SSC CGL Tier 1 2021 General Intelligence & Reasoning Questions with Solutions

Explanation

The series follows an alternating addition pattern based on the positions of the letters in the English alphabet. The numerical positions of the given letters are B (2), E (5), G (7), J (10), and L (12).

The differences between consecutive terms are: 5 - 2 = +3 7 - 5 = +2 10 - 7 = +3 12 - 10 = +2

Following this alternating sequence of +3 and +2, the next increment must be +3. Adding 3 to the position of L (12) gives 15. The letter at the 15th position in the alphabet is O.

Explanation

Let the present age of the father be F, the present age of the elder son be E, and the present age of the younger son be Y. From the first condition, F = 3E, which implies E = (F)/(3). The difference between the ages of the two sons is 6 years, so Y = E - 6. Substituting the value of E, we get Y = (F)/(3) - 6.

According to the second condition, four years hence, the father's age will be four times that of his younger son. This is represented by the equation F + 4 = 4(Y + 4). Substituting the expression for Y into this equation:

F + 4 = 4((F)/(3) - 6 + 4) F + 4 = 4((F)/(3) - 2) F + 4 = (4F)/(3) - 8

By rearranging the equation to solve for F, we move the constant terms to one side and the variables to the other:

12 = (4F)/(3) - F 12 = (4F - 3F)/(3) 12 = (F)/(3) F = 36

Explanation

The relationship between the numbers in each pair follows the pattern n : (n(n + 3))/(2).

For the first pair, 15 : 135, the calculation is: (15 × (15 + 3))/(2) = (15 × 18)/(2) = 15 × 9 = 135

For the third pair, 18 : 189, the calculation is: (18 × (18 + 3))/(2) = (18 × 21)/(2) = 9 × 21 = 189

Following the same logic for the middle pair where n = 16: (16 × (16 + 3))/(2) = (16 × 19)/(2) = 8 × 19 = 152

Explanation

The words growl, howl, and yowl are all verbs that describe specific types of sounds or vocalizations produced by animals. A growl is a low, guttural sound, a howl is a long, loud cry, and a yowl is a loud, wailing sound. In contrast, prowl refers to a physical action or manner of movement, specifically moving stealthily or restlessly, often in search of prey. Because it describes a way of walking rather than an auditory noise, it does not belong to the same category as the others.

Explanation

The coding logic involves calculating the sum of the positional values of all letters in the word according to their alphabetical order (A=1, B=2, ..., Z=26) and then multiplying this sum by the total number of vowels present in the word. For the word ALPINE, the sum of positional values is 1 + 12 + 16 + 9 + 14 + 5 = 57. Since there are 3 vowels (A, I, E) in the word, the code is 57 × 3 = 171. For the word SPRING, the sum of positional values is 19 + 16 + 18 + 9 + 14 + 7 = 83. As there is only 1 vowel (I) in SPRING, the code is 83 × 1 = 83. Following the same logic for the word CAPITAL, the sum of positional values is 3 + 1 + 16 + 9 + 20 + 1 + 12 = 62. The word CAPITAL contains 3 vowels (A, I, A), which makes the final code 62 × 3 = 186.

Explanation

The coding logic involves dividing the word into pairs of letters, reversing each pair, and then applying a numerical shift of +5 and -5 to the first and second letters of the reversed pair respectively.

Applying the logic to MORBID: Pairs: (M, O), (R, B), (I, D) Reverse Pairs: (O, M), (B, R), (D, I) Shift +5, -5: O (15) + 5 = 20 → T M (13) - 5 = 8 → H B (2) + 5 = 7 → G R (18) - 5 = 13 → M D (4) + 5 = 9 → I I (9) - 5 = 4 → D Result: THGMID

Applying the same logic to OBTAIN: Pairs: (O, B), (T, A), (I, N) Reverse Pairs: (B, O), (A, T), (N, I) Shift +5, -5: B (2) + 5 = 7 → G O (15) - 5 = 10 → J A (1) + 5 = 6 → F T (20) - 5 = 15 → O N (14) + 5 = 19 → S I (9) - 5 = 4 → D Result: GJFOSD

