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

Explanation

The coding logic follows an alternating pattern of adding 3 and subtracting 3 from the positional values of the letters in the English alphabet.

For the word CAKES: C (3) + 3 = F (6) A (1) - 3 = X (24) K (11) + 3 = N (14) E (5) - 3 = B (2) S (19) + 3 = V (22) This results in the code FXNBV.

For the word ABUSE: A (1) + 3 = D (4) B (2) - 3 = Y (25) U (21) + 3 = X (24) S (19) - 3 = P (16) E (5) + 3 = H (8) This results in the code DYXPH.

Applying the same logic to BARKS: B (2) + 3 = E (5) A (1) - 3 = X (24) R (18) + 3 = U (21) K (11) - 3 = H (8) S (19) + 3 = V (22) The resulting code is EXUHV.

Explanation

The logic followed in the letter-cluster analogies is a two-step process based on the vowels and consonants of the word. First, all the vowels are extracted from the word in their original order of appearance and placed at the beginning of the new cluster. Second, all the consonants are extracted in their original order, and each is shifted two positions backward in the English alphabetical sequence (Consonant - 2).

In the word STABLE, the vowels are A and E, which form the prefix AE. The consonants are S, T, B, and L. Shifting them gives S - 2 = Q, T - 2 = R, B - 2 = Z, and L - 2 = J. Combining them yields AEQRZJ. In the word TARGET, the vowels are A and E, while the consonants T, R, G, and T shift to R, P, E, and R respectively, resulting in AERPER.

Applying this logic to VISUAL: Extract vowels in order: I, U, A. Extract consonants in order: V, S, L. Shift consonants by -2: V (22) - 2 = T (20), S (19) - 2 = Q (17), and L (12) - 2 = J (10). Combine the results: IUATQJ.

Explanation

The coding pattern involves reversing the order of the letters in each word. For the word ENGINE, reversing the characters results in ENIGNE. Similarly, for the word TRAIN, reversing the sequence of letters yields NIART. Applying this logic to the word LEVEL, which is a palindrome, the reverse of the sequence L-E-V-E-L is also L-E-V-E-L.

Explanation

To determine which equation is not correct, we interchange the signs × and + and the numbers 7 and 4 in both equations and solve using the BODMAS rule.

For Equation I: 7 × 8 + 4 - 6 ÷ 3 = 57 After interchanging the signs and numbers, the expression becomes: 4 + 8 × 7 - 6 ÷ 3 Applying BODMAS, we first perform division, then multiplication, and finally addition and subtraction: 4 + (8 × 7) - 2 4 + 56 - 2 = 58 Since the calculated value is 58 and the given value is 57, Equation I is not correct.

For Equation II: 4 × 8 - 9 ÷ 3 + 7 = 3 After interchanging the signs and numbers, the expression becomes: 7 + 8 - 9 ÷ 3 × 4 Applying BODMAS: 7 + 8 - (3 × 4) 7 + 8 - 12 15 - 12 = 3 Since the calculated value matches the given value, Equation II is correct.

Because only Equation I is incorrect, the answer is Only I.

Explanation

The series is formed by applying specific arithmetic operations to the alphabetical positions of each letter in the terms. Let the positions of the letters be P₁, P₂, P₃, P₄.

First letter (P₁): C(3) → G(7) → K(11) → O(15) The pattern is an addition of +4. Next letter: 15 + 4 = 19 → S.

Second letter (P₂): O(15) → I(9) → C(3) → W(23) The pattern is a subtraction of -6. Note that 3 - 6 = -3; in a cyclic alphabet of 26 letters, -3 + 26 = 23 (W). Next letter: 23 - 6 = 17 → Q.

Third letter (P₃): M(13) → U(21) (+8) U(21) → C(3) (+8, since 21 + 8 = 29 and 29 - 26 = 3) C(3) → X(24) (-5, since 3 - 5 = -2 and -2 + 26 = 24) The pattern follows pairs of increments: +8, +8, followed by -5, -5. Next letter: 24 - 5 = 19 → S.

