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

Explanation

The relationship between the letter-clusters is established using alphabetical positions where A=1 and Z=26. The pattern follows a specific rule for each position in the cluster. For the first and third letters, the rule is to use the opposite letter in the alphabet, which is calculated using the formula 27 - Position of the letter. For the middle letter, the rule is to add 4 to its alphabetical position.

Applying this to the first pair JLT and QPG: The first letter J at position 10 becomes 27 - 10 = 17, which is Q. The second letter L at position 12 becomes 12 + 4 = 16, which is P. The third letter T at position 20 becomes 27 - 20 = 7, which is G.

Applying the same logic to the third cluster SGB: The first letter S at position 19 becomes 27 - 19 = 8, which is H. The second letter G at position 7 becomes 7 + 4 = 11, which is K. The third letter B at position 2 becomes 27 - 2 = 25, which is Y.

The resulting cluster is HKY.

Explanation

Substituting the mathematical signs from the first option into the given expression, we get the equation:

55 × 126 ÷ 14 = 520 - 30 + 5

Applying the BODMAS rule, we first perform the division on the left-hand side (LHS): 126 ÷ 14 = 9

Now, perform the multiplication on the LHS: 55 × 9 = 495

Next, solve the right-hand side (RHS) of the equation by performing subtraction and addition: 520 - 30 + 5 = 490 + 5 = 495

Comparing both sides, we find that 495 = 495, which confirms the equation is balanced.

Explanation

From the given information, T is the brother of P's husband, and Q is the daughter of S and P. This implies S is P's husband and thus S and T are brothers. Since U is the mother of T, she is also the mother of S. Q is the daughter of S, making U the paternal grandmother of Q. The problem states that Q is the granddaughter of R. In a standard family structure where U is the grandmother, R is the grandfather and U's husband. Consequently, as the father of S and T, R is the father of T.

Explanation

The pattern in the series is determined by the addition of squares of consecutive odd numbers starting from 3. 70 - 61 = 9 = 3² 95 - 70 = 25 = 5² Based on this sequence, the next difference must be 7² = 49. To find the missing number, we add 49 to the third term: 95 + 49 = 144. We can verify the pattern with the remaining terms in the series. The next difference should be 9² = 81, and 144 + 81 = 225. The final difference is 346 - 225 = 121, which is 11². The consistent addition of 3², 5², 7², 9², and 11² confirms the missing value.

Explanation

The given statements establish a hierarchical relationship between the sets: Bean Bags ⊂ Chairs ⊂ Couches ⊂ Sofas. This transitive property means that every member of a smaller set is also a member of all the larger sets containing it.

Conclusion I follows because the statement All couches are sofas implies that the set of couches is entirely contained within the set of sofas. In formal logic, the universal affirmative statement All A are B allows for the valid conversion Some B are A. Since all couches are sofas, it is a logical necessity that some portion of the sofa category consists of couches.

Conclusion II follows by combining the first two statements. Since all bean bags are chairs and all chairs are couches, it is logically deduced that all bean bags are couches. Following the same principle of logical conversion, if all bean bags are couches, then it must be true that some couches are bean bags. This confirms that the intersection between the set of couches and bean bags is non-empty.

Explanation

The series follows a pattern where each subsequent number is obtained by subtracting the squares of consecutive even numbers in descending order. Calculating the differences between the terms:

352 - 288 = 64 = 8² 288 - 252 = 36 = 6² 252 - 236 = 16 = 4²

The sequence of numbers being squared is 8, 6, 4, which are consecutive even numbers. Following this pattern, the next even number to be squared is 2. Subtracting 2² from the last term gives the missing number:

236 - 2² = 236 - 4 = 232

Explanation

The code is generated by dividing the eight-letter word into two equal halves of four letters each, reversing each half, and then incrementing each letter by one in the alphabetical sequence (+1).

For the word DURABLES: Divide into two halves: DURA and BLES. Reverse the first half (DURA → ARUD) and add 1 to each letter: A + 1 = B R + 1 = S U + 1 = V D + 1 = E This results in BSVE. Reverse the second half (BLES → SELB) and add 1 to each letter: S + 1 = T E + 1 = F L + 1 = M B + 1 = C This results in TFMC. Combining both parts gives the code: BSVETFMC.

