationship can be expressed by the formula b = a + 2c, where a, b, c are the first, second, and third numbers respectively.

In the first set (12, 40, 14): 12 + (2 × 14) = 12 + 28 = 40

In the second set (15, 33, 9): 15 + (2 × 9) = 15 + 18 = 33

Applying the same logic to the set (21, 91, 35): 21 + (2 × 35) = 21 + 70 = 91

Explanation

The letter series is based on a repeating pattern divided into four groups of five letters each. In each group, the first three letters (MNB) and the fifth letter (C) remain constant, while the fourth letter increases by one position in the alphabetical order.

The logical groups are as follows: M N B V C M N B W C M N B X C M N B Y C

In this sequence, the fourth letter of each group follows the progression: V (+1) → W (+1) → X (+1) → Y.

By placing the letters from the correct option into the blanks of the series, we get: MNB (V) C M (N) (B) W C M N B (X) (C) M (N) (B) Y C

Combining these filled letters in order from left to right gives the sequence: V, N, B, X, C, N, B.

Explanation

The logic followed in the given letter-clusters is the Opposite Letter relationship, where the sum of the positional values of the corresponding letters in the English alphabet is 27. In the first pair, LIGHT is coded as ORTSG because L(12) + O(15) = 27, I(9) + R(18) = 27, G(7) + T(20) = 27, H(8) + S(19) = 27, and T(20) + G(7) = 27. Similarly, in the second pair, FANCY is coded as UZMXB because F(6) + U(21) = 27, A(1) + Z(26) = 27, N(14) + M(13) = 27, C(3) + X(24) = 27, and Y(25) + B(2) = 27.

Applying the same logic to WATCH: W (23) yields 27 - 23 = 4, which is D. A (1) yields 27 - 1 = 26, which is Z. T (20) yields 27 - 20 = 7, which is G. C (3) yields 27 - 3 = 24, which is X. H (8) yields 27 - 8 = 19, which is S.

The resulting letter-cluster is DZGXS.

Explanation

Interchanging the - and + signs transforms the original equation into 1664 ÷ 4 × 2 - 712 + 316 = 436. Following the BODMAS rule, the division 1664 ÷ 4 yields 416. Multiplying this result by 2 gives 416 × 2 = 832. Substituting these values back into the equation gives 832 - 712 + 316. Performing the subtraction results in 832 - 712 = 120, and adding 316 to this result gives 120 + 316 = 436. The left-hand side is now equal to the right-hand side.

Explanation

The letter series is formed by the continuous repetition of the five-letter cluster DMBFG. To solve for the missing letters, the sequence can be divided into four identical groups of five:

DMBFG / DMBFG / DMBFG / DMBFG

By comparing the fixed letters in the series with this repeating pattern, we can identify the specific positions of the blanks. The full sequence, including the 8 missing letters from option b, is as follows:

(D)(M) B F G D M (B)(F) G (D) M B F (G) D (M) B (F) G

In this arrangement: The first two letters of the option (D, M) fill positions 1 and 2 to complete the first DMBFG block. The next two letters (B, F) fill positions 8 and 9 in the second block. The letter D fills position 11 in the third block. The letter G fills position 15 in the third block. The letters M and F fill positions 17 and 19 in the final block.

Sequentially placing these letters (D-M-B-F-D-G-M-F) completes the pattern of repeating the DMBFG unit four times.

Explanation

The letter series is formed by dividing the sequence into four distinct groups of five letters each. Each group contains the complete set of letters {M, N, P, O, S} in various permutations.

By dividing the string into these groups, we observe the following structure: Group 1: MN_ S Group 2: M _PO Group 3: N_OS Group 4: M _PS

When the letters from the correct option (P, O, N, S, M, P, N, O) are placed sequentially into the blanks, the groups are completed as follows: Group 1 becomes MN[P][O]S, which uses the five letters in a standard order. Group 2 becomes M[N][S]PO, which is a permutation of the same five letters. Group 3 becomes [M]N[P]OS, which repeats the permutation used in the first group. Group 4 becomes M[N][O]PS, which is another permutation of the five-letter set.

The logical consistency of the series is maintained by ensuring that every block of five characters contains each of the letters M, N, P, O, and S exactly once. Substituting the letters P, O, N, S, M, P, N, and O satisfies this requirement across the entire sequence.

Explanation

The relationship between the letter-clusters follows a pattern of adding or subtracting specific values based on the numerical positions of the letters in the alphabet where A=1, B=2, …, Z=26. The transformation rule applied to each cluster is +3, -2, +4.

