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

Explanation

Statement I is a universal negative proposition of the form No A is D, which implies that the sets A and D have no elements in common. In syllogistic logic, E-type propositions are perfectly reversible, meaning that if no A is D, it is logically certain that no D is A. Therefore, Conclusion I follows directly from Statement I. Statement II is a universal affirmative proposition of the form All D are E, which indicates that the set D is a subset of set E. This relationship implies a partial overlap from the perspective of the predicate; if every member of D is a member of E, then there exists at least some member of E that is a member of D. Consequently, Conclusion II follows as a valid immediate inference from Statement II.

Explanation

By substituting the mathematical signs from the sequence -, +, ÷, = into the given expression 25 2 220 11 43, we obtain the equation 25 - 2 + 220 ÷ 11 = 43.

Following the BODMAS rule, we first perform the division operation: 220 ÷ 11 = 20

Substituting this back into the equation gives: 25 - 2 + 20 = 43

Next, we perform addition and subtraction from left to right: 23 + 20 = 43 43 = 43

The left-hand side equals the right-hand side, confirming that the combination of signs in option d correctly balances the equation.

Explanation

The logic followed in the given number pairs is based on the formula y = (2 × x) - 1, where x is the first number and y is the second number of the pair.

For the first pair: 7 × 2 - 1 = 14 - 1 = 13

For the second pair: 16 × 2 - 1 = 32 - 1 = 31

Applying the same logic to the fifth number to find the required value: 46 × 2 - 1 = 92 - 1 = 91

Explanation

By substituting the signs from option d into the equation sequentially, we evaluate the expression [((44 - 38) + (2 × 5)) ÷ (4 × 2)] × 5 = 10 using the BODMAS rule.

First, calculate the values within the innermost parentheses: 44 - 38 = 6 2 × 5 = 10 4 × 2 = 8

Substitute these values into the next level of the expression: [(6 + 10) ÷ 8] × 5 = 10

Solve the addition within the brackets: 6 + 10 = 16

Now perform the division: 16 ÷ 8 = 2

Finally, perform the multiplication: 2 × 5 = 10

The calculation results in 10 = 10, which balances the equation.

Explanation

In the expression P + Q ÷ R, the operation P + Q indicates that P is the father of Q. The subsequent operation Q ÷ R indicates that Q is the sister of R. Since Q and R are siblings and P is the father of Q, it follows directly that P must also be the father of R. This satisfies the requirement that P is the father of R.

Explanation

To determine the relationship between P and T, we decode the expression P - Q - R S T based on the given definitions. R S indicates that R is the sister of S. Q - R establishes that Q is the mother of R, which by extension means Q is also the mother of S. S T defines S as the son of T. Since Q is the mother of S and T is the other parent of S, Q and T must be a married couple, with T being the husband of Q. P - Q states that P is the mother of Q. Therefore, because P is the mother of Q and T is the husband of Q, P is the mother-in-law of T.

Explanation

The relationship in the given pair is based on a specific field of scientific study and the professional associated with it. Botany is the branch of biology that deals with the study of plants, and a person who specializes in this field is known as a Botanist. Following the same logic, Zoology is the branch of biology dedicated to the study of the animal kingdom, including their structure, classification, and behavior. Therefore, a scientist who specializes in the study of animals is called a Zoologist.

Explanation

The relationship between the numbers in the given sets follows the formula n₃ = (n₁ × n₂) × 2, where n₁, n₂, and n₃ are the first, second, and third numbers respectively.

For the set (7, 4, 56): (7 × 4) × 2 = 28 × 2 = 56

For the set (8, 3, 48): (8 × 3) × 2 = 24 × 2 = 48

Applying this same logic to the set (9, 10, 180): (9 × 10) × 2 = 90 × 2 = 180

Explanation

To determine the dictionary order, we compare the words letter by letter. All five words begin with the same four letters Choc. The fifth letters are k in Chock and o in the other four words. Since k comes before o in the alphabet, Chock is the first word in the sequence. Among the remaining words Chocoholic, Chocolate, Chocolatier, and Chocolaty, we look at the sixth letter. Chocoholic has h, while the others have l. Since h precedes l, Chocoholic is the second word. For the final three words starting with Chocolat, we compare the ninth letters which are e in Chocolate, i in Chocolatier, and y in Chocolaty. Alphabetically, e comes before i and y, placing Chocolate in the third position. Followed by this, i comes before y, making Chocolatier the fourth and Chocolaty the fifth word. The resulting sequence is Chock, Chocoholic, Chocolate, Chocolatier, and Chocolaty.

