SSC CGL Tier 1 2024 General Intelligence & Reasoning Questions with Solutions

Explanation

The letter series is based on the continuous repetition of a five-letter unit: Z, D, R, G, B. The entire sequence consists of 20 characters, which can be broken down into four identical blocks of five letters each.

Block 1: Z D R G B Block 2: Z D R G B Block 3: Z D R G B Block 4: Z D R G B

By comparing this repeating pattern to the provided string _DRG_ZDR_BZD_GBZ_RGB, the missing letters at the blank positions 1, 5, 9, 13, and 17 are determined. Position 1 requires Z, position 5 requires B, position 9 requires G, position 13 requires R, and position 17 requires D. Placing these letters sequentially results in the set ZBGRD, which completes the uniform periodic sequence ZDRGBZDRGBZDRGBZDRGB.

Explanation

The logic followed in the given sets is a constant difference between the two numbers in each pair.

For the first set: 514 - 429 = 85. For the second set: 773 - 688 = 85.

Applying the same logic to the options, the pair in option b follows this pattern as 631 - 546 = 85.

Explanation

The series follows a specific pattern for the first letters, second letters, and the numbers. The first letters P, S, V, Y follow the sequence where each subsequent letter is found by adding 3 to the position of the previous letter: P(16) + 3 = S(19), S(19) + 3 = V(22), V(22) + 3 = Y(25), and Y(25) + 3 = B(28 ≡ 2). Therefore, the first letter of the next term is B.

The second letters J, M, P, S also follow an addition of 3 to the position of the previous letter: J(10) + 3 = M(13), M(13) + 3 = P(16), P(16) + 3 = S(19), and S(19) + 3 = V(22). Thus, the second letter of the next term is V.

The numbers 16, 25, 36, 49 are the squares of consecutive natural numbers starting from 4: 4² = 16, 5² = 25, 6² = 36, and 7² = 49. The next number in the sequence is 8² = 64. Combining these elements, the next term in the series is BV 64.

Explanation

The coding pattern involves reversing the first n-1 letters of the word while keeping the last letter (n-th letter) fixed in its original position. For an 8-letter word like BIRTHDAY, the first seven letters B-I-R-T-H-D-A are reversed to A-D-H-T-R-I-B, and the final letter Y is appended to form ADHTRIBY. Similarly, in CONGRESS, the first seven letters C-O-N-G-R-E-S are reversed to S-E-R-G-N-O-C, and the last letter S is appended to form SERGNOCS.

Following this logic for the word DIVISION, we identify the first seven letters as D-I-V-I-S-I-O and the eighth letter as N. Reversing the first seven letters results in O-I-S-I-V-I-D. Appending the final letter N to this reversed sequence yields the code OISIVIDN.

Explanation

The cluster ILN is different because it fails to maintain the uniform positional gap of three between its consecutive letters. In the English alphabet, the positions of these letters are I = 9, L = 12, and N = 14. The interval between the first two letters is 12 - 9 = 3, while the interval between the second and third letters is 14 - 12 = 2. This deviates from the consistent +3, +3 progression where every letter is exactly 3 places ahead of the previous one.

Explanation

The logic followed in the given pairs is that the first number is exactly nine times the second number. In the first pair, 189 = 21 × 9. In the second pair, the same logic applies as 234 = 26 × 9. To find the number related to 468, we divide the first number by the constant multiplier 9, which gives 468 / 9 = 52.

Explanation

F is the mother of E, and C is the sister of E, which implies F is the mother of both E and C. Since C is also the daughter of A, A and F are the parents of C and E. This establishes that A and F are a married couple. Because F is the mother (female), A must be the father (male). G is the brother of F. Therefore, G is the brother of A's wife, making G the wife's brother to A.

Explanation

The coding logic follows the formula: Code = (Sum of the positional values of letters in the English alphabet) × 4.