For the word FEASIBLE: Divide into two halves: FEAS and IBLE. Reverse the first half (FEAS → SAEF) and add 1 to each letter: S + 1 = T A + 1 = B E + 1 = F F + 1 = G This results in TBFG. Reverse the second half (IBLE → ELBI) and add 1 to each letter: E + 1 = F L + 1 = M B + 1 = C I + 1 = J This results in FMCJ. Combining both parts gives the code: TBFGFMCJ.

Explanation

Let the total marks in the examination be T. According to the given information, the marks obtained by Avanish and Kapil are 78% and 64% of T, respectively. The sum of their marks is expressed as:

78% of T + 64% of T = 923 142% of T = 923 ¹⁴²⁄₁₀₀ × T = 923

To find the marks obtained by Kapil, we need to calculate 64% of T:

Kapil's marks = ⁶⁴⁄₁₀₀ × T Kapil's marks = ⁶⁴⁄₁₀₀ × (923 × 100)/(142) Kapil's marks = (923 × 64)/(142)

Simplifying the fraction by dividing 142 and 64 by 2:

Kapil's marks = (923 × 32)/(71)

Dividing 923 by 71:

923 ÷ 71 = 13

Kapil's marks = 13 × 32 = 416

Explanation

Interchanging the plus and multiplication signs transforms the original equation 9 × 98 ÷ 14 + 3 - 19 = 11 into 9 + 98 ÷ 14 × 3 - 19 = 11. Following the BODMAS rule, we first perform the division 98 ÷ 14 = 7, which simplifies the expression to 9 + 7 × 3 - 19. Next, we carry out the multiplication 7 × 3 = 21, resulting in 9 + 21 - 19. Performing the addition 9 + 21 = 30 and the subsequent subtraction 30 - 19 = 11 yields a value that matches the right-hand side of the equation.

Explanation

In a circular arrangement where people sit with their backs towards the centre (facing outwards), left is counter-clockwise and right is clockwise. Let the six positions be numbered 1 to 6 in a counter-clockwise direction.

If Bhanu is at position 1: David is to the immediate left of Bhanu, placing him at position 2. Minto is to the immediate right of Bhanu, placing him at position 6. Nisan sits third to the right of Bhanu. Counting clockwise from position 1, the third position is 4 (1 to 6, 6 to 5, 5 to 4). Thus, Nisan is at position 4. The remaining positions are 3 and 5, to be occupied by John and Krita. The condition states John is not to the immediate left of David. David is at position 2, and his immediate left is position 3. Therefore, John must be at position 5. This leaves position 3 for Krita.

To find who is sitting second to the left of Bhanu, move two positions counter-clockwise from Bhanu: position 1 to 2 (David), and then position 2 to 3 (Krita). Krita is the person sitting second to the left of Bhanu.

Explanation

The code for each word is identified by comparing the phrases where they appear. Comparing take this vaccine (892) and vaccine protects us (263), the common word is vaccine and the common digit is 2, so vaccine = 2.

Comparing vaccine protects us (263) and take us safe (593), the common word is us and the common digit is 3, so us = 3. Comparing take this vaccine (892) and take us safe (593), the common word is take and the common digit is 9, so take = 9.

In the phrase take us safe (593), the codes for take and us are 9 and 3 respectively. The remaining digit 5 must correspond to the word safe. Therefore, safe vaccine is represented by the digits 5 and 2, which appears as 25.

Explanation

The coding logic follows a pattern where the code for a word is the square of the total number of letters it contains.

In the word SALT, there are 4 letters. Squaring this count gives 4² = 16.

In the word PICKLE, there are 6 letters. Squaring this count gives 6² = 36.

Following the same logic for the word PRESERVATIVE, we count the total number of letters: P-R-E-S-E-R-V-A-T-I-V-E. There are 12 letters in total. Squaring this count gives 12² = 144.

Explanation

The relationship between the first and second number is established by a constant difference. By calculating the difference between 321 and 68, we find: 321 - 68 = 253

To find the missing number, the same constant difference of 253 must be added to the third number: 525 + 253 = 778

Explanation

In the morning, the Sun rises in the East, which means all shadows are cast towards the West. The problem states that Ayaan shadow falls to the left of Chitrashi. Since every shadow in the morning must point West, it follows that West is to the left of Chitrashi. For the West direction to be on a person left side, that person must be facing North. Since Chitrashi and Ayaan are sitting facing each other, if Chitrashi is facing North, then Ayaan must be facing South.