Explanation

The series follows a pattern where each subsequent term is obtained by dividing the preceding term by 3. Applying this logic to the given numbers:

5103 ÷ 3 = 1701 1701 ÷ 3 = 567

To find the missing number, we divide the third term by 3:

567 ÷ 3 = 189

We can verify the pattern by continuing the division with the calculated value:

189 ÷ 3 = 63 63 ÷ 3 = 21

The results align perfectly with the remaining terms of the series, confirming that the missing number is 189.

Explanation

The numbers in the given groups follow the mathematical pattern y = x² - 5, where x is the first number and y is the second number. Applying this to the groups, we see 15² - 5 = 225 - 5 = 220, 16² - 5 = 256 - 5 = 251, and 17² - 5 = 289 - 5 = 284. In the first group, the calculation 14² - 5 = 196 - 5 results in 191. Since the provided number is 193 instead of 191, it does not follow the established logic of the other groups.

Explanation

The relationship between the words is based on an institution and its primary beneficiaries. A school is a functional establishment where students go to receive education and learning services. Similarly, a hospital is a functional establishment where patients go to receive medical treatment and healthcare services. In this analogy, the second term represents the individuals who seek the core service provided by the institution mentioned in the first term.

Explanation

The first statement All R are P establishes that R is a subset of P (R ⊆ P). The second statement All R are Q establishes that R is also a subset of Q (R ⊆ Q). Because R is contained within both P and Q, the intersection of P and Q must contain R (R ⊆ P ∩ Q). This proves that P and Q share common elements, making the conclusion No P is Q logically false. Additionally, since the first statement explicitly defines that every R is a P, the conclusion No R is P is a direct contradiction of the premise and cannot follow. Thus, neither conclusion is supported by the statements.

Explanation

The equation is solved by interchanging the signs + and - and the numbers 7 and 6 in the expression 4 × 7 + 6 - 3 ÷ 1 = 20.

Upon interchanging the values, the left-hand side (LHS) of the equation becomes: 4 × 6 - 7 + 3 ÷ 1

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

Division: 3 ÷ 1 = 3 The expression simplifies to: 4 × 6 - 7 + 3

Multiplication: 4 × 6 = 24 The expression simplifies to: 24 - 7 + 3

Addition and Subtraction: 24 + 3 - 7 27 - 7 = 20

The calculated value of the LHS is 20, which is equal to the value on the right-hand side (RHS).

Explanation

The series follows a logic of positional shifts and modifications between consecutive terms. By analyzing the first and last letters of each term, we can identify the following patterns:

First Letter: The first letters follow a consistent shift of +5 in the initial terms: A(1) +5 F(6) +5 K(11) +5 P(16). The next first letter in the sequence transitions to D(4) in the options.

Last Letter: The last letters of the terms follow a consistent shift of -8: D(4) -8 V(22) -8 N(14) -8 F(6). This pattern confirms the movement through the alphabet in reverse steps.

Internal Shifts: The transformation from T₃ (KPQN) to T₄ (PJXF) follows a specific alternating shift: K(11) + 5 = P(16) P(16) - 6 = J(10) Q(17) + 7 = X(24) N(14) - 8 = F(6)

Applying a similar logic to the next term, the shifts lead to the letters D, K, N, E, F, C in the final term of the series. Among the given options, only DKNEFC satisfies the structural development of the sequence.

Explanation

The coding logic follows a specific sequence of operations for each character position in the six-letter words. For the letters at positions 1 and 5, a shift of +3 is applied. For the letters at positions 2 and 6, a shift of +4 is applied. The letters at positions 3 and 4 are interchanged.

Applying this logic to the word AGENCY: The first letter A (1) shifts by +3 to become D (4). The second letter G (7) shifts by +4 to become K (11). The third letter E and the fourth letter N are interchanged, resulting in N and E. The fifth letter C (3) shifts by +3 to become F (6). The sixth letter Y (25) shifts by +4 to become C (25 + 4 = 29; 29 - 26 = 3).