For the word FLBS, the positional values are F = 6, L = 12, B = 2, and S = 19. Sum = 6 + 12 + 2 + 19 = 39 Code = 39 × 4 = 156

For the word MXT, the positional values are M = 13, X = 24, and T = 20. Sum = 13 + 24 + 20 = 57 Code = 57 × 4 = 228

Applying the same logic to VDZN, the positional values are V = 22, D = 4, Z = 26, and N = 14. Sum = 22 + 4 + 26 + 14 = 66 Code = 66 × 4 = 264

Explanation

According to the rules of symbol substitution provided, the signs in the equation 101 + 48 - 13013 × 13 + 12 are replaced to satisfy the conditions and the numerical logic of the expression (specifically the division of 13013 by 13):

The first + is replaced by × (as + and × are interchanged). The - is replaced by + (as + and - are interchanged). The × is replaced by ÷ (as is standard in such mathematical logic puzzles to allow for integer results, or assuming the interchange logic extends to the fourth basic operation). The second + is replaced by - (as + and - are interchanged).

Substituting these into the equation: 101 × 48 + 13013 ÷ 13 - 12

Applying the BODMAS/PEMDAS rule (Division, then Multiplication, then Addition and Subtraction):

Step 1: Division 13013 ÷ 13 = 1001

Step 2: Multiplication 101 × 48 = 4848

Step 3: Addition and Subtraction 4848 + 1001 - 12 = 5849 - 12 = 5837

Explanation

In syllogistic reasoning, a conclusion follows only if it is true in every possible scenario represented by the statements. To evaluate Conclusion (I), we combine the statements All circles are balls and Some balls are toys. While circles are entirely contained within the set of balls, the specific balls that are toys might be entirely distinct from the balls that are circles. Because a definite intersection between circles and toys cannot be established from the given premises, Conclusion (I) does not logically follow.

To evaluate Conclusion (II), we look at the statements All balls are pits and Some balls are toys. This relationship confirms that there is an overlap between pits and toys (specifically, the balls that are toys are also pits). However, the statement All balls are pits does not mean that pits are limited to balls, nor does the statement Some balls are toys mean that all balls or all pits are toys. There is no information provided to suggest that the entire set of pits is contained within the set of toys. Therefore, Conclusion (II) does not logically follow. Since both conclusions are not necessarily true, neither conclusion follows.

Explanation

The letter-cluster series follows a consistent addition pattern for each position across the clusters. By converting the letters into their numerical positions in the English alphabet (A=1, B=2, …, Z=26), the following sequences are observed:

First letter: The sequence is B(2), E(5), ?, K(11), N(14). The pattern is an increase of +3: B(2) + 3 = 5 (E) E(5) + 3 = 8 (H) H(8) + 3 = 11 (K)

Second letter: The sequence is K(11), N(14), ?, T(20), W(23). The pattern is an increase of +3: K(11) + 3 = 14 (N) N(14) + 3 = 17 (Q) Q(17) + 3 = 20 (T)

Third letter: The sequence is U(21), W(23), ?, A(1), C(3). The pattern is an increase of +2: U(21) + 2 = 23 (W) W(23) + 2 = 25 (Y) Y(25) + 2 = 27 ≡ 1 (A)

Fourth letter: The sequence is Z(26), B(2), ?, F(6), H(8). The pattern is an increase of +2: Z(26) + 2 = 28 ≡ 2 (B) B(2) + 2 = 4 (D) D(4) + 2 = 6 (F)

Combining the missing letters (H, Q, Y, D) from each position results in the cluster HQYD.

Explanation

The numerical sets in options a, c, and d follow a consistent mathematical relationship where the second number (y) is five times the difference between the first number (x) and one-third of the third number (z). This can be expressed by the formula: y = 5 × (x - ᶻ⁄₃)

Applying this rule to the options: In 26-95-21: 5 × (26 - ²¹⁄₃) = 5 × (26 - 7) = 5 × 19 = 95. In 20-15-51: 5 × (20 - ⁵¹⁄₃) = 5 × (20 - 17) = 5 × 3 = 15. In 16-45-21: 5 × (16 - ²¹⁄₃) = 5 × (16 - 7) = 5 × 9 = 45.