Fourth letter (P₄): B(2) → R(18) (+16) R(18) → H(8) (+16, since 18 + 16 = 34 and 34 - 26 = 8) H(8) → K(11) (+3) The pattern follows pairs of increments: +16, +16, followed by +3, +3. Next letter: 11 + 3 = 14 → N.

Combining these results, the next term in the series is SQSN.

Explanation

The relationship between the categories is established through logical inclusion and exclusion. Statement 2 specifies that all medicines are chemicals (M ⊆ C), and statement 1 states that some spices are medicines. Since these medicines are part of the chemical set, it follows that some chemicals are spices, which validates conclusion II. Furthermore, statement 3 asserts that no chemical is cheap (C ∩ Cheap = ∅). Because all medicines are contained within the set of chemicals, they must also be excluded from the set of cheap items. This confirms conclusion III, which states that no medicine is cheap. Conclusion I is logically impossible because it contradicts the deduction that no medicine can be cheap.

Explanation

The letter-clusters follow a specific positional shift pattern in the English alphabet where the first two letters are increased by 2 and the last two letters are decreased by 2.

In the first pair HERO to JGPM: H is the 8th letter, and 8 + 2 = 10, which is J. E is the 5th letter, and 5 + 2 = 7, which is G. R is the 18th letter, and 18 - 2 = 16, which is P. O is the 15th letter, and 15 - 2 = 13, which is M.

In the second pair FLOW to HNUM: F is the 6th letter, and 6 + 2 = 8, which is H. L is the 12th letter, and 12 + 2 = 14, which is N. O is the 15th letter, and 15 - 2 = 13, which is M. W is the 23rd letter, and 23 - 2 = 21, which is U.

Applying this +2, +2, -2, -2 logic to the fifth letter-cluster DIAL: D is the 4th letter, and 4 + 2 = 6, which is F. I is the 9th letter, and 9 + 2 = 11, which is K. A is the 1st letter, and moving 2 steps backward in the circular alphabet (27 - 2 = 25) gives Y. L is the 12th letter, and 12 - 2 = 10, which is J.

The resulting letter-cluster is FKYJ.

Explanation

The numbers in the given sets follow the relationship where the third number is equal to four times the product of the first two numbers. The general formula is: 1ˢᵗ Number × 2ⁿᵈ Number × 4 = 3ʳᵈ Number

For the set (6, 17, 408): 6 × 17 × 4 = 102 × 4 = 408

For the set (13, 27, 1404): 13 × 27 × 4 = 351 × 4 = 1404

Applying the same logic to the set (4, 26, 416): 4 × 26 × 4 = 104 × 4 = 416

Explanation

Substituting the signs +,× ,÷ , = into the given expression 50 ∗ 25 ∗ 10 ∗ 2 ∗ 175 results in the following equation:

50 + 25 × 10 ÷ 2 = 175

Following the BODMAS rule, operations are performed in the order of Division, Multiplication, Addition, and Subtraction.

Step 1: Perform the division. 10 ÷ 2 = 5 The equation now reads: 50 + 25 × 5 = 175

Step 2: Perform the multiplication. 25 × 5 = 125 The equation now reads: 50 + 125 = 175

Step 3: Perform the addition. 50 + 125 = 175

Since 175 = 175, the equation is perfectly balanced.

Explanation

The letter-clusters follow a pattern based on the positional values of the letters in the English alphabet, where A=1, B=2, …, Z=26. In the clusters TRQ, LJI, and NLK, the difference between the first and second letter is -2, and the difference between the second and third letter is -1. For TRQ, the positions are T(20), R(18), Q(17), resulting in 20 - 2 = 18 and 18 - 1 = 17. For LJI, the positions are L(12), J(10), I(9), resulting in 12 - 2 = 10 and 10 - 1 = 9. For NLK, the positions are N(14), L(12), K(11), resulting in 14 - 2 = 12 and 12 - 1 = 11.