Explanation

The letter-cluster WEKP is the different one because it fails to follow the pattern of having two pairs of opposite letters. In the English alphabet, opposite letters are defined by a positional sum of exactly 27. For the cluster WEKP, the alphabetical positions are W (23), E (5), K (11), and P (16). While the third and fourth letters K and P form an opposite pair (11 + 16 = 27), the first two letters W and E have a positional sum of 23 + 5 = 28. This deviation from the required sum of 27 for the first pair distinguishes this cluster as the outlier in the group.

Explanation

The first statement establishes that the set of all oranges is contained within the set of apples. The second statement specifies that an intersection exists between oranges and bananas. Since any orange is also an apple, the part of the orange set that overlaps with bananas must also overlap with apples, which confirms that some apples are bananas (conclusion II). The third statement clarifies that the entire set of bananas is contained within the set of fruits. Because oranges overlap with bananas, those oranges are necessarily part of the fruit set, which validates that some oranges are fruits (conclusion III). Consequently, since there are oranges that are both apples and fruits, it logically follows that an intersection exists between fruits and apples, confirming that some fruits are apples (conclusion I). All three conclusions are logically derived from the statements.

Explanation

The series follows a pattern where the difference between consecutive terms increases by a constant value of 0.7. By calculating the differences between the given terms:

13.5 - 12.8 = 0.7 14.9 - 13.5 = 1.4 17.0 - 14.9 = 2.1

The differences are multiples of 0.7, specifically 0.7 × 1, 0.7 × 2, and 0.7 × 3. Following this arithmetic progression of differences, the next difference must be 0.7 × 4 = 2.8. Adding this value to the last known term gives the next number in the series:

17.0 + 2.8 = 19.8

Explanation

The given expression F | G @ H # I @ J describes the family structure through sequential relationships. Starting with G @ H, G is the husband of H, establishing G as male and H as his wife. The next segment, H # I, indicates that I is the son of H. Since G is married to H, G is the father of I. Finally, I @ J signifies that I is the husband of J, making J the daughter-in-law of G. Because G is the father of J's husband I, the relationship of G to J is that of a father-in-law.

Explanation

The coding logic follows two steps: first, add the numerical position of each letter within the word to its alphabetical rank; second, reverse the sequence of the resulting letters.

For the word LABOUR: L (12) + 1 = 13 (M) A (1) + 2 = 3 (C) B (2) + 3 = 5 (E) O (15) + 4 = 19 (S) U (21) + 5 = 26 (Z) R (18) + 6 = 24 (X) Reversing the results (M, C, E, S, Z, X) gives the code: XZSECM.

Following the same logic for EARNED: E (5) + 1 = 6 (F) A (1) + 2 = 3 (C) R (18) + 3 = 21 (U) N (14) + 4 = 18 (R) E (5) + 5 = 10 (J) D (4) + 6 = 10 (J) Reversing the results (F, C, U, R, J, J) gives the code: JJRUCF.

Explanation

The pattern of the letter-clusters is determined by the sum of the numerical positions of the first two letters in the English alphabet. Let P₁ and P₂ be the positions of the first and second letters respectively. The rule for the group is P₁ + P₂ = 28. For the cluster CXA, substituting the values for C (3) and X (24) yields 3 + 24 = 27. Because 27 ≠ 28, CXA is the odd one out. Although it follows the secondary rule where the third letter is two positions behind the first (3 - 2 = 1 for A), the difference in the initial summation distinguishes it from the other clusters in the set.

Explanation

The numerical relationship established in the other groups follows a geometric progression where each subsequent term is three times the preceding term. For a group of numbers (x, y, z), the pattern is defined by the operations y = 3x and z = 3y. In the set (17- 51- 147), the first operation holds as 17 × 3 = 51, but the second operation fails because 51 × 3 = 153, which does not match the provided value of 147.