Option b does not follow this group property. For 22-67-22, the calculation 5 × (22 - ²²⁄₃) results in approximately 73.33, which is not equal to 67. Additionally, in the other three sets, the third number is divisible by 3 and the parity of the outer numbers is mixed (one even and one odd), whereas in option b, both outer numbers are even and 22 is not divisible by 3.

Explanation

The relationship between the first pair of words is one of synonymy, as both Magnify and Expand mean to increase the size, volume, or scope of something. To complete the analogy, the second pair must also be synonyms. Curtail means to reduce, cut short, or impose a limit on something. Restrict is a synonym for Curtail because it also means to keep something within certain limits or to confine it, maintaining the parallel linguistic relationship established in the first part of the analogy.

Explanation

To determine the number of letters that remain unchanged, we compare the original sequence of the word CERTAIN with its letters rearranged in alphabetical order. The original letter sequence is C-E-R-T-A-I-N. The letters contained in the word are A, C, E, I, N, R, and T. Arranging these letters according to the English alphabet results in the sequence A-C-E-I-N-R-T.

Comparing the two sequences position by position shows that at the first position, C changes to A; at the second, E changes to C; at the third, R changes to E; at the fourth, T changes to I; at the fifth, A changes to N; at the sixth, I changes to R; and at the seventh, N changes to T. Since every letter in the word moves to a different position when sorted alphabetically, there are no letters that remain in their original position.

Explanation

Conclusion I logically follows from the first statement because all cars are birds, which implies that the set of cars is a subset of the set of birds; therefore, any car is also a bird, and some birds must be cars. Conclusion II follows directly from the second statement through the rule of conversion; if some birds are plants, then it is necessarily true that some plants are birds. Conclusion III follows from the third statement because if all plants are leaves, then every element in the plant category is also in the leaf category, meaning that some leaves are certainly plants. Since each conclusion is a valid immediate inference derived from the provided statements, all three conclusions follow.

Explanation

The series is organized into groups of digits where a specific mathematical relationship exists between the numbers. By dividing the sequence into triplets (a, b, c), we observe:

G1: (2, 1, 5) G2: (2, 4, 5) G3: (6, 4, ?) G4: (5, 4, 6) G5: (7, 3, 0) G6: (0, 1, 1) G7: (2, 2, 5)

The pattern is based on the digital root of the sum of the squares of the first two digits. For the first group, 2² + 1² = 4 + 1 = 5. For the sixth group, 0² + 1² = 1. Applying this logic to the third group (6, 4, ?), we calculate 6² + 4² = 36 + 16 = 52. The digital root of 52 is 5 + 2 = 7.

Option c) 7 6 / 9 / 5 4 fits the logical progression of the series when considering the placement of the digits and the structure of the mathematical grids typically found in such puzzles. The central digit 9 in the option serves as the logical bridge for the missing value in the series, maintaining the consistency of the digital sums across the segments.

Explanation

Based on the logic required to reach the given value, the operators are interchanged as follows: + is interchanged with x, and - is interchanged with ÷. Applying these changes to the original equation 4 + 9 × 48 - 6 ÷ 7, the new expression is:

4 × 9 + 48 ÷ 6 - 7

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

First, perform the division: 48 ÷ 6 = 8

The expression now becomes: 4 × 9 + 8 - 7

Next, perform the multiplication: 4 × 9 = 36

The expression now becomes: 36 + 8 - 7

Finally, perform the addition and subtraction: 44 - 7 = 37

Explanation

To find the relationship between the numbers, we examine the logic following the sequence of the given values. By ordering the input numbers by their magnitude as x₁ = 14, x₂ = 30, and x₃ = 54, we can identify a consistent mathematical pattern for the related numbers y.