Combining these results, the word AGENCY is written as DKNEFC.

Explanation

The logic followed in the given sets is that the square of the difference between the first and third numbers equals the second number. This relationship can be expressed by the formula (First number - Third number)² = Second number.

In the first set (9, 16, 5), the operation is (9 - 5)² = 4² = 16. In the second set (7, 9, 4), the operation is (7 - 4)² = 3² = 9.

Applying this same logic to the set (11, 36, 5), the difference between the first number 11 and the third number 5 is 6. Squaring this difference gives 6² = 36, which is the second number in the set.

Explanation

The first statement establishes that some bottles are towels, and the third statement asserts that all bottles are coats. Since every bottle is a coat, those bottles that are towels must necessarily be coats as well. This creates a definite intersection between the sets of coats and towels, making the conclusion "Some coats are towels" logically certain.

Conclusion II is contradictory to the established intersection, and Conclusion III cannot be determined because the statements only specify that the bottles which are towels are not pillows, without providing any information regarding whether other bottles are pillows. Therefore, only conclusion I follows.

Explanation

The pattern in the clusters follows a rule where the first and third letters are reverse alphabetical opposites, and the second and fourth letters are also reverse alphabetical opposites. Two letters are opposites if the sum of their positional values in the English alphabet is 27.

In PRKI, P(16) + K(11) = 27 and R(18) + I(9) = 27. In UWFD, U(21) + F(6) = 27 and W(23) + D(4) = 27. In XZCA, X(24) + C(3) = 27 and Z(26) + A(1) = 27.

In the cluster JFOQ, the sum of the positions for the first and third letters is J(10) + O(15) = 25, and the sum for the second and fourth letters is F(6) + Q(17) = 23. Since these sums are not 27, this cluster does not follow the established pattern of the other three groups.

Explanation

The series follows a specific arithmetic pattern for each corresponding letter in the triplets. By assigning numerical values to the letters where A=1, B=2, …, Z=26, we can determine the logic for each position.

For the first letter of each triplet, the sequence is N(14), J(10), F(6), and B(2). The pattern is a constant subtraction of 4 from the previous term. Subtracting 4 from B(2) gives 2 - 4 = -2. In the 26 letter alphabetical cycle, -2 corresponds to 24 (26 - 2 = 24), which is the letter X.

For the second letter of each triplet, the sequence is T(20), Z(26), F(6), and L(12). Here, the pattern is a constant addition of 6. Adding 6 to Z(26) results in 32, and 32 - 26 = 6 (F). Adding 6 to L(12) results in 18, which is the letter R.

For the third letter of each triplet, the sequence is S(19), F(6), S(19), and F(6). This is an alternating pattern that can be viewed as a constant addition of 13 in the alphabetical cycle. Since 19 + 13 = 32 ≡ 6 26 and 6 + 13 = 19, the next term in the sequence after F(6) is 19, which is the letter S.

Combining these results, the first letter is X, the second letter is R, and the third letter is S.

Explanation

The dictionary order of the words is: 1. Nation, 2. National, 3. Nationalism, 4. Nationality, and 5. Native. Comparing Nationalism and Nationality, both share the prefix Nationali-; since 's' comes before 't' in the alphabet, Nationalism appears first, making it the word at the third position.

Explanation

The transformation logic involves two distinct steps applied to the letter-cluster. First, the positions of the first and second letters are swapped. Second, all the remaining letters from the third position to the end of the word are written in reverse order.

Applying this to COMPLEX: the first two letters C-O are swapped to become O-C, and the remaining letters M-P-L-E-X are reversed to become X-E-L-P-M, resulting in OCXELPM.

Applying this to BALANCE: the first two letters B-A are swapped to become A-B, and the remaining letters L-A-N-C-E are reversed to become E-C-N-A-L, resulting in ABECNAL.

Following the same logic for AIRLINE: the first two letters A-I are swapped to become I-A. The remaining letters R-L-I-N-E are reversed to become E-N-I-L-R. Combining these two parts gives the final letter-cluster IAENILR.