In the first pair BPX : ENB, the logic is B(2) + 3 = 5(E), P(16) - 2 = 14(N), and X(24) + 4 = 28. In a cyclical alphabet of 26 letters, 28 - 26 = 2, which is B. Similarly, for the third and fourth clusters KUW : NSA, the logic is K(11) + 3 = 14(N), U(21) - 2 = 19(S), and W(23) + 4 = 27, where 27 - 26 = 1, which is A.

Applying this established pattern to the fifth cluster FOY, the first letter F (6) plus 3 results in 9, which is I. The second letter O (15) minus 2 results in 13, which is M. The third letter Y (25) plus 4 results in 29. Calculating the cyclical position, 29 - 26 = 3, which corresponds to the letter C. This results in the letter-cluster IMC.

Explanation

The logic followed by the number-pairs is the mathematical operation y = (x × 8) + 3, where x is the first number and y is the second. In the pair (25, 200), the second number is calculated simply as 25 × 8 = 200. This pair is the odd one out because it fails to include the addition of 3 that defines the consistent relationship found in the rest of the set.

Explanation

To determine the relationship, break down the description provided by Veronica from the end of the phrase. Veronica's husband's brother is her brother-in-law. The daughter of her husband's brother is the daughter of this brother-in-law. The mother of that daughter must be the wife of the husband's brother. Therefore, the girl in the picture is Veronica's husband's brother's wife.

Explanation

The numbers in each set follow the pattern (Number₁ - Number₂) × 3 = Number₃. Applying this rule to the first given set (54, 32, 66), we calculate (54 - 32) × 3 = 22 × 3 = 66. Applying the same logic to the second given set (49, 31, 54), we find (49 - 31) × 3 = 18 × 3 = 54.

Following this relationship for option a, (39, 18, 63), the operation (39 - 18) × 3 results in 21 × 3 = 63, which matches the third number of the set.

Explanation

The series follows a pattern where the difference between consecutive terms increases by a constant value. By calculating the differences between the numbers: 11 - 4 = 7 20 - 11 = 9 31 - 20 = 11 44 - 31 = 13 The differences form an arithmetic progression of 7, 9, 11, 13, … where each subsequent difference increases by 2. To find the next number in the series, we identify the next difference in the pattern, which is 13 + 2 = 15. Adding this difference to the last term gives 44 + 15 = 59.

Explanation

Conclusion III follows directly from the second statement, which states that some doormats are pillows. In syllogistic logic, the conversion of a particular affirmative statement is always valid; thus, if some doormats are pillows, then it is logically certain that some pillows are doormats. Conclusions I and II are not necessarily true because the premises only link bedsheets to pillows and pillows to doormats. This chain does not guarantee a mandatory intersection between bedsheets and doormats or curtains, as the portion of pillows that are bedsheets may be entirely distinct from the portion of pillows that are doormats.

Explanation

In a non-leap year, there are 365 days. The total duration given is 1 year and 2 days, which equals 365 + 2 = 367 days. To determine the change in the day of the week, we calculate the number of odd days by finding the remainder when the total number of days is divided by 7.

367 ÷ 7 = 52 weeks and 3 odd days.

This means that the day 1 year and 2 days from now is 3 days ahead in the weekly cycle from today. To find today's day, we count 3 days backward from Tuesday. Counting back 1 day gives Monday, 2 days gives Sunday, and 3 days gives Saturday. Thus, today is Saturday.

Explanation

The coding logic for the six-letter words follows a specific pattern of positional shifts and interchanges:

The letter at the first position is shifted by +4 (P → T, S → W). The letters at the second and fifth positions are interchanged (U ↔ I in PUBLIC, E ↔ E in SERVER). The letter at the third position is shifted by +3 (B → E, R → U). The letter at the fourth position is shifted by -3 (L → I, V → S). The letter at the sixth position is shifted by -4 (C → Y, R → N).

Applying this logic to DIRECT: The first letter D (4) shifted by +4 gives H (8). The second letter I and the fifth letter C are interchanged, placing C at the second position and I at the fifth position. The third letter R (18) shifted by +3 gives U (21). The fourth letter E (5) shifted by -3 gives B (2). The sixth letter T (20) shifted by -4 gives P (16).

Assembling these results in order, the code for DIRECT is HCUBIP.

Explanation

The relationship between the numbers in each set follows the logic (A ÷ B) × 3 = C, where A, B, and C represent the first, second, and third numbers respectively.

