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

Explanation

The second statement establishes that all engineers are soldiers. In the logic of categorical syllogisms, a universal affirmative statement of the form All A are B allows for the valid conversion to the particular affirmative form Some B are A. Since the set of engineers is a subset of the set of soldiers, it is logically certain that some soldiers are engineers, supporting conclusion III. Conclusion I does not follow because the first statement confirms an overlap between girls and engineers, and since all engineers are soldiers, there must be girls who are soldiers. Conclusion II does not follow as it directly contradicts the first statement which asserts that some girls are engineers. Consequently, conclusion III is the only valid deduction that can be made from the provided statements.

Explanation

The series follows a specific addition pattern for each letter position in the clusters, while the clusters alternate between uppercase and lowercase.

Position 1: The first letter increases by +2 in each step. H (8) + 2 = j (10) j (10) + 2 = L (12)

Position 2: The second letter increases by +3 in each step. O (15) + 3 = r (18) r (18) + 3 = U (21)

Position 3: The third letter follows a pattern of -3 for the first jump, then +4 for all subsequent jumps. A (1) + 4 = e (5) e (5) + 4 = I (9)

Position 4: The fourth letter increases by +5 in each step. L (12) + 5 = q (17) q (17) + 5 = v (22)

Following the pattern of alternating cases, the sixth cluster is entirely lowercase (jreq). The seventh cluster follows the letter sequence L-U-I-v, which matches the letters in the first option.

Explanation

Let the starting position be the origin (0, 0). Shashank moves X meters West to reach the point (-X, 0). A left turn from West leads South, so walking 35 meters results in the position (-X, -35). A subsequent right turn from South leads West; walking 18 meters results in (-X - 18, -35). From there, a left turn from West leads South; walking 9 meters results in (-X - 18, -44). Turning left again from South leads East; walking 60 meters results in (-X - 18 + 60, -44), which simplifies to (42 - X, -44). A left turn from East leads North; walking 9 meters results in (42 - X, -35). A left turn from North leads West; walking 12 meters results in (42 - X - 12, -35), which is (30 - X, -35). Finally, a right turn from West leads North; walking 35 meters results in (30 - X, -35 + 35) = (30 - X, 0). Since this final point is exactly 10 meters East of the starting point, it corresponds to the coordinate (10, 0). Equating the x-coordinates, we get 30 - X = 10, which yields X = 20.

Explanation

The relationship between the letter-clusters is determined by two specific rules applied to the positions of the letters in the English alphabet. The first and third letters of each cluster are replaced by their alphabetical opposites, where the sum of the numerical positions of the original and the resulting letters equals 27. The middle letter is transformed by adding 2 to its numerical position.

In the first pair DFC:WHX, the letter D is at position 4, and its opposite is W at position 23, satisfying 4 + 23 = 27. The middle letter F is at position 6, and adding 2 results in position 8, which is H. The third letter C is at position 3, and its opposite is X at position 24, as 3 + 24 = 27.

Applying these rules to the third letter-cluster KFQ, the letter K is at position 11, so its opposite is P at position 16, because 11 + 16 = 27. The middle letter F is at position 6, and adding 2 results in position 8, which is H. The letter Q is at position 17, and its opposite is J at position 10, because 17 + 10 = 27. Consequently, the cluster KFQ transforms into PHJ.

Explanation

The coding logic involves calculating the reverse alphabetical position of each letter and then multiplying that value by 2. The reverse position of a letter is found by subtracting its standard forward position from 27. For the word STREAM, the calculations are as follows: S is the 19th letter, so (27 - 19) × 2 = 16; T is the 20th letter, so (27 - 20) × 2 = 14; R is the 18th letter, so (27 - 18) × 2 = 18; E is the 5th letter, so (27 - 5) × 2 = 44; A is the 1st letter, so (27 - 1) × 2 = 52; and M is the 13th letter, so (27 - 13) × 2 = 28. Concatenating these values results in 161418445228.