In contrast, the letter-cluster GDA follows a different numerical pattern. The positional values for GDA are G(7), D(4), A(1). Here, the difference between the first and second letter is 7 - 4 = 3, and the difference between the second and third letter is 4 - 1 = 3. Because GDA uses a constant subtraction of 3 instead of the sequential subtraction of 2 and 1 seen in the other three groups, it is the odd one out.

Explanation

The relationship between L and P is determined by tracing the lineage from L through the subsequent symbols in the expression. In the segment E % Z | L, E is the father of Z and Z is the son of L. This implies that E and L are a married couple, where L is the mother of Z. Moving to the next part, L # M indicates that L is the sister of M. Since M - N states that M is the daughter of N, it follows that L is also the daughter of N. Finally, N * P establishes that N is the wife of P. As P is the husband of N and the father of N's children, L is the daughter of P.

Explanation

The relationship between the terms in each pair follows the logic y = 1.5x², where x is the first term and y is the second term.

For the first pair (8:96): 1.5 × 8² = 1.5 × 64 = 96

For the third pair (12:216): 1.5 × 12² = 1.5 × 144 = 216

Following the same logic for the middle pair, where the third term (x) is 2, we find the fourth term (y): 1.5 × 2² = 1.5 × 4 = 6

Explanation

The terms of the series follow the general formula aₙ = 3ⁿ - 1{2}. Calculating the values for each position n: a₁ = 3¹ - 1{2} = 1 a₂ = 3² - 1{2} = 4 a₃ = 3³ - 1{2} = 13 a₄ = 3⁴ - 1{2} = 40

To find the missing fifth term, substitute n = 5 into the formula: a₅ = 3⁵ - 1{2} = (243 - 1)/(2) = ²⁴²⁄₂ = 121

The pattern is verified by the sixth term a₆ = 3⁶ - 1{2} = (729 - 1)/(2) = 364. Alternatively, the series can be solved using the recursive relation aₙ = 3aₙ₋₁ + 1. Applying this to the fourth term gives (40 × 3) + 1 = 121.

Explanation

The numbers in the group are expected to follow a progression where each term is the previous term divided by 5, defined by the relations n₂ = n₁ / 5 and n₃ = n₂ / 5. Applying this logic to the first number, 400 / 5 = 80, which matches the second term. However, the next step requires 80 / 5 = 16. Because the group contains 14 instead of 16, it fails to maintain the consistent mathematical ratio of 5 between consecutive numbers.

Explanation

In option A, P is the sister of R and R is the father of Q, which establishes that P is the paternal aunt of Q. The other options describe P as having no relationship to Q, being the father of Q, or being the mother of Q.

Explanation

To find the day of the week for 26th November 1994, we calculate the number of odd days from the reference point of 1st January 0001 until the given date. We first calculate the odd days for 1993 completed years. In 1600 years, there are 0 odd days. In the next 300 years, there is 1 odd day. For the remaining 93 years, the number of leap years is the integer part of 93 / 4, which is 23. The number of ordinary years is 93 - 23 = 70. The odd days in these 93 years are (23 × 2) + (70 × 1) = 116. Reducing this modulo 7, we get 116 7 = 4 odd days. Therefore, the total odd days up to 31st December 1993 are 0 + 1 + 4 = 5.

Next, we calculate the odd days in 1994 up to 26th November. Since 1994 is not a leap year, the odd days for the months are: January (3), February (0), March (3), April (2), May (3), June (2), July (3), August (3), September (2), and October (3). The sum of these is 24 odd days. Adding the 26 days of November, we get 24 + 26 = 50 days. Reducing this modulo 7, we get 50 7 = 1 odd day.

The total number of odd days is 5 + 1 = 6. In the standard counting system where 0 is Sunday, 1 is Monday, 2 is Tuesday, 3 is Wednesday, 4 is Thursday, 5 is Friday, and 6 is Saturday, 6 odd days indicate that the day was Saturday.

Explanation

In the expression P × Q - R, the symbol × indicates that P is the father of Q. The symbol - indicates that Q is the sister of R. Since Q and R are siblings, the person who is the father of Q must also be the father of R. Therefore, P is the father of R.