Explanation

Conclusion I follows from the combination of Statement 2 and Statement 3. Since Some cars are trucks and All trucks are cycles, the specific group of cars that are trucks must also be cycles, which confirms that Some cars are cycles. Conclusion II follows directly from Statement 3 through the rule of conversion; if All trucks are cycles, it is logically necessary that Some cycles are trucks. Conclusion III does not follow because there is no statement that creates a definite intersection between bikes and trucks. While all bikes are cars, the cars that are trucks might not include any bikes, making the relationship between bikes and trucks uncertain rather than logically necessary.

Explanation

The series follows a consistent pattern for each position within the four-letter clusters. For the first position, the letters move forward by one step: A +1 B +1 C +1 D +1 E. For the second position, the letters move backward by one step: Z -1 Y -1 X -1 W -1 V. For the third position, the letters move forward by one step: B +1 C +1 D +1 E +1 F. For the fourth position, the letters move backward by one step: Y -1 X -1 W -1 V -1 U. Applying these transformations to the third cluster CXDW yields the missing cluster DWEV. Each cluster is also composed of two pairs of positional opposites in the alphabet, where the first two letters and the last two letters respectively sum to 27 in their numerical positions.

Explanation

The numbers in the given sets follow the logic 2 × First Number + Second Number = Third Number.

In the first set (17, 24, 58): 2 × 17 + 24 = 34 + 24 = 58

In the second set (26, 37, 89): 2 × 26 + 37 = 52 + 37 = 89

In option a (15, 17, 47), the same pattern is applied: 2 × 15 + 17 = 30 + 17 = 47

The third number is successfully derived by doubling the first number and adding the second number.

Explanation

The series is formed by the cubes of consecutive prime numbers starting from 11. The first term is 11³ = 1331 and the second term is 13³ = 2197. Following the sequence of prime numbers, the prime number after 13 is 17. Therefore, the missing value is 17³ = 4913. This logic is consistent with the final term in the series, 19³ = 6859, as 19 is the prime number that follows 17.

Explanation

The relationship between the numbers in the given sets follows the logic that the second number is equal to half of the product of the first and third numbers. This mathematical pattern can be represented by the formula: (First number × Third number) ÷ 2 = Second number

In the first provided set (13, 39, 6), the calculation is: (13 × 6) ÷ 2 = 78 ÷ 2 = 39

In the second provided set (9, 18, 4), the calculation follows the same rule: (9 × 4) ÷ 2 = 36 ÷ 2 = 18

In the set (12, 48, 8) found in option a, the identical relationship is applied: (12 × 8) ÷ 2 = 96 ÷ 2 = 48

The operation uses whole numbers as required, demonstrating that multiplying the first and third terms and then dividing the result by two consistently yields the middle term across these sets.

Explanation

Interchanging the numbers 7 and 14 in the original expression 7 × 4 ÷ 14 + 12 + 30 results in the modified equation 14 × 4 ÷ 7 + 12 + 30 = 50. Following the BODMAS rule, the multiplication and division are addressed first. The term 14 × 4 ÷ 7 can be calculated as (14 × 4) / 7, which is 56 / 7 = 8. Substituting this value back into the equation yields 8 + 12 + 30. Summing these values gives 20 + 30 = 50. Since the left-hand side now equals the right-hand side, the equation is balanced.

Explanation

Based on Statement I, we know there is an intersection between the set of tables and chairs, meaning at least some tables are chairs and some chairs are tables. This does not allow us to conclude that all chairs are tables, so Conclusion I is invalid. Statement II explicitly states that no chair is a stool, which means the set of chairs and the set of stools are disjoint. This directly contradicts Conclusion II, which claims some chairs are stools. Furthermore, because Statement I establishes that some tables are chairs and Statement II establishes that no chair is a stool, it follows that the specific tables which are chairs cannot be stools. This makes Conclusion III, which asserts all tables are stools, logically impossible. Since none of the conclusions are supported by the statements, neither conclusion follows.

Explanation

The coding logic involves adding a sequence of increasing integers starting from +2 to the numerical positional values of the letters, proceeding from the last letter of the word to the first. For a five-letter word, the additions are +2, +3, +4, +5, and +6 applied to the 5th, 4th, 3rd, 2nd, and 1st letters respectively.