Applying the same logic to the word PERIOD: P is the 16th letter: (27 - 16) × 2 = 22 E is the 5th letter: (27 - 5) × 2 = 44 R is the 18th letter: (27 - 18) × 2 = 18 I is the 9th letter: (27 - 9) × 2 = 36 O is the 15th letter: (27 - 15) × 2 = 24 D is the 4th letter: (27 - 4) × 2 = 46

Combining these values in sequence produces the code 224418362446.

Explanation

The series follows a pattern where the difference between consecutive terms corresponds to the cubes of consecutive even integers starting from 2.

The difference between the first and second term is 63 - 55 = 8, which is 2³. According to the pattern of consecutive even cubes, the difference between the second and third term must be 4³ = 64. Adding this value to the second term gives 63 + 64 = 127.

This logic is validated by the remaining terms in the sequence. The difference between the third and fourth term is 343 - 127 = 216, which is 6³. The difference between the fourth and fifth term is 855 - 343 = 512, which is 8³. Finally, the difference between the fifth and sixth term is 1855 - 855 = 1000, which is 10³.

Explanation

The series follows the mathematical pattern Tₙ = (n + 1)³ + n, where n is the position of the term in the series. Substituting the values for n:

For n = 1: (1 + 1)³ + 1 = 2³ + 1 = 9 For n = 2: (2 + 1)³ + 2 = 3³ + 2 = 29 For n = 3: (3 + 1)³ + 3 = 4³ + 3 = 67 For n = 4: (4 + 1)³ + 4 = 5³ + 4 = 129

To find the fifth term (n = 5), we apply the same formula: T₅ = (5 + 1)³ + 5 = 6³ + 5 = 216 + 5 = 221

Checking for the next term (n = 6): T₆ = (6 + 1)³ + 6 = 7³ + 6 = 343 + 6 = 349

This confirms the pattern, and the missing number is 221.

Explanation

Interchanging the minus (-) and multiplication (×) signs in the given equation transforms 95 ÷ 19 × 3 - 7 + 29 = 13 into 95 ÷ 19 - 3 × 7 + 29 = 13.

Following the BODMAS rule, the calculation proceeds as follows:

First, perform the division: 95 ÷ 19 = 5

Next, perform the multiplication: 3 × 7 = 21

Substitute these values back into the expression: 5 - 21 + 29

Finally, perform the addition and subtraction from left to right: 5 - 21 = -16 -16 + 29 = 13

The result of the expression after interchanging the signs is 13, which makes the equation correct.

Explanation

After interchanging the signs minus and multiplication in the fourth equation, the expression becomes 119 ÷ 17 × 6 + 24 - 34. Following the BODMAS rule, the division operation is performed first, resulting in 119 ÷ 17 = 7. This value is then multiplied by 6 to get 7 × 6 = 42. Adding 24 to this product gives 42 + 24 = 66. Subtracting 34 from 66 yields the final result of 32, which matches the right-hand side of the equation.

Explanation

The relationship followed in the given pair is that the second number is the sum of the square of the first number and the square of its succeeding integer. The pattern is expressed as n : n² + (n+1)².

For the pair 14:421: 14² + (14+1)² = 196 + 15² = 196 + 225 = 421

Applying the same logic to the pair in option b: 11² + (11+1)² = 121 + 12² = 121 + 144 = 265

The calculation yields 265, which matches the second number in the pair 11:265.

Explanation

The coding scheme is determined by counting the number of letters in each word of the given sentence. In the phrase Red fort is in Delhi, the word Red has 3 letters, fort has 4, is has 2, in has 2, and Delhi has 5, which corresponds to the code 34225. Similarly, in the phrase Delhi is very polluted, the word Delhi has 5 letters, is has 2, very has 4, and polluted has 8, resulting in the code 5248. Following this logic for the phrase Pollution level is changing, the word Pollution has 9 letters, level has 5 letters, is has 2 letters, and changing has 8 letters. Arranging these counts in sequence yields the code 9528.