Explanation

The statements provided are universal affirmative propositions of the form All A are B. From the first statement, All W are L, it logically follows that the set W is a subset of set L (W ⊆ L), which implies the particular affirmative conclusion Some L are W. The second statement, All L are M, indicates that set L is a subset of set M (L ⊆ M), implying Some M are L. By the transitive property of inclusion, if W ⊆ L and L ⊆ M, then W ⊆ M, meaning All W are M, which further implies Some M are W. All three conclusions (No L is W, No M is L, and No M is W) are universal negative propositions. These conclusions directly contradict the existence of the positive relationships established by the premises. Since a negative conclusion cannot be validly drawn from purely affirmative premises in categorical syllogisms, none of the conclusions follow.

Explanation

The logic followed in the given sets is that the second number is the sum of the squares of the first and third numbers. This can be expressed by the formula a² + c² = b, where a, b, and c represent the first, second, and third numbers respectively.

In the first set (12, 313, 13): 12² + 13² = 144 + 169 = 313

In the second set (11, 185, 8): 11² + 8² = 121 + 64 = 185

Following this logic in the set (9, 90, 3): 9² + 3² = 81 + 9 = 90

This confirms that the set (9, 90, 3) satisfies the established relationship a² + c² = b.

Explanation

The relationship established between the first two words is that of a collective noun or a group and its constituent parts. In a legal context, a panel refers to a group or body of individuals who are selected to serve as jurors. Similarly, in a financial context, a portfolio represents a collective grouping of various financial assets and investment instruments, which are collectively referred to as securities. Just as jurors form a panel, securities form a portfolio.

Explanation

The series follows a specific incremental pattern for each corresponding letter position in the four-letter terms. By converting letters to their numerical positions in the alphabet (A=1, B=2, ..., Z=26), the logic is as follows:

First letter: The increment is +7. A(1) +7 H(8) +7 O(15) +7 V(22) +7 29 ≡ 3 (C)

Second letter: The increment is +5. B(2) +5 G(7) +5 L(12) +5 Q(17) +5 22 (V)

Third letter: The increment is +9. C(3) +9 L(12) +9 U(21) +9 30 ≡ 4 (D) +9 39 ≡ 13 (M)

Fourth letter: The increment is +11. D(4) +11 O(15) +11 Z(26) +11 37 ≡ 11 (K) +11 48 ≡ 22 (V)

Following these shifts, the next term in the sequence is CVMV.

Explanation

The series follows a specific pattern based on the starting letter of each cluster and the number of letters skipped between clusters.

Starting Letter Pattern: The first letters of the clusters are a (1), f (6), ?, s (19), and a (27). Calculating the differences between these positions: Between 1st and 2nd: 6 - 1 = +5 Between 4th and 5th: 27 - 19 = +8 The differences follow an increasing sequence: +5, +6, +7, +8. The starting letter of the missing cluster is 6 + 6 = 12, which is the letter l.

Gap Between Clusters: Cluster 1 ends at D (4) and Cluster 2 starts at f (6), leaving a gap of 1 letter (e). Cluster 4 ends at V (22) and Cluster 5 starts at a (27), leaving a gap of 4 letters (w, x, y, z). Following the increasing gap pattern (1, 2, 3, 4), there must be a gap of 2 letters after the second cluster. The second cluster ends at I (9). Skipping 2 letters (j, k) leads to the 12th letter, l.

Internal Cluster Pattern: Each cluster consists of four consecutive letters. The first two letters are lowercase and the last two are uppercase (llUU). Starting from the 12th letter (l): 12th: l (lowercase) 13th: m (lowercase) 14th: N (uppercase) 15th: O (uppercase)

The resulting cluster is lmNO. Note that in many sans-serif fonts used in exams, the lowercase l and uppercase I appear nearly identical. Based on the alphabetical sequence, the cluster is lmNO.