Applying this pattern to the word HANDS: The 5th letter S (19) + 2 = 21 (U) The 4th letter D (4) + 3 = 7 (G) The 3rd letter N (14) + 4 = 18 (R) The 2nd letter A (1) + 5 = 6 (F) The 1st letter H (8) + 6 = 14 (N)

Arranging these results in order gives the code UGRFN. This same logic is consistent with the example GHOST: T(20)+2=V, S(19)+3=V, O(15)+4=S, H(8)+5=M, and G(7)+6=M, which produces VVSMM. Similarly, for EATER: R(18)+2=T, E(5)+3=H, T(20)+4=X, A(1)+5=F, and E(5)+6=K, producing THXFK.

Explanation

The expression P ÷ Q × R satisfies the condition using the defined relationships. In the first part, P ÷ Q signifies that P is the sister of Q, which establishes that P is female and a sibling of Q. In the second part, Q × R signifies that Q is the brother of R, establishing that Q and R are also siblings. Since P is a sibling of Q and Q is a sibling of R, it follows that P, Q, and R all belong to the same generation and share the same parentage. Because P is female, she is the sister of R.

Explanation

The logic followed by the other pairs is that the second number is obtained by multiplying the first number by 2 and then subtracting 2. This can be expressed as Second Number = (First Number × 2) - 2. For instance, 16 × 2 - 2 = 30, 14 × 2 - 2 = 26, and 18 × 2 - 2 = 34. In the case of the pair 44-84, the calculation 44 × 2 - 2 results in 86, whereas the given number is 84. Thus, this pair does not conform to the established rule.

Explanation

The relationship between the numbers in the given sets follows the logic that the third number is four times the difference between the first and the second numbers. This can be represented by the formula (a - b) × 4 = c.

In the set (45, 15, 120): (45 - 15) × 4 = 30 × 4 = 120

In the set (27, 8, 76): (27 - 8) × 4 = 19 × 4 = 76

Applying this same logic to the numbers in option d, which are (56, 48, 32): (56 - 48) × 4 = 8 × 4 = 32

Explanation

To find the values of equations (I) and (II), we interchange the numbers 6 and 9 and the signs + and - as specified.

For equation (I): 6 - 5 × 9 + 8 ÷ 2 Replacing 6 with 9, 9 with 6, - with +, and + with -, we get: 9 + 5 × 6 - 8 ÷ 2 Applying the BODMAS rule: Division: 8 ÷ 2 = 4 Multiplication: 5 × 6 = 30 Equation: 9 + 30 - 4 Addition and Subtraction: 39 - 4 = 35

For equation (II): 6 - 4 + 9 × 5 ÷ 3 Replacing 6 with 9, 9 with 6, - with +, and + with -, we get: 9 + 4 - 6 × 5 ÷ 3 Applying the BODMAS rule: Division and Multiplication: 6 × 5 ÷ 3 = 6 × ⁵⁄₃ = 10 Equation: 9 + 4 - 10 Addition and Subtraction: 13 - 10 = 3

Explanation

The relationship established in the given pair is Animal : Dwelling Place, where a kennel is the specific shelter or house intended for a dog. Similarly, a hive is the natural or man-made structure where bees live and store honey. Both pairs represent a creature and its characteristic habitation.

Explanation

In the expression X @ Y J M, the individual relations are decoded as follows: X @ Y indicates that X is the daughter of Y. The symbol Y J specifies that Y is the husband of J, which means Y and J are a married couple. From these two relations, it follows that X is the daughter of both Y and J. Finally, J M means J is the mother of M. Since X and M are both children of the same mother J and father Y, they are siblings. Because X is established as a daughter, her gender is female, making her the sister of M.

Explanation

The coding logic involves assigning each letter its corresponding numerical position in the English alphabet, where A = 1, B = 2, ..., Z = 26. The final code is then formed by writing these numerical values in reverse order, starting from the last letter of the word to the first.

In the word CRUST, the alphabetical positions are C = 3, R = 18, U = 21, S = 19, and T = 20. Reversing this sequence gives 20, 19, 21, 18, 3, which results in the code 201921183. Similarly, for BLAME, the positions are B = 2, L = 12, A = 1, M = 13, and E = 5. Reversing these positions yields 5, 13, 1, 12, 2, resulting in the code 5131122.