Explanation

The given series consists of 16 positions that follow a repeating cycle of four letters: L, G, P, and Q. By substituting the letters from the first option (P, L, Q, G, L, P) into the blanks, the sequence is completed as LGPQ LGPQ LGPQ LGPQ.

The pattern is identified by dividing the 16-character string into four equal groups of four letters each: Group 1: L G (P) Q Group 2: (L) G P (Q) Group 3: L (G) P Q Group 4: (L) G (P) Q

Each group consistently forms the segment LGPQ. The sequential placement of P, L, Q, G, L, and P into the respective blanks maintains this logical repetition throughout the entire series.

Explanation

The difference in percentage marks between Vaidehi and Kavyanjali is 92% - 78% = 14%. This difference is given as 105 marks. To find the marks obtained by Vaidehi, we calculate 92% of the total marks using the relation:

14% = 105 1% = ¹⁰⁵⁄₁₄

Vaidehi's marks (92%) can be calculated as: Marks = ¹⁰⁵⁄₁₄ × 92

Simplifying the expression by dividing both 105 and 14 by 7: Marks = ¹⁵⁄₂ × 92 Marks = 15 × 46 = 690

Explanation

Based on the third statement, all springs are contained within the set of chains (S ⊆ C). The second statement establishes that no key is a chain (K ∩ C = ∅), which means the set of keys and the set of chains are entirely disjoint. Since all springs are part of the chain set and the chain set has no overlap with the key set, it is impossible for any spring to be a key. Therefore, the deduction No key is a spring (K ∩ S = ∅) is logically certain, making conclusion II correct. Conclusion I is false as it contradicts this certain deduction. Conclusion III does not necessarily follow because while some locks are keys (and therefore cannot be springs), the statements do not provide enough information to rule out an intersection between the remaining locks and the set of springs.

Explanation

Ranjana's father is the paternal grandfather of Piyush. This implies that Piyush's father is the son of Ranjana's father, making Ranjana and Piyush's father siblings. Since Piyush is the son of Ranjana's brother, the relationship between Piyush and Ranjana is that of a nephew to his aunt.

Explanation

The six students are ranked from 1 to 6. Ekta is at the lowest rank, which is rank 6. There are two students between Ekta and David, which means David must be at rank 3, as ranks 4 and 5 constitute the two positions between them. Bhanu is given to be at rank 4. The condition that Bhanu is between the ranks of Charu and David necessitates that Charu is at rank 5, given that David is at rank 3. The remaining two ranks, 1 and 2, are filled by Farheen and Abhay respectively, with Abhay immediately below Farheen.

Explanation

The coding logic involves reversing the letters of the word and then adding an increasing sequence of integers (+1, +2, +3, +4, +5, +6) to the numerical position of each letter in the reversed sequence.

To find the code for MASTER, first reverse the word to get RETSAM. Then, apply the incremental addition to the alphabetical positions of these letters:

R (18) + 1 = 19 (S) E (5) + 2 = 7 (G) T (20) + 3 = 23 (W) S (19) + 4 = 23 (W) A (1) + 5 = 6 (F) M (13) + 6 = 19 (S)

Following this pattern, the letters transform into SGWWFS. The same rule is applied to PENCIL, where the reverse LICNEP becomes MKFRJV (12+1, 9+2, 3+3, 14+4, 5+5, 16+6), and to ERASER, where the reverse RESARE becomes SGVEWK (18+1, 5+2, 19+3, 1+4, 18+5, 5+6).

Explanation

The words are arranged by comparing their letters from left to right according to the sequence of the English alphabet. All words begin with the common prefix Tra. Comparing the fourth letter, Training (5) contains i while the remaining four words contain n. Since i precedes n in the alphabet, Training (5) is the first word in the sequence. Among the remaining words beginning with Tran, the fifth letter in Tranquil (1) is q, whereas it is s in Transfer (3), Transient (4), and Transit (2). Because q precedes s, Tranquil (1) occupies the second position. For the words starting with Trans, the sixth letter in Transfer (3) is f, while it is i in both Transient (4) and Transit (2). Since f precedes i, Transfer (3) is the third word. Comparing the seventh letters of the final two words, Transient (4) has e and Transit (2) has t. As e precedes t, Transient (4) comes fourth and Transit (2) comes last. This results in the order 5, 1, 3, 4, 2.