Explanation

The series follows a pattern where the difference between consecutive terms increases by a multiple of 3. Calculating the differences between the given terms: 4 - 2 = 2 10 - 4 = 6 28 - 10 = 18

The differences are 2, 6, and 18. Each difference is 3 times the preceding difference (2 × 3 = 6 and 6 × 3 = 18). Following this geometric progression of differences, the next difference must be 18 × 3 = 54. To find the missing number, we add this difference to the previous term: 28 + 54 = 82

We can verify this by finding the next term in the series. The next difference would be 54 × 3 = 162. Adding this to our result gives 82 + 162 = 244, which matches the final term provided in the question. Alternatively, the series can be expressed by the general formula Tₙ = 3ⁿ⁻¹ + 1. For the fifth term, T₅ = 3⁵⁻¹ + 1 = 3⁴ + 1 = 81 + 1 = 82.

Explanation

To arrange words in dictionary order, they are compared letter by letter from left to right. Comparing the first three letters, Latterly (4) and Lattice (2) both start with L-a-t, which alphabetically precedes L-a-u found in the other three words. Between words 4 and 2, the fifth letter e in Latterly comes before the fifth letter i in Lattice, making the starting sequence 4, 2. For the remaining words, Laudable (5), Laudanum (1), and Laudation (3) all share the first five letters L-a-u-d-a. Comparing their sixth letters, b in Laudable comes first, then n in Laudanum, and finally t in Laudation. This establishes the sequence 5, 1, 3, completing the full dictionary order as 4, 2, 5, 1, 3.

Explanation

The pattern followed by the numbers in the other groups is that each subsequent number is exactly half of the preceding number. This can be expressed as y = ˣ⁄₂ and z = ʸ⁄₂, resulting in a constant ratio of 4:2:1 among the three numbers. In group a, the second number (200) is half of the first number (400), but the third number (50) is not half of the second number, as ²⁰⁰⁄₂ = 100. This deviation from the z = ʸ⁄₂ rule makes it the odd group.

Explanation

The given statements are all particular affirmative propositions of the form Some A are B. In categorical syllogisms, a definite conclusion cannot be drawn between two terms if they are only linked through a middle term in two I-type (Some) statements. The first and second statements establish an overlap between fingers and toes and between toes and rings, but they do not provide a necessary connection between fingers and rings. This makes conclusions II and IV logically uncertain. Similarly, the second and third statements show an intersection between toes and rings and between rings and hands, but this does not ensure that any toes are hands, which invalidates conclusion I. Finally, there is no logical path connecting the set of fingers to the set of hands across the intermediate categories of toes and rings, meaning conclusion III also fails to follow. Because each conclusion describes a possibility rather than a logical necessity, none of them follow from the premises.

Explanation

The series follows a specific pattern for each character position based on alphabetical rank. The first letter remains constant as M in every term. For the second letter, there is a consistent subtraction of 9 from the alphabetical position: H(8) - 9 = -1 ≡ 25(Y), Y(25) - 9 = 16(P), P(16) - 9 = 7(G), and G(7) - 9 = -2 ≡ 24(X).

For the third letter, the pattern involves adding 8 to the alphabetical position of the previous term: D(4) + 8 = 12(L), L(12) + 8 = 20(T), T(20) + 8 = 28 ≡ 2(B), and B(2) + 8 = 10(J). For the fourth letter, there is a consistent subtraction of 10 from the alphabetical position: M(13) - 10 = 3(C), C(3) - 10 = -7 ≡ 19(S), S(19) - 10 = 9(I), and I(9) - 10 = -1 ≡ 25(Y). Applying these rules to the last term MGBI results in the next term MXJY.

Explanation

To arrange the words in dictionary order, we compare them letter by letter from left to right. All seven words begin with the prefix Am. Comparing the third letter of each word, the letters are b for words 3, 2, and 6; e for word 7; o for word 5; and p for words 1 and 4. Since b precedes e, e precedes o, and o precedes p alphabetically, words starting with Amb come first. Among Ambience, Ambiguous, and Ambivalent, the fourth letter i is common, but the fifth letters are e, g, and v respectively. Thus, 3 comes before 2, which comes before 6. Following these is Ameliorate (7) and then Amorphous (5). Finally, comparing Amphibian (1) and Amplify (4) at the fourth letter, h comes before l. Therefore, the correct dictionary sequence is 3, 2, 6, 7, 5, 1, 4.