Applying this pattern to the word PLASTIC: P = 16 L = 12 A = 1 S = 19 T = 20 I = 9 C = 3

Arranging these positions in reverse order (from the last letter to the first) gives the sequence 3, 9, 20, 19, 1, 12, 16. Concatenating these numbers together produces the code 39201911216.

Explanation

The letter cluster JIG consists of the 10th, 9th, and 7th letters of the alphabet. In this cluster, the position value decreases by 1 between the first two letters (10 - 9 = 1) and by 2 between the next two (9 - 7 = 2). This sequence deviates from the consistent pattern of subtracting 2 from each letter position to reach the next (n, n-2, n-4) that is shared by the other clusters in the group.

Explanation

The numbers in the given sets follow the mathematical pattern (n, n², n³). In the first set (9, 81, 729), the relationship is established as 9¹ = 9, 9² = 81, and 9³ = 729. In the second set (14, 196, 2744), the same logic applies where 14¹ = 14, 14² = 196, and 14³ = 2744.

Following this logic, the set (17, 289, 4913) is the only one that satisfies the pattern because the second number is the square of the first (17² = 289) and the third number is the cube of the first (17³ = 4913).

Explanation

In the expression P - Q + R, the part P - Q indicates that P is the mother of Q, which establishes that P is the parent of Q. The part Q + R indicates that Q is the father of R. Since Q is a father, Q is necessarily male. A male child of a parent P is defined as the son of P. Therefore, this expression confirms that Q is the son of P.

Explanation

In the given expression W @ Q # T | Y @ M % K, the relationships are established as follows: W @ Q indicates W is the son of Q. Q # T indicates Q is the sister of T. T | Y indicates T is the father of Y. Y @ M indicates Y is the son of M. Since T is the father of Y, it follows that T and M are a married couple where T is the husband and M is the wife. M % K indicates M is the mother of K. Because T and M are the parents of both Y and K, T is the father of K. Given that Q is the sister of T, Q is the sister of K's father.

Explanation

By interchanging the numbers 56 and 9 and the signs + and ×, the equation 98 - 9 × 21 ÷ 7 + 56 = 69 is rewritten as 98 - 56 + 21 ÷ 7 × 9 = 69. Applying the BODMAS rule, we first solve the division part: 21 ÷ 7 = 3. This changes the expression to 98 - 56 + 3 × 9. Next, we perform the multiplication: 3 × 9 = 27. The expression now stands as 98 - 56 + 27. Finally, we execute the addition and subtraction: 98 - 56 = 42, and 42 + 27 = 69. Because the calculated value matches the right-hand side of the equation, the interchange is correct.

Explanation

By interchanging the signs + and - in the equation 15 - 7× 8 + 18 ÷ 3 = 65, the expression becomes 15 + 7× 8 - 18 ÷ 3 = 65. Following the BODMAS rule, we first perform the division 18 ÷ 3 = 6, then the multiplication 7× 8 = 56. Substituting these values back into the expression gives 15 + 56 - 6. Performing the addition results in 71 - 6, which simplifies to 65. Since the left-hand side matches the right-hand side, the equation is correct after the interchange.

Explanation

To determine the dictionary order, we compare the words letter by letter from left to right. All five words share the first three letters R-E-M. We then compare the fourth letters of each word:

Remain, Remark, and Remanent have the letter 'a' in the fourth position. Remember has the letter 'e' in the fourth position. Remnant has the letter 'n' in the fourth position.

In alphabetical order, 'a' comes before 'e', and 'e' comes before 'n'. Therefore, the three words starting with R-E-M-A will occupy the first three positions. To arrange them, we compare their fifth letters: 'i' in Remain, 'n' in Remanent, and 'r' in Remark. Since 'i' precedes 'n' and 'n' precedes 'r', the sequence is: 1st: Remain 2nd: Remanent 3rd: Remark

The next letter in the alphabetical sequence for the fourth position is 'e', which belongs to the word Remember. Consequently, Remember occupies the fourth position. The word Remnant, with 'n' as its fourth letter, comes fifth.