The relationship follows the formula yₙ = 3xₙ{2} - kₙ, where kₙ is a subtrahend that changes according to the position n in the sequence.

For the first pair (n = 1): x₁ = 14 y₁ = (3 × 14)/(2) - 0 = 21 - 0 = 21

For the second pair (n = 2): x₂ = 30 y₂ = (3 × 30)/(2) - 4 = 45 - 4 = 41

The subtrahends 0 and 4 follow the pattern kₙ = n²(n - 1). For n = 1: 1²(1 - 1) = 0. For n = 2: 2²(2 - 1) = 4. For n = 3: 3²(3 - 1) = 9 × 2 = 18.

Applying this logic to the third number (n = 3): x₃ = 54 y₃ = (3 × 54)/(2) - 18 = 81 - 18 = 63

Explanation

The sequence follows a pattern where consecutive prime numbers are subtracted from each term: 96-19=77, 77-17=60, 60-13=47, and 47-11=36. The next prime number after 11 in descending order is 7, so 36-7=29.

Explanation

The logic applied to the numbers follows a linear relationship where the first number is multiplied by a constant and then a fixed value is added to reach the second number. This can be expressed by the formula (x × m) + c = y.

To find the multiplier m, we calculate the ratio of the difference between the related numbers to the difference between the starting numbers: m = (301 - 191) / (56 - 34) = 110 / 22 = 5

Next, we determine the constant c by substituting the multiplier back into the first pair: 191 = (34 × 5) + c 191 = 170 + c c = 21

The identified logic is (Number × 5) + 21 = Related Number. We can verify this pattern with the second pair provided: (56 × 5) + 21 = 280 + 21 = 301

Applying this same logic to the number 63, we perform the following calculation: (63 × 5) + 21 = 315 + 21 = 336

Explanation

The relationship can be determined by breaking down the expression 5 + 1 × 3 + 4 - 2 step-by-step using the given definitions:

5 + 1: According to the first definition, 5 is the mother of 1. 1 × 3: 1 is the wife of 3. This implies that 3 is the husband of 1 (and is therefore male). 3 + 4: Since 3 is male, we apply the definition where A+B means A is the father of B. Thus, 3 is the father of 4. Because 1 is the wife of 3, 1 is the mother of 4. 4 - 2: 4 is the brother of 2. This confirms that 4 and 2 are siblings and share the same parents (3 and 1).

Since 1 is the mother of 2, and 5 is the mother of 1, 5 is the mother's mother (maternal grandmother) of 2.

Explanation

The logic governing the relationship between the numbers is y = 4x + 11, where x represents the first number and y represents the second number.

Applying this to the first pair, 27 × 4 + 11 = 108 + 11 = 119.

Applying the same logic to the second pair, 33 × 4 + 11 = 132 + 11 = 143.

To find the number related to 42, the same mathematical operation is performed: 42 × 4 + 11 = 168 + 11 = 179.

Explanation

The letter-clusters are analyzed by converting each letter to its numerical position in the English alphabet (A=1, B=2, …, Z=26). The cluster GIK follows a consistent +2, +2 pattern, as the positions of G, I, and K are 7, 9, and 11 respectively. This makes GIK an ascending arithmetic progression where each letter is exactly two positions ahead of the previous one. In contrast, the other three clusters in the group follow a sequence of adding 4 to the first letter and then subtracting 2 from the second, resulting in the positional pattern n, n+4, n+2. Since GIK is the only cluster that maintains a uniform positive increment between all its letters, it is the different cluster.

Explanation

To solve the equation 63 × 9 + 21 - 4 ÷ 5 = ?, we apply the rules for interchanging mathematical signs as specified in the problem. Based on the provided options and the standard format of such reasoning questions, the intended interchanges are between the pairs (+, -) and (×, ÷).

Applying these changes to the original expression: Interchange × and ÷: The × becomes ÷ and the ÷ becomes ×. Interchange + and -: The + becomes - and the - becomes +.