Explanation

The relationship between the numbers in the given sets follows the logic that the sum of the squares of the first two numbers is equal to the third number. The pattern is defined by the formula a² + b² = c, where a and b are the first and second numbers, and c is the third number.

In the set (2, 4, 20): 2² + 4² = 4 + 16 = 20

In the set (4, 5, 41): 4² + 5² = 16 + 25 = 41

In the set (4, 3, 25): 4² + 3² = 16 + 9 = 25

The third number is obtained by squaring the first two numbers and adding them together, which is consistent across the example sets and the correct option.

Explanation

The first statement, No tyre are white, is a universal negative proposition of the form No A is B. In categorical logic, this statement is reversible, which means No B is A is also true. Thus, Conclusion I, No white is tyre, follows directly from the first statement.

The second statement, All grey are white, indicates that the set of grey items is a subset of the set of white items (G ⊆ W). According to the first statement, the set of tyres and the set of white items are disjoint (T ∩ W = ∅). Since all grey items are contained within the set of white items, and no white item is a tyre, it logically follows that no grey item can be a tyre. Therefore, Conclusion II, No tyre is grey, is a valid inference. Conclusion III does not necessarily follow because the statement All grey are white does not preclude the possibility that the set of white items and grey items are identical, in which case the claim that some white items are not grey would be false.

Explanation

The relationship between the numbers in the given sets is based on the division of the first number by the second number to obtain the third number. Alternatively, the first number is the product of the second and third numbers.

For the set (76, 4, 19): 76 ÷ 4 = 19 or 4 × 19 = 76

For the set (98, 2, 49): 98 ÷ 2 = 49 or 2 × 49 = 98

Applying the same mathematical logic to the set (72, 4, 18): 72 ÷ 4 = 18 or 4 × 18 = 72

Explanation

The relationship in the first pair is based on a physical reaction and its corresponding emotional state. Trembling is a physical manifestation or involuntary response often caused by the emotion of fear. Similarly, a sigh is a physical action involving a deep, audible breath that is commonly released as an expression of relief, typically occurring after a period of stress, tension, or anxiety has passed.

Explanation

The series follows a logical progression where each subsequent term is generated by multiplying the preceding term by 2 and then adding 2 to the product. This can be expressed by the recursive formula Tₙ₊₁ = 2Tₙ + 2.

Beginning with the first term, 5, the second term is calculated as 5 × 2 + 2 = 12. The third term follows the same pattern, calculated as 12 × 2 + 2 = 26. To find the missing number in the fourth position, we apply the rule to the third term: 26 × 2 + 2 = 54.

The accuracy of this logic is verified by checking the remaining terms of the sequence. The fifth term is 54 × 2 + 2 = 110, and the sixth term is 110 × 2 + 2 = 222. Because the pattern holds consistently throughout the entire series, the number that replaces the question mark is 54.

Explanation

The expression S @ T # P @ Q # R | V defines the family hierarchy through the given symbols. From S @ T, S is the husband of T, which establishes that T is the wife and a female member of the family. The segment T # P indicates that P is the son of T. Next, P @ Q means that P is the husband of Q, identifying Q as P's wife. Since T is the mother of P and P is the husband of Q, T is the mother of Q's husband. This relationship makes T the mother-in-law of Q.

Explanation

The logic followed by the other pairs in the set is y = (x - 1) × 4, where x represents the first number and y represents the second number. In the pair 11- 39, applying this rule results in (11 - 1) × 4 = 40. Because the provided value is 39 instead of 40, this pair does not follow the consistent mathematical relationship shared by the other alternatives.

Explanation

The coding logic involves summing the standard alphabetical positional values of the letters in the word and then adding the total number of letters in that word to the sum. For ICE, the positional values are I = 9, C = 3, and E = 5. Their sum is 9 + 3 + 5 = 17. Adding the number of letters in the word (3) gives 17 + 3 = 20. For HOT, the positional values are H = 8, O = 15, and T = 20. Their sum is 8 + 15 + 20 = 43. Adding the number of letters (3) gives 43 + 3 = 46. Following this same pattern for POT, the positional values are P = 16, O = 15, and T = 20. The sum of these values is 16 + 15 + 20 = 51. Adding the number of letters (3) to this sum results in 51 + 3 = 54.