Explanation

The relationship in the given pair is that of an individual or plural entity and its specific collective noun. A group of cattle is collectively referred to as a herd. Similarly, a collective group of sailors working together on a ship, boat, or aircraft is known as a crew. This follows the exact semantic pattern where the second word represents the standard collective noun for the individuals mentioned in the first word.

Explanation

Statement I states that Some L are Z, which only guarantees a partial overlap between the sets L and Z. This information is insufficient to conclude that All Z are L, as a particular affirmative premise cannot support a universal affirmative conclusion. Statement II states that Some L are T. While both Z and T are linked to the middle term L, there is no statement defining the relationship between Z and T. In formal logic, two affirmative premises cannot yield a negative conclusion like No T is Z. Since there is no definite connection or exclusion established between Z and T, and the first conclusion exceeds the scope of the premise, neither conclusion follows.

Explanation

The coding language follows a simple reversal pattern where the letters of the word are written in reverse order from the last character to the first.

By observing the word MOTIVATION: M (1), O (2), T (3), I (4), V (5), A (6), T (7), I (8), O (9), N (10) Reversing the positions results in: N (10), O (9), I (8), T (7), A (6), V (5), I (4), T (3), O (2), M (1) This gives the code NOITAVITOM.

Applying this same reversal logic to the word FRIENDSHIP: F - 1 R - 2 I - 3 E - 4 N - 5 D - 6 S - 7 H - 8 I - 9 P - 10

Writing the letters in reverse order: 10 - P 9 - I 8 - H 7 - S 6 - D 5 - N 4 - E 3 - I 2 - R 1 - F

The resulting code is PIHSDNEIRF.

Explanation

To establish that P is the paternal grandmother of R, P must be the mother of R's father. In the given notation, P ÷ Q indicates that P is the mother of Q, and Q × R indicates that Q is the father of R. By combining these, the expression P ÷ Q × R depicts that P is the mother of Q, who in turn is the father of R. Therefore, P is the mother of R's father, which satisfies the definition of a paternal grandmother.

Explanation

To determine which equation is not correct, we substitute the numbers 3 and 5 for each other and interchange the plus (+) and minus (-) signs in the first equation.

Original equation: 5 - 3 + 8× 4÷ 2 = 10

Applying the interchanges (3 for 5 and + for -): 3 + 5 - 8× 4÷ 2

Following the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction), we first perform the division: 3 + 5 - 8× 2

Next, we perform the multiplication: 3 + 5 - 16

Then, we perform the addition: 8 - 16

Finally, we perform the subtraction: -8

The calculated value of the left-hand side is -8, whereas the right-hand side of the equation is given as 10. Because -8 ≠ 10, this equation is not correct after the specified interchanges.

Explanation

The logic applied to the number pairs is n : n³ - 3. In the first pair, using n = 4, the calculation is 4³ - 3 = 64 - 3 = 61. In the second pair, using n = 9, the calculation is 9³ - 3 = 729 - 3 = 726. Applying this same pattern to the fifth number, n = 6, we calculate 6³ - 3 = 216 - 3 = 213.

Explanation

The series follows a specific pattern based on the numerical positions of the letters in the English alphabet. For the first letter of each cluster, the positions are I (9), B (2), U (21), N (14), and G (7). The logic applied here is a constant subtraction of 7 from the previous letter's position. Starting from I (9), 9 - 7 = 2 (B); then 2 - 7 = -5, which in a circular alphabet (26 - 5) corresponds to 21 (U); then 21 - 7 = 14 (N); and 14 - 7 = 7 (G). Applying this to the next step, 7 - 7 = 0, which corresponds to the 26th letter, Z.

For the second letter of each cluster, the positions are R (18), Y (25), F (6), M (13), and T (20). The logic applied is a constant addition of 7 to the previous letter's position. Starting from R (18), 18 + 7 = 25 (Y); then 25 + 7 = 32, which in a circular alphabet (32 - 26) corresponds to 6 (F); then 6 + 7 = 13 (M); and 13 + 7 = 20 (T). Applying this to the next step, 20 + 7 = 27, which corresponds to the 1st letter, A. Additionally, each cluster consists of a pair of opposite letters where the sum of their positional values equals 27. Combining the first letter Z and the second letter A gives the cluster ZA.