Following this dictionary arrangement, the word at the fourth position is Remember. The option HOVM represents the word Remember (specifically its first four letters R-E-M-E) through a transformation where each letter is shifted numerically in the alphabet: R(18) shifts 10 places back to H(8), E(5) shifts 10 places forward to O(15), M(13) shifts 9 places forward to V(22), and the second E(5) shifts 8 places forward to M(13).

Explanation

The series follows a specific arithmetic pattern for each letter position within the clusters. By converting the letters to their corresponding numerical positions in the alphabet (A=1, B=2, …, Z=26), the transformations can be identified.

For the first letter, there is a constant addition of 5: N(14) +5 S(19) +5 X(24) +5 C(3) +5 H(8).

For the second letter, there is a constant subtraction of 6: M(13) -6 G(7) -6 A(1) -6 U(21) -6 O(15).

For the third letter, there is a constant addition of 7: T(20) +7 A(1) +7 H(8) +7 O(15) +7 V(22).

For the fourth letter, there is a constant subtraction of 8: S(19) -8 K(11) -8 C(3) -8 U(21) -8 M(13).

Applying these specific increments and decrements to the last given term CUOU results in the sequence H, O, V, M.

Explanation

In the expression P - Q + R, the relationship symbols are defined such that - indicates the mother and + indicates the brother. Analyzing the sequence, P - Q establishes that P is the mother of Q. The subsequent part of the expression, Q + R, establishes that Q is the brother of R. Because Q and R are siblings and P is the mother of Q, it logically follows that P is also the mother of R.

Explanation

In the equation 6 ÷ 2 × 8 + 3 - 1 = 17, we interchange the numbers 3 and 8 to get the new expression 6 ÷ 2 × 3 + 8 - 1. Following the BODMAS rule, we first perform division 6 ÷ 2 = 3. Next, we perform multiplication 3 × 3 = 9. Then we proceed with addition 9 + 8 = 17, and finally subtraction 17 - 1 = 16. The resulting value of 16 does not equal the given value of 17 on the right hand side, making this equation incorrect after the interchange.

Explanation

The signs from option a are substituted sequentially into the mathematical structure ((32 % 28) % (6 % 4)) % (1 % 7) % 5 = 20. By applying the signs -, +, ×, ÷, ×, ×, =, the equation becomes ((32 - 28) + (6 × 4)) ÷ (1 × 7) × 5 = 20. Following the BODMAS rule, the innermost parentheses are solved first: 32 - 28 = 4, 6 × 4 = 24, and 1 × 7 = 7. The equation then simplifies to (4 + 24) ÷ 7 × 5 = 20. Solving the next parenthesis gives 28 ÷ 7 × 5 = 20. Performing the division yields 4 × 5 = 20, and finally, the multiplication results in 20 = 20. Since the left-hand side balances with the right-hand side, this combination of signs is correct.

Explanation

The coding logic follows a specific pattern of shifting the alphabetical positions of the letters. The first, second, fourth, and fifth letters of each word are shifted backward by 2 positions, represented as n - 2. The third (middle) letter is shifted forward by 2 positions, represented as n + 2.

Applying this to the word ABOUT: A (1) - 2 = 25 (Y) B (2) - 2 = 26 (Z) O (15) + 2 = 17 (Q) U (21) - 2 = 19 (S) T (20) - 2 = 18 (R)

Similarly, for the word PARTS: P (16) - 2 = 14 (N) A (1) - 2 = 25 (Y) R (18) + 2 = 20 (T) T (20) - 2 = 18 (R) S (19) - 2 = 17 (Q)

Following the same pattern for the word PLANT: P (16) - 2 = 14 (N) L (12) - 2 = 10 (J) A (1) + 2 = 3 (C) N (14) - 2 = 12 (L) T (20) - 2 = 18 (R)

The resulting code for PLANT is NJCLR.

Explanation

The relationship between the terms follows the mathematical logic n : n² × (n + 1) or n : n³ + n².

For the first pair, 5 : 150, the calculation is 5² × (5 + 1) = 25 × 6 = 150.

For the third pair, 8 : 576, the calculation is 8² × (8 + 1) = 64 × 9 = 576.

Applying the same logic to the second pair where n = 6, the missing value is 6² × (6 + 1) = 36 × 7 = 252.