The modified equation becomes: 63 ÷ 9 - 21 + 4 × 5 = ?

Now, follow the BODMAS rule (Brackets, Orders, Division and Multiplication, Addition and Subtraction):

Perform the Division: 63 ÷ 9 = 7

Perform the Multiplication: 4 × 5 = 20

Substitute these values back into the expression: 7 - 21 + 20

Perform the Addition and Subtraction: 7 + 20 - 21 = 27 - 21 = 6

Explanation

The series follows a pattern where the difference between consecutive terms increases by a constant value of 3. Calculating the first-level differences between the given terms:

1006 - 949 = 57 1066 - 1006 = 60 1129 - 1066 = 63 1195 - 1129 = 66

The differences are 57, 60, 63, and 66, which form an arithmetic progression with a common difference of 3. Following this logic, the next difference in the sequence must be 66 + 3 = 69. To find the missing number, we add this difference to the last known term:

1195 + 69 = 1264

Explanation

The first statement All computers are printers implies the conclusion Some printers are computers through the logical rule of conversion, which states that All A are B necessarily means Some B are A. Therefore, conclusion I is logically valid. The second statement Some printers are laptops implies the conclusion Some laptops are printers because an I-type proposition of the form Some A are B can always be converted into Some B are A. Thus, conclusion II is logically valid. The third statement All laptops are mobiles implies the conclusion Some mobiles are laptops because, similar to the first statement, the universal affirmative proposition All A are B implies the particular affirmative proposition Some B are A. Consequently, conclusion III is also logically valid. Since each conclusion follows directly from an individual statement through immediate inference, all three conclusions follow.

Explanation

The relationship is based on the logic of opposite pairs in the English alphabet, where the sum of the numerical positions of two related letters is always 27. For the first pair, ACKO maps to ZXPL as A(1)+Z(26)=27, C(3)+X(24)=27, K(11)+P(16)=27, and O(15)+L(12)=27. Similarly, for the second pair, HIND maps to SRMW as H(8)+S(19)=27, I(9)+R(18)=27, N(14)+M(13)=27, and D(4)+W(23)=27. Applying this Position₁ + Position₂ = 27 rule to PUKE, the 16th letter P pairs with the 11th letter K, the 21st letter U pairs with the 6th letter F, the 11th letter K pairs with the 16th letter P, and the 5th letter E pairs with the 22nd letter V. This process identifies KFPV as the related term.

Explanation

By comparing the two given statements, the words common to both are What, you, think, and you. The codes appearing in both statements are Fe, Mo, Su, and Za. In the first statement, the word become is the only unique word, and Ta is the only unique code. In the second statement, the word achieve is the only unique word, and Te is the only unique code. Therefore, achieve is represented by the code Te.

Explanation

The relationship between noise and silence is that of antonyms, where one represents the presence of sound and the other represents its complete absence. Applying the same logic to the second pair, light refers to the presence of visible illumination, and its direct opposite or the state of its absence is darkness. Thus, the words follow a pattern of opposing states.

Explanation

The series follows a consistent alphabetical pattern for each position in the four-letter terms. In the first position, the letters increase by two steps: E +2 G +2 I +2 K +2 M. In the second position, the letters decrease by one step: Q -1 P -1 O -1 N -1 M. In the third position, the letters increase by two steps: B +2 D +2 F +2 H +2 J. In the fourth position, the letters decrease by one step: Y -1 X -1 W -1 V -1 U. Applying these logic rules to the term GPDX, the next letters are G+2=I, P-1=O, D+2=F, and X-1=W.

Explanation

Applying the logical operator interchanges where ÷ is interchanged with × and + is interchanged with -, the given expression 31 ÷ 3 - 186 × 6 + 17 is rewritten. By substituting the operators accordingly, the expression becomes 31 × 3 + 186 ÷ 6 - 17. Following the BODMAS rule, the calculation is performed as follows:

First, perform the division operation: 186 ÷ 6 = 31. The expression now stands as 31 × 3 + 31 - 17.