Explanation

The analogy is based on the relationship between a state of matter and the physical process that results in that state from a liquid. Freezing is the phase transition process where a liquid changes into a solid. Similarly, evaporation is the process by which a liquid transitions into a gas.

Explanation

By interchanging the numbers 45 and 13 and the signs × and +, the original equation 13 - 65 ÷ 45 × 21 + 2 = 82 transforms into 45 - 65 ÷ 13 + 21 × 2 = 82. Following the BODMAS rule, the calculation proceeds as follows:

First, perform the division: 65 ÷ 13 = 5 The equation becomes: 45 - 5 + 21 × 2 = 82

Next, perform the multiplication: 21 × 2 = 42 The equation becomes: 45 - 5 + 42 = 82

Finally, perform addition and subtraction from left to right: 40 + 42 = 82 82 = 82

The substitution satisfies the equation.

Explanation

To find the incorrect equation after interchanging the signs + and ÷, we substitute these signs into the expression 7× 8÷ 4 + 2 - 6 = 49. After the interchange, the expression becomes 7× 8 + 4÷ 2 - 6. Following the BODMAS rule, we first perform the division operation: 4÷ 2 = 2. The equation now stands as 7× 8 + 2 - 6. Proceeding with multiplication, we calculate 7× 8 = 56, leading to 56 + 2 - 6. Finally, performing addition and subtraction results in 58 - 6 = 52. Since the result 52 does not match the value on the right-hand side of the equation, which is 49, this equation is incorrect.

Explanation

The logic followed by the numbers in each set (n₁, n₂, n₃) is given by the formula (n₂ - 2 × n₁)² = n₃.

In the first set (17, 59, 625), we take the second number 59 and subtract twice the first number 17, which gives 59 - 34 = 25. Squaring this result, 25², gives the third number 625.

In the second set (8, 44, 784), we take the second number 44 and subtract twice the first number 8, which gives 44 - 16 = 28. Squaring this result, 28², gives the third number 784.

Applying this logic to the set (12, 69, 2025), we find that subtracting twice the first number 12 from the second number 69 yields 69 - 24 = 45. Squaring this result, 45², produces 2025.

Explanation

The logic followed in the given sets is (a + c) × 7 = b, where a is the first number, b is the second number, and c is the third number. In the first set (5, 98, 9), the sum of the first and third numbers is 5 + 9 = 14. Multiplying this sum by 7 results in the second number: 14 × 7 = 98. In the second set (10, 168, 14), the sum of the first and third numbers is 10 + 14 = 24, and 24 × 7 = 168. Following this logic for the set (1, 28, 3), the sum of the first and third numbers is 1 + 3 = 4, and multiplying by 7 gives 4 × 7 = 28.

Explanation

To determine the dictionary order, we compare the given words letter by letter from left to right. All five words share the common initial sequence Aqua. Comparing the fifth letter of each word, we have r in Aquarial and Aquarium, t in Aquatic and Aquatint, and v in Aquavit. In alphabetical order, r comes before t, and t comes before v. Therefore, the words starting with Aquari- will occupy the first two positions. Between Aquarial and Aquarium, the seventh letter a in Aquarial precedes the u in Aquarium, placing Aquarial first and Aquarium second. Next, we compare the words starting with Aquat- to find the third position. Between Aquatic and Aquatint, the seventh letter c in Aquatic comes before the n in Aquatint. Consequently, Aquatic is the third word in the dictionary arrangement, followed by Aquatint in fourth and Aquavit in fifth.

Explanation

The series follows a specific pattern for each letter position. By converting letters to their numerical positions in the alphabet (A=1, B=2, ..., Z=26), we can identify the following transformations.

1st letter: The first letter in every term is constant as A.

2nd letter: B (2), X (24), T (20), P (16). Taking B as 28 (26 + 2), the sequence decreases by 4 in each step: 28, 24, 20, 16. The next value is 16 - 4 = 12, which corresponds to L.

3rd letter: C (3), U (21), M (13), E (5). Taking C as 29 (26 + 3), the sequence decreases by 8 in each step: 29, 21, 13, 5. The next value is 5 - 8 = -3. In cyclic alphabetical order, -3 corresponds to 26 - 3 = 23, which is W.