In the first set (36, 6, 18): (36 ÷ 6) × 3 = 6 × 3 = 18

In the second set (35, 5, 21): (35 ÷ 5) × 3 = 7 × 3 = 21

Applying this same logic to the set (49, 7, 21): (49 ÷ 7) × 3 = 7 × 3 = 21

Explanation

Substituting the signs from the sequence -, ÷, +, ×, = into the equation 17 ∗ 21 ∗ 7 ∗ 5 ∗ 4 ∗ 34 results in the following mathematical expression:

17 - 21 ÷ 7 + 5 × 4 = 34

Applying the BODMAS rule, which dictates the order of operations as Division, Multiplication, Addition, and then Subtraction, the calculation proceeds as follows:

First, perform the division: 21 ÷ 7 = 3

Next, perform the multiplication: 5 × 4 = 20

The equation now simplifies to: 17 - 3 + 20 = 34

Performing the addition and subtraction from left to right: 14 + 20 = 34 34 = 34

The left-hand side equals the right-hand side, confirming that this combination of signs balances the equation.

Explanation

To arrange words in dictionary order, we compare letters sequentially from left to right. All five words begin with the prefix Si. Comparing the third letters, we find g in Significant and Signed, m in Simplify, and n in Sinful and Singing. Since g appears before m and n in the alphabet, Significant and Signed must come first. Comparing the fifth letters of these two words, the e in Signed precedes the i in Significant, establishing the order as Signed (3) followed by Significant (1). Next, Simplify (5) follows because its third letter m comes after g but before n. For the remaining words starting with Sin, the fourth letter f in Sinful (2) precedes the fourth letter g in Singing (4). Thus, the alphabetical sequence of the words is 3, 1, 5, 2, 4.

Explanation

W is the father of D and P because they are his daughters. D is the mother of M. The maternal grandmother of M is Y, which implies that Y is the mother of D. Since D and P are daughters of the same father, W, they are sisters. Consequently, the mother of D, who is Y, is also the mother of P.

Explanation

The given number series follows a pattern where the difference between consecutive terms increases by a constant value of 3. Calculating the differences between the known terms reveals an arithmetic progression of multiples of 3:

42 - 39 = 3 48 - 42 = 6 57 - 48 = 9 69 - 57 = 12

Following this logic, the next difference in the sequence should be 12 + 3 = 15. Adding this difference to the last known term results in 69 + 15 = 84. To verify the pattern, adding the next multiple of 3, which is 18, to this result yields 84 + 18 = 102, which matches the final number in the series.

Explanation

The logic followed in the given sets is that the sum of the first and third numbers is multiplied by 4 to obtain the middle number. The pattern is (1st number + 3rd number) × 4 = 2nd number.

For the set (8, 44, 3): (8 + 3) × 4 = 11 × 4 = 44

For the set (12, 60, 3): (12 + 3) × 4 = 15 × 4 = 60

Similarly, in the set (12, 68, 5): (12 + 5) × 4 = 17 × 4 = 68

Explanation

The given series follows a pattern based on alternating differences between consecutive terms. By calculating the differences between the visible terms at the beginning of the sequence, we observe that: 80 - 33 = 47 108 - 80 = 28 Similarly, the differences between the terms at the end of the series are: 230 - 183 = 47 258 - 230 = 28 This confirms that the sequence progresses by adding 47 and 28 in a repeating cycle. To find the missing number, we apply the next difference in the sequence, which is 47, to the third term: 108 + 47 = 155 The validity of this result is confirmed by adding the subsequent difference of 28 to the result, as 155 + 28 = 183, which matches the next term provided in the series.

Explanation

Applying the signs sequentially from the first option results in the mathematical expression 150 ÷ 3 + 10 - 2 × 7 = 46. To solve this, the BODMAS rule is applied, which establishes the order of operations as Division, Multiplication, Addition, and Subtraction.

First, perform the division operation: 150 ÷ 3 = 50. The equation now reads 50 + 10 - 2 × 7 = 46.

Second, perform the multiplication operation: 2 × 7 = 14. The equation simplifies further to 50 + 10 - 14 = 46.

Third, perform the addition operation: 50 + 10 = 60. This results in 60 - 14 = 46.

Finally, perform the subtraction operation: 60 - 14 = 46. This yields the final identity 46 = 46. Because the left-hand side equals the right-hand side, the combination of signs correctly balances the given equation.

Explanation

The numbers in the given sets (a, b, c) follow a specific arithmetic relationship where the second number is 16 more than the first number, and the third number is 4 more than the first number. This can be expressed by the formulas b = a + 16 and c = a + 4.

In the first set (31, 47, 35): 31 + 16 = 47 31 + 4 = 35

In the second set (51, 67, 55): 51 + 16 = 67 51 + 4 = 55

The set (13, 29, 17) follows this same logic: 13 + 16 = 29 13 + 4 = 17

Alternatively, the relationship can be defined by the differences between the numbers: b - a = 16 and b - c = 12. For the set (13, 29, 17), the differences are 29 - 13 = 16 and 29 - 17 = 12.