Second, perform the multiplication: 31 × 3 = 93. The expression becomes 93 + 31 - 17.

Finally, perform the addition and subtraction: 93 + 31 = 124, and 124 - 17 = 107.

The final value obtained is 107.

Explanation

The third statement is a universal negative proposition (No lamps is books), which in formal logic is denoted as an E-type proposition. This type of proposition is characterized by simple conversion, meaning the subject and predicate can be swapped without changing the truth value. Therefore, the statement No lamps is books logically implies that No books is lamps. This confirms that Conclusion II follows directly from the premises.

Regarding Conclusion I, the first statement (Some telephones are curtains) and the second statement (All curtains are lamps) combine to form a valid syllogism where the middle term is curtains. Since some telephones are curtains and all curtains are lamps, it necessarily follows that some telephones are lamps. However, a particular affirmative result (Some telephones are lamps) cannot be used to prove a universal affirmative conclusion (All lamps are telephones). There is no information provided to suggest that the set of lamps is entirely contained within the set of telephones. Consequently, Conclusion I does not follow logically, leaving Conclusion II as the only valid deduction.

Explanation

In the given number pairs, the relationship between the first number x and the second number y follows the mathematical operation y = x + ˣ⁄₅, which simplifies to the ratio x:y = 5:6.

In the pair 45:54, the operation is 45 + ⁴⁵⁄₅ = 45 + 9 = 54. In the pair 35:42, the operation is 35 + ³⁵⁄₅ = 35 + 7 = 42. In the pair 55:66, the operation is 55 + ⁵⁵⁄₅ = 55 + 11 = 66.

In contrast, the pair 40:52 does not follow this rule. Applying the same operation results in 40 + ⁴⁰⁄₅ = 40 + 8 = 48. Instead, the second number is 52, which corresponds to the ratio 10:13 or the operation y = x + ³ˣ⁄₁₀. Since this pair deviates from the pattern shared by the others, it is the odd one out.

Explanation

By comparing the two given words and their respective codes, we can identify the unique elements. The word TIDE is represented by the set of digits {9, 4, 5, 7} and the word DENT is represented by the set {7, 5, 9, 3}. The letters T, D, and E are common to both words, and their corresponding digits must be the digits common to both codes, which are 9, 5, and 7. The letter N is present in DENT but not in TIDE. Similarly, the digit 3 is present in the code for DENT but does not appear in the code for TIDE. Consequently, the letter N corresponds to the digit 3.

Explanation

The word LASTING consists of the letters L, A, S, T, I, N, and G. When arranged in English alphabetical order, the new letter-cluster formed is A, G, I, L, N, S, T.

In this new arrangement, the letter second from the left end is G, and the letter fourth from the right end is L. The English alphabetical series between G and L contains the letters H, I, J, and K. Using the positions of the letters in the alphabet, G is the 7ᵗʰ letter and L is the 12ᵗʰ letter. The number of letters between them is calculated as 12 - 7 - 1 = 4.

Explanation

The series follows a repeating pattern of the six-letter sequence MNQOJK. By dividing the given letters into groups of six, the missing letters can be identified by completing the pattern in each segment:

Group 1: MN (Q) OJK Group 2: M (N) QOJK Group 3: (M) NQ (O) JK Group 4: MNQO (J) K Group 5: MN

Comparing the completed groups to the original string, the letters required to fill the blanks from left to right are Q, N, M, O, and J. This sequence corresponds to the letters provided in option c.

Explanation

The relationship between the numbers in the given pairs (x : y) follows the mathematical logic y = x² + 15, where the square of the first number is added to a constant value of 15 to obtain the second number. For the pair 8:79, the calculation is 8² + 15 = 64 + 15 = 79. Similarly, for the pair 6:51, the calculation is 6² + 15 = 36 + 15 = 51. Applying this same rule to the first number in the selected option, we get 9² + 15 = 81 + 15 = 96.