4th letter: D (4), R (18), F (6), T (20). This position follows an alternating pattern of +14 and -12. 4 + 14 = 18 (R), 18 - 12 = 6 (F), 6 + 14 = 20 (T). The next step is 20 - 12 = 8, which corresponds to H.

Combining these results, the missing term is ALWH.

Explanation

The letter-clusters are organized according to a dual pattern where the first and third letters are alphabetical opposites, meaning the sum of their numerical positions in the English alphabet is 27. Additionally, the third letter is positioned 3 places after the second letter. In the cluster HDX, the first letter H (8) and the third letter X (24) sum to 32 rather than 27. Furthermore, the third letter X (24) is 20 positions ahead of the second letter D (4), which deviates from the +3 increment seen in the other clusters.

Explanation

The logical validity of the conclusions can be determined using Venn diagrams or syllogism rules. Statement I, All S are B, implies that the set S is a subset of set B. Statement II, Some B are C, indicates an intersection between set B and set C.

Conclusion I, All S are C, does not follow because there is no direct relationship established between S and C. While S is inside B, C only overlaps with some part of B, which may or may not include the part containing S. Conclusion II, No C is B, is logically impossible as it directly contradicts Statement II, which confirms that some B are C. Conclusion III, All B are S, does not follow because a universal affirmative statement like All S are B cannot be converted into All B are S; it only guarantees that Some B are S. Since none of the conclusions I, II, or III are logically certain based on the given statements, neither conclusion follows.

Explanation

Conclusion I follows because all cups are utensils and no cup is a plate. Since the entire set of cups is contained within the set of utensils, those specific utensils that are cups cannot be plates. This establishes that some utensils are not plates.

Conclusion II follows because some bottles are cups and no cup is a plate. The specific portion of bottles that overlaps with cups cannot belong to the set of plates. Therefore, it is logically certain that some bottles are not plates.

Conclusion III does not follow because the statements only provide information about the bottles that are cups. While we know those specific bottles are not plates, there is no information to rule out the possibility that other bottles (those that are not cups) could be plates. A universal negative statement like no bottle is a plate requires a complete separation of the two sets, which cannot be derived from the given premises.

Explanation

The expression W @ Q % T | Y @ M % K can be decoded step by step to find the relationship between W and K. W @ Q indicates that W is the son of Q. Q % T indicates that Q is the mother of T. Since W is the son of Q and T is also the child of Q, W and T are siblings. Moving further, T | Y means T is the father of Y. Y @ M means Y is the son of M. Because T is the father of Y and M is the parent of Y, T and M are a married couple where T is the husband and M is the wife. M % K shows that M is the mother of K, which implies K is the child of T and M. Consequently, T is the father of K. Since W is the brother of T, W is the brother of K's father.

Explanation

The coding logic follows a specific positional rearrangement of the letters in the five-letter words. By assigning numerical positions 1-2-3-4-5 to the letters of the original word, the code transforms them into the sequence 4-5-2-1-3. In the word HABIT, where H=1, A=2, B=3, I=4, and T=5, the fourth and fifth letters (I, T) move to the first and second spots, the second letter (A) moves to the third spot, the first letter (H) moves to the fourth spot, and the third letter (B) moves to the fifth spot, resulting in ITAHB. This same pattern applies to BASED (1=B, 2=A, 3=S, 4=E, 5=D), yielding EDABS. For the word GAMES, where G=1, A=2, M=3, E=4, and S=5, applying the 4-5-2-1-3 sequence places E in the first position, S in the second, A in the third, G in the fourth, and M in the fifth, producing the code ESAGM.

Explanation

The group (12- 14- 18) is the odd one because the difference between its consecutive terms is not constant. In this set, the first difference is 14 - 12 = 2, and the second difference is 18 - 14 = 4. This inconsistent spacing distinguishes it from the uniform arithmetic progression pattern where each subsequent number is obtained by adding a constant value of 4 to the previous one.

Explanation

The series follows an arithmetic progression where each term is obtained by adding a common difference d to the previous term. Using the first two terms, the common difference is d = 15 - 25 = -10. Applying this to find the third term, we calculate 15 + (-10) = 5. This result is verified by the subsequent terms in the sequence, as 5 - 10 = -5 and -5 - 10 = -15.