Explanation

The cluster WTP is the different one because it follows a positional subtraction pattern of -3 and -4 based on its alphabetical ranks. The letter W is at the 23rd position, T is at the 20th position, and P is at the 16th position. This results in the calculation 23 - 3 = 20 and 20 - 4 = 16. In contrast, the other clusters in the group follow a consistent logic where the second letter is 3 positions before the first and the third letter is 2 positions before the second. The decrease of 4 instead of 2 for the final letter distinguishes WTP from the shared pattern of the set.

Explanation

The relationship between the numbers in each pair follows the pattern (n - 2)³, where n is the first number in the pair.

For the first pair, the first number is 13. Subtracting 2 from it gives 11. The cube of 11 is 11³ = 11 × 11 × 11 = 1331.

Following the same logic for the second pair where the first number is 17, we subtract 2 to get 15. The required number is the cube of 15: 15³ = 15 × 15 × 15 = 225 × 15 = 3375.

Explanation

The relationship between the first and second letter-clusters is established by applying a specific numerical shift to the alphabetical position of each letter. In the pair JST:HPX, the first letter J (10th position) moves to H (8th position), which is a shift of -2. The second letter S (19th position) moves to P (16th position), representing a shift of -3. The third letter T (20th position) moves to X (24th position), representing a shift of +4.

Applying this same pattern of (-2, -3, +4) to the letter-cluster PWJ, where P is the 16th letter, W is the 23rd, and J is the 10th: the first letter P (16 - 2 = 14) becomes N. The second letter W (23 - 3 = 20) becomes T. The third letter J (10 + 4 = 14) becomes N. Therefore, the resulting letter-cluster is NTN.

Explanation

Interchanging the multiplication (×) and division (÷) signs results in the equation 16 - 18 ÷ 216 × 432 + 40 = 20. Following BODMAS, 18 ÷ 216 equals 1/12, and (1/12) × 432 equals 36, so 16 - 36 + 40 = 20, which is correct. Option B contains a typographical error but is the intended answer based on this mathematical logic.

Explanation

The problem requires substituting characters with mathematical operators where A = +, B = ×, C = -, and D = ÷. The expression given is: (45 D 9) B 5 A 8 B (7 A 3 C 6) C (28 D (4 D 4))

Substituting the operators into the expression: (45 ÷ 9) × 5 + 8 × (7 + 3 - 6) - (28 ÷ (4 ÷ 4))

Following the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction), simplify the terms within the parentheses first: (45 ÷ 9) = 5 (7 + 3 - 6) = 4 (4 ÷ 4) = 1

Substituting these simplified values back into the expression: 5 × 5 + 8 × 4 - (28 ÷ 1)

Now, perform the remaining division and the multiplications: 25 + 32 - 28

Finally, perform the addition and subtraction from left to right: 57 - 28 = 29

Explanation

The coding logic uses the opposite pairs of letters in the English alphabet, where the sum of their numerical positions equals 27. Following this pattern for GARDEN, G becomes T, A becomes Z, R becomes I, D becomes W, E becomes V, and N becomes M, resulting in TZIWVM.

Explanation

The coding pattern follows the rule where the alphabetical positional value of each letter is multiplied by 3. The positional values in the English alphabet are A=1, B=2, ..., Z=26.

For the word GANGA: G is the 7th letter, so 7 × 3 = 21 A is the 1st letter, so 1 × 3 = 3 N is the 14th letter, so 14 × 3 = 42 G is the 7th letter, so 7 × 3 = 21 A is the 1st letter, so 1 × 3 = 3 This results in the code 21-3-42-21-3.

For the word KOSHI: K is the 11th letter, so 11 × 3 = 33 O is the 15th letter, so 15 × 3 = 45 S is the 19th letter, so 19 × 3 = 57 H is the 8th letter, so 8 × 3 = 24 I is the 9th letter, so 9 × 3 = 27 This results in the code 33-45-57-24-27.