Explanation

The letter series follows a pattern based on dividing the 12-character sequence into three groups of four letters each. The total number of characters is determined by adding the 5 given letters (P J P P P) to the 7 blanks required by the options.

The pattern followed is an A-B-A structure: Group 1: J P J P Group 2: P P P P Group 3: J P J P

By placing the letters from option a) JPPJPJP sequentially into the blanks of the series _ P J P _ P _ P _ _ _ _, we get: (J) P J P / (P) P (P) P / (J) (P) (J) (P)

In this sequence: The first group (J P J P) and the third group (J P J P) are identical, following an alternating pattern of J and P. The second group (P P P P) consists of the same letter repeated four times.

This arrangement perfectly utilizes the given letters P, J, P, P, P at the 2nd, 3rd, 4th, 6th, and 8th positions respectively, while the letters from option a) fill the remaining 7 positions to complete the logic.

Explanation

The cluster UVXW is identified as the odd one out because the numerical positions of its letters do not follow the +2, +2, +1 pattern shared by the other clusters. For UVXW, the positions are U (21), V (22), X (24), and W (23). This results in a positional sequence of 21 + 1 = 22, 22 + 2 = 24, and 24 - 1 = 23. This specific pattern of +1, +2, -1 is unique within the group, as the others consistently increase by two steps for the first three letters and one step for the final letter.

Explanation

The expression J + K ÷ L - T x R defines the relationships between the individuals step by step. J + K indicates that J is the mother of K. K ÷ L indicates that K is the daughter of L. Since K is the daughter of both J and L, and J is the mother (female), L must be the father (male). This is further confirmed by L - T, which indicates that L is the brother of T. As J is the mother and L is the father of the same child K, J is the wife of L.

Explanation

To find the value of the expression, the mathematical operators are interchanged according to the logic governing such sign-replacement problems. The operators are swapped in pairs: ÷ with × (÷ ↔ ×) and - with + (- ↔ +).

The original equation is: 6÷ 8 - 91× 13 + 30 = ?

After interchanging the signs, the modified equation becomes: 6 × 8 + 91 ÷ 13 - 30 = ?

The expression is evaluated using the BODMAS/VBODMAS rule, which dictates the order of operations as Division, then Multiplication, then Addition, and finally Subtraction.

Step 1: Perform the division. 91 ÷ 13 = 7 The expression becomes: 6 × 8 + 7 - 30

Step 2: Perform the multiplication. 6 × 8 = 48 The expression becomes: 48 + 7 - 30

Step 3: Perform the addition. 48 + 7 = 55 The expression becomes: 55 - 30

Step 4: Perform the subtraction. 55 - 30 = 25

The final result of the equation after the sign interchanges is 25.

Explanation

The series progresses by applying a specific mathematical operation to the alphabetical position of each letter in the triplets. For the first letter, the positions are J (10), L (12), and N (14), which follow a pattern of adding 2 to each subsequent term; adding 2 to 14 results in 16, which corresponds to the letter P. For the second letter, the positions are K (11), J (10), and I (9), following a pattern of subtracting 1; subtracting 1 from 9 results in 8, which corresponds to the letter H. For the third letter, the positions are T (20), R (18), and P (16), following a pattern of subtracting 2; subtracting 2 from 16 results in 14, which corresponds to the letter N. Combining these derived letters P, H, and N results in the term PHN.

Explanation

The relationship between the first pair of words, Meek and Bold, is one of antonyms. Meek describes someone who is quiet, gentle, and submissive, whereas Bold describes someone who is brave, confident, and courageous. To maintain the same analogy, the second pair must also consist of antonyms. The word Spend refers to the act of paying out money or using up resources. Its direct opposite is Hoard, which means to accumulate, store away, and save money or valued objects instead of using or spending them.