Explanation

The relationship between the letter-clusters follows a pattern where the original word is reversed and then each letter is shifted forward by increasing natural numbers (+1, +2, +3, +4, +5, +6).

For the word BEAUTY: Reverse the word: Y T U A E B Apply the numerical shifts: Y (25) + 1 = 26 (Z) T (20) + 2 = 22 (V) U (21) + 3 = 24 (X) A (1) + 4 = 5 (E) E (5) + 5 = 10 (J) B (2) + 6 = 8 (H)

Following this pattern, the resulting letter-cluster is ZVXEJH. This logic is consistent with the other examples provided: in TABLE (reversed E-L-B-A-T), adding +1, +2, +3, +4, +5 results in F-N-E-E-Y; and in CROWN (reversed N-W-O-R-C), adding +1, +2, +3, +4, +5 results in O-Y-R-V-H.

Explanation

The series follows a pattern where the difference between consecutive terms increases by a constant value of 3. By calculating the differences between the known later terms, we observe: 29 - 20 = 9 41 - 29 = 12 56 - 41 = 15

The differences are 9, 12, and 15, which form an arithmetic progression with a common difference of 3. Extending this pattern backward, the difference between the second and third terms should be 9 - 3 = 6, and the difference between the first and second terms should be 6 - 3 = 3.

Applying these differences to the start of the series: The first term is 11. The second term is 11 + 3 = 14. Checking the next step, the third term is 14 + 6 = 20, which matches the given series.

Explanation

The general relationship between the numbers in the pairs is defined by the formula y = x² - 3. For the pair 48:144, substituting x = 48 into the formula yields 48² - 3 = 2304 - 3 = 2301. Since the given value 144 is instead obtained by the operation 48 × 3 = 144, it does not satisfy the squared-minus-three condition that governs the set.

Explanation

Priya's brother's paternal grandmother is also Priya's paternal grandmother. By definition, a paternal grandmother is the mother of one's father. If this grandmother has only one child, that child must be the father of the grandchildren. Since the man is the only child of Priya's paternal grandmother, he is the father of Priya and her brother.

Explanation

The series follows a systematic pattern of alphabetical subtraction for each letter position within the clusters. By converting the letters to their numerical positions in the English alphabet (A=1, B=2, …, Z=26), the logic for each position is as follows:

The first letter of each cluster decreases by 3 positions: M(13) - 3 = J(10), J(10) - 3 = G(7), G(7) - 3 = D(4). Following this sequence, 4 - 3 = 1, which corresponds to the letter A.

The second letter of each cluster decreases by 4 positions: I(9) - 4 = E(5), E(5) - 4 = A(1), A(1) - 4 = W(23). Note that for A(1) - 4, we cycle back through the alphabet (27 - 4 = 23). Continuing the pattern, 23 - 4 = 19, which corresponds to the letter S.

The third letter of each cluster decreases by 3 positions: T(20) - 3 = Q(17), Q(17) - 3 = N(14), N(14) - 3 = K(11). Applying this logic to the next step, 11 - 3 = 8, which corresponds to the letter H.

By combining these results, the next cluster in the series is ASH.

Explanation

The code is determined by the sum of the reverse alphabetical positions of each letter in the word. The reverse position of a letter is calculated as 27 - (Forward Position).

For the word LAMP: L is the 12th letter, so its reverse position is 27 - 12 = 15. A is the 1st letter, so its reverse position is 27 - 1 = 26. M is the 13th letter, so its reverse position is 27 - 13 = 14. P is the 16th letter, so its reverse position is 27 - 16 = 11. Sum: 15 + 26 + 14 + 11 = 66.

For the word OATS: O is 15th, so reverse is 27 - 15 = 12. A is 1st, so reverse is 27 - 1 = 26. T is 20th, so reverse is 27 - 20 = 7. S is 19th, so reverse is 27 - 19 = 8. Sum: 12 + 26 + 7 + 8 = 53.

For the word YESS: Y is 25th, so reverse is 27 - 25 = 2. E is 5th, so reverse is 27 - 5 = 22. S is 19th, so reverse is 27 - 19 = 8. S is 19th, so reverse is 27 - 19 = 8. Sum: 2 + 22 + 8 + 8 = 40.

Explanation

To find the code for the letter W, compare the letters and digits of the two given words. The word THIN contains the letters T, H, I, N and is coded as 1723. The word WITH contains the letters W, I, T, H and is coded as 2417. The letters T, H, and I are common to both words. Correspondingly, the digits 1, 2, and 7 are common to both code sets. In the word WITH, the only letter not present in THIN is W. Similarly, in the code 2417, the only digit not present in the code for THIN (1723) is 4. Therefore, the letter W corresponds to the digit 4.