Applying the same logic to GOMTI: G: 7 × 3 = 21 O: 15 × 3 = 45 M: 13 × 3 = 39 T: 20 × 3 = 60 I: 9 × 3 = 27

The numerical sequence for GOMTI is therefore 21-45-39-60-27.

Explanation

Let the two numbers be x and y. The given condition states that the ratio of the sum of these numbers to their difference is 6:5, which is mathematically represented as:

(x+y)/(x-y) = ⁶⁄₅

Using the property of Componendo and Dividendo, if (a)/(b) = (c)/(d), then (a+b)/(a-b) = (c+d)/(c-d). Applying this to the equation:

((x+y) + (x-y))/((x+y) - (x-y)) = ⁶⁺⁵⁄₆₋₅

(2x)/(2y) = ¹¹⁄₁

(x)/(y) = ¹¹⁄₁

The ratio of the two numbers x and y is found to be 11:1. Alternatively, cross-multiplying the initial equation gives 5(x+y) = 6(x-y), leading to 5x + 5y = 6x - 6y. Rearranging the terms results in x = 11y, which simplifies to x:y = 11:1.

Explanation

In the expression C @ J K % M # R, the relation C @ J establishes that C is the wife of J, which identifies J as the husband (male). The relation J K states that J is the father of K. Furthermore, K % M indicates that K is the brother of M, and M # R indicates that M is the sister of R. These relations collectively establish that K, M, and R are siblings. Since J is the father of K, he is necessarily the father of R as well.

Explanation

To find the code for the word you, we use the method of comparison and elimination between the given sentences. By comparing the first sentence are you ready (541) and the second sentence we are going (261), the common word is are and the common digit is 1, which means are is coded as 1. Next, by comparing the first sentence are you ready (541) and the third sentence she is ready (498), the common word is ready and the common digit is 4, which means ready is coded as 4. In the first sentence are you ready, the words are and ready correspond to the digits 1 and 4 respectively. This leaves the word you and the digit 5. Therefore, you is coded as 5.

Explanation

The given sequence is a combination of two alternating sub-series.

The first sub-series consists of the terms at odd positions: 1, 2, 6, 42, 1806. The logic for this sequence is xₙ = xₙ₋₁² + xₙ₋₁. This is verified by the following calculations: the third term is 1² + 1 = 2, the fifth term is 2² + 2 = 6, the seventh term is 6² + 6 = 42, and the ninth term is 42² + 42 = 1764 + 42 = 1806.

The second sub-series consists of the terms at even positions: 1, 2, 10, ?. The logic for this sequence is yₙ = yₙ₋₁³ + yₙ₋₁. Applying this pattern, the fourth term is 1³ + 1 = 2, and the sixth term is 2³ + 2 = 10. To find the missing number at the eighth position, we apply the same logic to the sixth term: 10³ + 10 = 1000 + 10 = 1010.

Explanation

Conclusion II follows directly from the second statement through the principle of conversion. The statement Some peelers are spatulas is a particular affirmative proposition, which is logically reversible. If a relationship of intersection exists between the set of peelers and the set of spatulas, then some members of the set of spatulas are necessarily members of the set of peelers.

Conclusion I does not follow because it contradicts the first statement. The premise All peelers are funnels establishes that the entire set of peelers is contained within the set of funnels. In formal logic, the universal affirmative proposition All A are B is the contradictory of the particular negative proposition Some A are not B. Since the premises are assumed to be true, Conclusion I is logically impossible and cannot follow. Consequently, only the second conclusion is valid.

Explanation

The series follows a pattern based on the numerical positions of letters in the English alphabet: E is 5, F is 6, I is 9, N is 14, and U is 21. The differences between consecutive terms are 6 - 5 = 1, 9 - 6 = 3, 14 - 9 = 5, and 21 - 14 = 7. These differences represent the sequence of consecutive odd numbers starting from 1. Following this pattern, the next difference must be 9. Adding 9 to the position of U gives 21 + 9 = 30. Since the alphabet cycles every 26 letters, the position is calculated as 30 - 26 = 4. The 4th letter of the alphabet is D.