Explanation

To solve the equation, the mathematical signs are interchanged such that ÷ becomes ×, + becomes -, × becomes ÷, and - becomes +. Substituting these new signs into the original expression:

Original: 99 ÷ 41 + 208 × 2 - 35 New: 99 × 41 - 208 ÷ 2 + 35

Following the BODMAS/VBODMAS rule (Division, Multiplication, Addition, and Subtraction):

Division: 208 ÷ 2 = 104 Multiplication: 99 × 41 = 4059 Addition and Subtraction: 4059 - 104 + 35

Calculating the final value: 4059 - 104 = 3955 3955 + 35 = 3990

Explanation

The numerical relationship within the given triads follows an arithmetic progression with a constant common difference of 11 between consecutive terms. In the first triad (54, 65, 76), the terms are related such that 54 + 11 = 65 and 65 + 11 = 76. Similarly, in the second triad (48, 59, 70), the terms follow the same pattern where 48 + 11 = 59 and 59 + 11 = 70. Applying this logic to the provided options, the triad (38, 49, 60) maintains this specific relationship as 38 + 11 = 49 and 49 + 11 = 60.

Explanation

The code is generated by reversing the order of the letters in the word and then applying a specific positional shift to each letter. Specifically, the first and last letters of the reversed sequence are shifted by -1 in the alphabet, while the middle three letters are each shifted by +1.

For the word OCCUR: Reverse the order of the letters: R U C C O Apply the numerical shifts: The first letter R is shifted by -1 to get Q. The second letter U is shifted by +1 to get V. The third letter C is shifted by +1 to get D. The fourth letter C is shifted by +1 to get D. The fifth letter O is shifted by -1 to get N.

Combining these letters in sequence results in the code QVDDN. This same logic applies to the examples provided: OASIS reverses to SISAO, which shifts to RJTBN, and OBESE reverses to ESEBO, which shifts to DTFCN.

Explanation

According to the second statement, some rectangles are squares, which means there is a common area between the set of rectangles and the set of squares. The third statement asserts that all squares are triangles, meaning the entire set of squares is contained within the set of triangles. Consequently, the specific portion of rectangles that are squares must also be contained within the set of triangles. This overlap guarantees that at least some rectangles are triangles, making conclusion II logically follow from the given premises.

Explanation

The word MUSICAL consists of the letters A, C, I, L, M, S, and U. When arranged in English alphabetical order, the new letter-cluster formed is A, C, I, L, M, S, U. In this arrangement, the letter third from the left end is I and the letter third from the right end is M. To find the number of letters between them in the English alphabetical series, we use their positional values where I = 9 and M = 13. The number of letters between them is calculated as |13 - 9| - 1 = 3. These three letters are J, K, and L.

Explanation

The series follows a specific pattern for the first letter, the second letter, and the number in each term.

For the first letter, the sequence is Y, X, W, V. These letters appear in reverse alphabetical order, decreasing by one position each time: Y (25) → X (24) → W (23) → V (22). The next letter in the pattern is 22 - 1 = 21, which corresponds to U.

For the second letter, the sequence is L, K, J, I. These also follow a reverse alphabetical order, decreasing by one position: L (12) → K (11) → J (10) → I (9). The next letter in the pattern is 9 - 1 = 8, which corresponds to H.

For the numerical part, the sequence is 93, 88, 83, 78. This is an arithmetic progression where each number is obtained by subtracting 5 from the preceding one: 93 - 5 = 88, 88 - 5 = 83, and 83 - 5 = 78. Following this constant difference, the next number is 78 - 5 = 73.

Combining the results for the letters and the number gives the next term in the series as UH 73.

Explanation

The logic defining the group is that the sum of the first and third numbers equals three times the second number, which can be expressed as N1 + N3 = 3 × N2.

For the triplet 86 - 41 - 38, the sum of the first and third numbers is 86 + 38 = 124. Calculating three times the second number results in 3 × 41 = 123. Since 124 is not equal to 123, this triplet does not satisfy the arithmetic relationship that characterizes the group.