Explanation

The letter-clusters are analyzed based on the alphabetical positions of their letters where A=1, B=2, ..., Z=26. In each cluster, the second letter is the immediate alphabetical successor of the third letter: in EUT, U (21) and T (20); in TFE, F (6) and E (5); in RHG, H (8) and G (7); and in TRQ, R (18) and Q (17).

The clusters are further defined by the relationship between the first and third letters. For the clusters EUT, TFE, and RHG, the sum of the positional values of the first and third letters is consistently 25. For EUT, the sum is 5 + 20 = 25. For TFE, the sum is 20 + 5 = 25. For RHG, the sum is 18 + 7 = 25. In the case of TRQ, the sum of the first letter T (20) and the third letter Q (17) is 37, which violates this pattern.

Explanation

Applying the BODMAS rule to the equation 16 × 3 ÷ 2 - 11 + 9 = 22, we evaluate the expression sequentially. First, we perform the multiplication and division operations from left to right. Multiplying 16 by 3 gives 48, and then dividing 48 by 2 results in 24.

The equation now simplifies to 24 - 11 + 9 = 22. Proceeding with addition and subtraction, subtracting 11 from 24 yields 13. Finally, adding 9 to 13 results in 22. Since the calculated value matches the value on the right side of the equation, the combination of signs is correct.

Explanation

The series follows a pattern where the last three letters BCD remain constant in every cluster. The first letter of each cluster follows the sequence of English vowels in alphabetical order: A, E, I, O, and U. Following A and E, the next vowel in the sequence is I. By replacing the first letter of the third cluster with I and keeping the suffix BCD, we get IBCD.

Explanation

The logic followed in the given sets is that the second number is the sum of twice the first number and the third number. This can be expressed by the formula: 2 × (First Number) + Third Number = Second Number

Applying this to the first set (4, 13, 5): 2 × 4 + 5 = 8 + 5 = 13

Applying this to the second set (3, 12, 6): 2 × 3 + 6 = 6 + 6 = 12

Following the same logic for the set in option d (5, 17, 7): 2 × 5 + 7 = 10 + 7 = 17

Explanation

The third statement provides that some chairs are pencils. In syllogistic logic, a statement of the form Some A are B can be converted into Some B are A. Therefore, if some chairs are pencils, it logically follows that some pencils are chairs, validating conclusion III.

For conclusions involving non-adjacent categories, the chain of logic relies on the statements Some benches are tables, Some tables are chairs, and Some chairs are pencils. In formal logic, two particular premises (both starting with Some) do not allow for a definite conclusion between the terms they do not share. Because the link between benches and chairs is mediated by tables, and the link between tables and pencils is mediated by chairs—all via Some relations—no certain connection can be established. Thus, while those relationships are possible, they are not logically necessary, leaving conclusion III as the only one that follows.

Explanation

This analogy is based on the functional purpose of the instruments mentioned. A telescope is an optical tool designed to observe and magnify distant objects that are far away from the viewer. Following the same logic, a microscope is an optical instrument specifically engineered to magnify and observe tiny objects that are otherwise too small to be seen clearly by the naked eye. Therefore, the relationship between the second pair must mirror the magnifying function of the first pair relative to the scale or distance of the objects viewed.

Explanation

The coding logic follows a specific rearrangement of the letters based on their positions in the 9-letter word. The word is divided into three segments: the first four letters (positions 1-4), the middle letter (position 5), and the last four letters (positions 6-9). The code is then formed by placing the last four letters first, followed by the middle letter, and then the first four letters.