Explanation

In the letter-cluster CXBH, the first and second letters are alphabetical opposites as their positions 3 and 24 sum to 27. However, the subsequent letters do not follow the uniform +5 increment rule. For the other clusters in the set, the third letter is 5 positions ahead of the second, and the fourth letter is 5 positions ahead of the third. In CXBH, the third letter B (2) is only 4 positions after X (24 → 2), and the fourth letter H (8) is 6 positions after B (2 → 8). This deviation in the positional gaps makes CXBH the outlier.

Explanation

The first letter of each cluster decreases by 3 in alphabetical order: C(3) - 3 = Z(26), Z(26) - 3 = W(23), W(23) - 3 = T(20), and T(20) - 3 = Q(17). The second letter increases by 4: A(1) + 4 = E(5), E(5) + 4 = I(9), I(9) + 4 = M(13), and M(13) + 4 = Q(17). The third letter decreases by 5: L(12) - 5 = G(7), G(7) - 5 = B(2), B(2) - 5 = W(23), and W(23) - 5 = R(18). The fourth letter follows the standard sequence of English vowels A, E, I, O, U in a cyclical manner. Starting from I, the vowels are I → O → U → A → E. Joining these four letters results in the cluster QQRE.

Explanation

To determine the members of each line, we analyze the positional relationships starting with the person facing G, which is C. The statement that B is to the immediate right of the person facing G means B is to the immediate right of C. Furthermore, H is to the immediate right of B, which establishes that C, B, and H are seated in the same line. Since F faces H, F must be in the opposite line. The condition that D is to the immediate left of F places D in the same line as F. Given that A faces D, A must be in the line opposite D, which is the line already containing C, B, and H. This confirms that A, B, C, and H are sitting in the same line. The remaining friends, D, E, F, and G, occupy the second line, which is consistent with the information that E is to the immediate left of G and C faces G.

Explanation

To make the equation 8 + 48 ÷ 12 × 5 - 13 = 29 correct, we interchange the numbers 8 and 12. The modified equation becomes:

12 + 48 ÷ 8 × 5 - 13 = 29

Following the BODMAS rule (Division, Multiplication, Addition, and Subtraction), we first perform the division: 48 ÷ 8 = 6

Now, the equation is: 12 + 6 × 5 - 13 = 29

Next, we perform the multiplication: 6 × 5 = 30

The equation becomes: 12 + 30 - 13 = 29

Finally, we perform the addition and subtraction: 42 - 13 = 29 29 = 29

The Left Hand Side (LHS) is equal to the Right Hand Side (RHS), confirming that interchanging 8 and 12 satisfies the equation.

Explanation

The cluster MPI is the odd one out because it fails to satisfy the rule where the second letter is the first letter plus 2, and the third letter is the alphabetical opposite of the second. Alphabetical opposites are pairs where the sum of their positional values equals 27. In MPI, the transition from M (13) to P (16) is a shift of 3 positions. Furthermore, the positional values of the second and third letters, P (16) and I (9), add up to 25 rather than 27.

Explanation

The relationship between the letter-clusters is based on a fixed numerical shift for each position. By assigning numerical values to the letters where A=1, B=2, …, Z=26, the transformation from GTQ to JVP follows the pattern: G(7) + 3 = J(10), T(20) + 2 = V(22), and Q(17) - 1 = P(16). Applying this +3, +2, -1 logic to the cluster SDK, we calculate the first letter as S(19) + 3 = 22 (V), the second letter as D(4) + 2 = 6 (F), and the third letter as K(11) - 1 = 10 (J). This sequence of operations yields the cluster VFJ.