Explanation

The logic followed in the given set is that the sum of the first two numbers equals the third number: 168 + 122 = 290. In the set (236, 118, 356), the sum of the first two numbers is 236 + 118 = 354. Since the third number in this set is 356, it does not satisfy the addition rule a + b = c observed in the base set and the other alternatives.

Explanation

By interchanging the numbers 5 and 20 and the mathematical signs - and × in the given expression 72÷ 6 - 20 + 30× 5 = 70, the equation is rewritten as 72÷ 6 × 5 + 30 - 20 = 70. Applying the BODMAS rule, we first solve the division 72÷ 6, which equals 12. Substituting this value back into the expression results in 12 × 5 + 30 - 20. Next, performing the multiplication 12 × 5 gives 60, transforming the expression into 60 + 30 - 20. Summing 60 and 30 gives 90, and subtracting 20 from 90 results in 70. This confirms that the modified left-hand side is equal to the right-hand side.

Explanation

Substituting the signs from option d into the expression [((14 @ 6) @ (2 @ 3)) @ (1 @ 7)] @ 2 @ 4 results in the equation [((14 - 6) + (2 × 3)) ÷ (1 × 7)] × 2 = 4. According to the BODMAS rule, the operations within the innermost parentheses are performed first. This gives 14 - 6 = 8, 2 × 3 = 6, and 1 × 7 = 7. The equation then simplifies to [(8 + 6) ÷ 7] × 2 = 4. Next, the addition within the brackets is calculated as 8 + 6 = 14, reducing the expression to [14 ÷ 7] × 2 = 4. Performing the division inside the square brackets results in 2, leading to the final multiplication 2 × 2 = 4. Since the left-hand side matches the right-hand side, the equation is perfectly balanced.

Explanation

To determine the word in the fifth position, the words are arranged alphabetically by comparing each letter from left to right. All five words share the initial prefix Overl. Examining the sixth letter of each word, two words contain the letter a and two words contain the letter o, while Overplay contains the letter p. In the English alphabet, a and o both precede p. Consequently, the words beginning with the sequences Overla and Overlo must occupy the first four positions in the dictionary order. As p is the alphabetically latest sixth letter among this group, Overplay follows all other words, placing it in the fifth position.

Explanation

The pattern in the given sets is (First Number + 1) * Third Number = Second Number. For the first set (8, 540, 60), (8 + 1) * 60 = 9 * 60 = 540. For the second set (9, 70, 7), (9 + 1) * 7 = 10 * 7 = 70. Applying this logic to option B (8, 63, 7), (8 + 1) * 7 = 9 * 7 = 63, which correctly follows the pattern.

Explanation

To establish that P is the paternal uncle of R, P must be the brother of R's father. In the expression P÷ Q× R, the symbol ÷ indicates that P is the brother of Q. The symbol × indicates that Q is the father of R. By combining these relations, P is the brother of R's father Q, which makes P the paternal uncle of R.

Explanation

The series follows a systematic decrement pattern for each corresponding letter in the clusters according to their numerical positions in the alphabet, where A = 1, B = 2, and so on.

For the first position, the letters decrease by 1: V (22) → U (21) → T (20) → S (19) → R (18). For the second position, the letters decrease by 2: S (19) → Q (17) → O (15) → M (13) → K (11). For the third position, the letters decrease by 2: N (14) → L (12) → J (10) → H (8) → F (6). For the fourth position, the letters decrease by 4: Y (25) → U (21) → Q (17) → M (13) → I (9).

Applying these logical steps to transition from the second cluster (UQLU) to the missing cluster, we subtract 1 from U to get T, subtract 2 from Q to get O, subtract 2 from L to get J, and subtract 4 from U to get Q. This sequence of operations results in the cluster TOJQ.

Explanation

The logic followed in the given pairs is that the second term is the square of the sum of the first term and 6. This can be expressed by the formula y = (x + 6)², where x is the first term and y is the second term.

For the first pair 14 : 400: x = 14 y = (14 + 6)² = 20² = 400

For the third pair 42 : 2304: x = 42 y = (42 + 6)² = 48² = 2304

Applying the same logic to the second pair with x = 37: y = (37 + 6)² = 43² 43² = 1849