Pattern: [1 2 3 4] [5] [6 7 8 9] → [6 7 8 9] [5] [1 2 3 4]

Applying this to SCATTERED: First four: SCAT (1-4) Middle: T (5) Last four: ERED (6-9) Result: ERED + T + SCAT = EREDTSCAT

Applying this to EXPLOSION: First four: EXPL (1-4) Middle: O (5) Last four: SION (6-9) Result: SION + O + EXPL = SIONOEXPL

Explanation

The numerical relationship follows the formula (n₁ × n₃) + 1 = n₂, where n₁ is the first number, n₂ is the second number, and n₃ is the third number. In the given sets, this is demonstrated as (4 × 6) + 1 = 25 and (8 × 3) + 1 = 25. Applying this logic to the set (7, 22, 3), the product of the first and third numbers plus one results in (7 × 3) + 1 = 21 + 1 = 22, which matches the middle number.

Explanation

Based on the given statements, we can use set theory to analyze the logical relationship. Statement I states that All A are D (A ⊆ D), meaning the entire set A is contained within set D. Statement II states that No D is E (D ∩ E = ∅), meaning there is no overlap between sets D and E. Since A is entirely contained within D and D has no intersection with E, it follows that A can have no intersection with E (A ∩ E = ∅). This validates Conclusion I, which states No E is A. The other conclusions do not follow because being a subset does not imply the sets are identical, and Statement II explicitly forbids any overlap between E and D.

Explanation

Substitute the signs -, +, ÷, +, = sequentially into the expression to check for balance:

65 - 45 + 25 ÷ 5 + 35 = 60

According to the BODMAS rule, division is performed first: 25 ÷ 5 = 5

The equation then simplifies to: 65 - 45 + 5 + 35 = 60

Now, perform addition and subtraction from left to right: 65 - 45 = 20 20 + 5 + 35 = 25 + 35 = 60

The calculation results in 60 = 60, which balances the equation.

Explanation

The expression W @ Q % T | Y @ M % K can be decoded step by step to determine the relationships. Q % T indicates that Q is the mother of T. T | Y shows that T is the father of Y. Since Y @ M means Y is the son of M, and T is already identified as Y's father, M must be the wife of T and the mother of Y. Finally, M % K states that M is the mother of K. Because T and M are husband and wife, and M is the mother of K, T is the father of K. Therefore, Q is the mother of K's father (T), which makes Q the father's mother of K.

Explanation

The letter-clusters are organized based on two specific alphabetical rules. First, the first and second letters are opposites, meaning the sum of their numerical positions in the English alphabet is 27 (P₁ + P₂ = 27). Second, the fourth letter is determined by subtracting 6 from the position of the third letter (P₃ - 6 = P₄). In the cluster IRMT, the positions are I (9), R (18), M (13), and T (20). While the first two letters satisfy the opposite-pair rule (9 + 18 = 27), the relationship between the third letter M and the fourth letter T is an addition of 7 (13 + 7 = 20). This deviation from the required subtraction of 6 distinguishes this cluster from the group logic.

Explanation

The coding logic involves finding the sum of the numerical positions of the letters in reverse alphabetical order (where A=26, B=25, ..., Z=1) and then multiplying that sum by 5.

For BYE: Reverse positions: B = 25, Y = 2, E = 22 Sum = 25 + 2 + 22 = 49 Code = 49 × 5 = 245

For OLA: Reverse positions: O = 12, L = 15, A = 26 Sum = 12 + 15 + 26 = 53 Code = 53 × 5 = 265

Applying the same logic to CAR: Reverse positions: C = 24, A = 26, R = 9 Sum = 24 + 26 + 9 = 59 Code = 59 × 5 = 295

Explanation

The first statement establishes that the set of employees is a subset of the set of tax-payers. The second statement indicates an intersection between the set of employees and the set of farmers. Since all employees are tax-payers, those individuals who are both employees and farmers must also be tax-payers. This logically results in the fact that some farmers are tax-payers. Using set theory, if E ⊆ T and E ∩ F ≠ ∅, it follows that T ∩ F ≠ ∅. This derivation proves that the second conclusion is valid, while the first conclusion, which suggests no overlap between farmers and tax-payers, is logically impossible under these conditions.