Explanation

Let the number be x. According to the problem, 80% of x = 768. The requirement is to find 40% of 5% of x. We can simplify the requested percentages into a single calculation relative to x: 40% of 5% = ⁴⁰⁄₁₀₀ × 5% = 0.40 × 5% = 2%

Since we know that 80% of the number is 768, we can find 2% of the same number by applying a direct proportion. If 80 parts equal 768, then 2 parts are calculated by dividing the known value by 40: Value = ⁷⁶⁸⁄₈₀ × 2 Value = ⁷⁶⁸⁄₄₀ Value = 19.2

Explanation

The given sequence follows an arithmetic progression where each term increases by a constant common difference. By calculating the difference between consecutive terms, we find that 101 - 74 = 27, 128 - 101 = 27, and 155 - 128 = 27. To find the missing number in the series, add the common difference of 27 to the last term: 155 + 27 = 182.

Explanation

To make the equation 13 + 15 × 8 ÷ 96 - 4 = 109 correct, the signs ÷ and - are interchanged. Replacing ÷ with - and - with ÷, the equation becomes:

13 + 15 × 8 - 96 ÷ 4 = 109

Following the BODMAS rule, the division operation is performed first: 96 ÷ 4 = 24

Substituting this back into the equation: 13 + 15 × 8 - 24 = 109

Next, the multiplication operation is performed: 15 × 8 = 120

The equation now reads: 13 + 120 - 24 = 109

Finally, the addition and subtraction are carried out from left to right: 133 - 24 = 109 109 = 109

Since the left-hand side equals the right-hand side, the interchange of ÷ and - satisfies the equation.

Explanation

To arrange the words in alphabetical order as they appear in a dictionary, we examine the letters of each word from left to right. All given words share the first three letters Mal. Comparing the fourth letters, we find f in Malfunction, i in Malice, i in Malignant, l in Mallows, and w in Malware. Alphabetically, f comes first, placing Malfunction (4) at the beginning of the list. Between Malice (1) and Malignant (2), which both have i in the fourth position, we move to the fifth letter; since c in Malice precedes g in Malignant, Malice (1) comes before Malignant (2). Next, comparing the remaining fourth letters l and w, l in Mallows (3) appears earlier in the alphabet than w in Malware (5). Following this logical progression, the sequence is established as 4, 1, 2, 3, 5.

Explanation

Comparing the two phrases, we identify common words and their corresponding codes. The words Is and Big appear in both India Is Big and Tiger Is A Big Cat. Similarly, the codes Dim and Kim appear in both Tim Dim Kim and Dim Gim Kim Se Rim. This implies that Dim and Kim represent Is and Big in some order. In the first phrase, the only word remaining after accounting for the common terms is India, and the only code remaining in that set is Tim. Consequently, Tim must be the code for India.

Explanation

The series is formed by the repetition of the eight-letter word IMMOBILE. By dividing the 24-character sequence into three segments of eight letters each, the pattern becomes clear: IMMOBILE | IMMOBILE | IMMOBILE.

Filling in the gaps sequentially with the letters from the correct option results in the following structure: First segment: IMM(OB)ILE Second segment: I(MM)OBI(LE) Third segment: IMMO(BI)LE

When the letters O, B, M, M, L, E, B, and I are placed in the blanks, they complete the three-fold repetition of the word. Thus, the sequence of letters required to complete the series is OBMMLEBI.

Explanation

The pattern is based on the differences between consecutive terms. Calculating the first differences gives: 20 - 14 = 6 34 - 20 = 14 72 - 34 = 38 182 - 72 = 110

Now, find the second differences (the differences between the first differences): 14 - 6 = 8 38 - 14 = 24 110 - 38 = 72

The second differences follow a geometric progression where each term is multiplied by 3: 8 × 3 = 24 and 24 × 3 = 72. Applying this ratio, the next second difference is 72 × 3 = 216.

To find the next first difference, add this value to the previous first difference: 110 + 216 = 326. Adding this final difference to the last number in the series yields the missing number: 182 + 326 = 508.

Explanation

The series is based on adding a sequence of numbers that follow the pattern n² + 1 to each preceding term.

The difference between the first two terms is 47 - 45 = 2, which can be expressed as 1² + 1. The difference between the next two terms is 52 - 47 = 5, which is 2² + 1. The difference between the third and fourth terms is 62 - 52 = 10, which is 3² + 1. The difference between the fourth and fifth terms is 79 - 62 = 17, which is 4² + 1.

Following this logic, the next difference should be 5² + 1 = 25 + 1 = 26. Adding this value to the last term of the series gives 79 + 26 = 105. Alternatively, the second-order differences between these values are consecutive odd numbers: 5 - 2 = 3, 10 - 5 = 5, and 17 - 10 = 7. The next difference in this secondary sequence is 9, making the primary difference 17 + 9 = 26.

Explanation

The eight friends are seated at equal intervals of 360° / 8 = 45° around the circular table. Since the friends P, Q, R, S, T, U, V and W are sitting in an anticlockwise order, we determine the position of W by counting the steps from Q in the anticlockwise direction. Starting from Q, the sequence follows R, S, T, U, V, and then W. This means W is the sixth person after Q in the anticlockwise direction, which corresponds to a displacement of 6 × 45° = 270° anticlockwise.

Moving 270° anticlockwise is mathematically equivalent to moving 360° - 270° = 90° in the clockwise direction. Q is given to be in the South-East direction. Moving 90° clockwise from South-East, the first 45° interval points to South, and the second 45° interval points to South-West. Consequently, W is sitting in the South-West direction.

Explanation

The relationship between the first and second number follows the pattern where the first number is divided by 2 and then 1 is added to the result to obtain the second number. In the first pair 18:10, the calculation is 18 ÷ 2 + 1 = 9 + 1 = 10. Applying the same logic to the third number 24, we divide 24 by 2 to get 12 and then add 1, which results in 13.

Explanation

To arrange the words in dictionary order, we compare them letter by letter. All five words begin with the prefix Photo. The next letters are c in Photocopier (2) and Photocopy (5), and g in Photographic (1), Photography (3), and Photographer (4). Since c precedes g in the alphabet, words 2 and 5 come first. Between Photocopier and Photocopy, the eighth letter i in Photocopier comes before y in Photocopy, placing them in the order 2, 5.

For the remaining words, all share the common root Photograph. Comparing the subsequent letters, Photographer (4) has e, Photographic (1) has i, and Photography (3) has y. Following alphabetical order e, i, y, the sequence for these three is 4, 1, 3. Combining both sets results in the final dictionary arrangement 2, 5, 4, 1, 3.

Explanation

The coding logic follows the pattern of summing the numerical positions of each letter in the English alphabet (A=1, B=2, ..., Z=26) and then multiplying that sum by a constant factor of 3.

For the word RAHUL, the positions are R=18, A=1, H=8, U=21, and L=12. The sum of these values is 18 + 1 + 8 + 21 + 12 = 60. Multiplying this sum by 3 yields 60 × 3 = 180.

For the word POOJA, the positions are P=16, O=15, O=15, J=10, and A=1. The sum of these values is 16 + 15 + 15 + 10 + 1 = 57. Multiplying this sum by 3 yields 57 × 3 = 171.

Applying this logic to the word RAJIV, the positions are R=18, A=1, J=10, I=9, and V=22. The sum of these values is 18 + 1 + 10 + 9 + 22 = 60. Multiplying this sum by 3 yields 60 × 3 = 180.

Explanation

The series follows a pattern where in each subsequent step, the last letter of the current cluster is moved to a specific position that increments by one with each move. Starting from ORGANS, the last letter S moves to the first position to form SORGAN. In the next step, the last letter N of SORGAN moves to the second position to form SNORGA. Following this logic, to find the fourth cluster, the last letter A of SNORGA must move to the third position, resulting in SNAORG.

This pattern is verified by the remaining steps in the series. From SNAORG, the last letter G moves to the fourth position to produce SNAGOR. Finally, from SNAGOR, the last letter R moves to the fifth position to result in SNAGRO. The movement of the last letter to the n-th position where n = 1, 2, 3, 4, 5 confirms the sequence.