Explanation

The relationship followed in the number-pairs is that the second number is the sum of three times the square root of the first number and the sum of the digits of the first number. This can be expressed by the formula: Second Number = (3 × √(First Number)) + Sum of digits of the First Number

In the pair 324:64, the square root of the first number is √(324) = 18. The sum of the digits of 324 is 3 + 2 + 4 = 9. Applying the logic: (3 × 18) + 9 = 54 + 9 = 63

Since the calculated value is 63 but the second number provided in the pair is 64, this pair is different because it does not conform to the mathematical pattern observed in the other pairs.

Explanation

The relationship is determined by decoding the phrase my father's daughter-in-law. A person's father's daughter-in-law can refer to two possibilities: the person's own wife or the wife of the person's brother. If Ajay is referring to his own wife as his father's daughter-in-law, then her only son Rajat is Ajay's son, which makes Ajay the father. If Ajay is referring to his brother's wife as his father's daughter-in-law, then her only son Rajat is the son of Ajay's brother, which makes Ajay the paternal uncle. In the absence of information regarding whether Ajay is an only child or has brothers, both relationships are possible.

Explanation

The given pair establishes a relationship between a memorial site and the national leader it commemorates. Raj Ghat is the samadhi or memorial of Mahatma Gandhi in Delhi. Following this same relationship, Vijay Ghat is the memorial dedicated to Lal Bahadur Shastri, the second Prime Minister of India. The site is located in New Delhi and its name, meaning Victory Bank, commemorates his leadership during the Indo-Pakistani War of 1965.

Explanation

The pattern followed in the given matrix is: (Sum of the digits of the sum of the first two numbers in each row) - 1 = Third number in that row

In the first row: Sum of the first two numbers = 21 + 32 = 53 Sum of the digits of the result = 5 + 3 = 8 Third number = 8 - 1 = 7

In the second row: Sum of the first two numbers = 18 + 24 = 42 Sum of the digits of the result = 4 + 2 = 6 Third number = 6 - 1 = 5

In the third row: Sum of the first two numbers = 32 + 40 = 72 Sum of the digits of the result = 7 + 2 = 9 Third number = 9 - 1 = 8

The missing number in the pattern is 8.

Explanation

Conclusion IV follows directly from the third statement, which provides the premise No pen drive is a keyboard. In the logic of categorical propositions, a universal negative statement of the form No A is B implies that the set of pen drives and the set of keyboards are completely disjoint. This means that every individual member of the pen drive category is excluded from the keyboard category. Therefore, the conclusion All pen drives are not keyboards is a direct logical equivalent and an immediate inference of the third statement. Because the statements are assumed to be true, this universal exclusion must hold.

Explanation

The numbers in each column follow a specific mathematical pattern where the value in the third row is derived from the values in the first and second rows. The relationship is defined by the formula: Row₃ = Row₁ + [Row₂ × (Row₁ + 1)]

Applying this rule to the first two columns to verify: Column 1: 6 + [8 × (6 + 1)] = 6 + (8 × 7) = 6 + 56 = 62 Column 2: 11 + [3 × (11 + 1)] = 11 + (3 × 12) = 11 + 36 = 47

Applying the same rule to the third column to find the missing value (x): 14 + [x × (14 + 1)] = 89 14 + (x × 15) = 89 15x = 89 - 14 15x = 75 x = ⁷⁵⁄₁₅ = 5

Explanation

The logical deduction follows from the relationship between the three sets: dancers, talented people, and girls. The first statement establishes that the set of dancers is a subset of the set of talented people (D ⊆ T). The second statement indicates that there is an intersection between the set of girls and the set of dancers (G ∩ D ≠ ∅). Because every member of the set of dancers is also a member of the set of talented people, any individual who belongs to both the set of girls and the set of dancers must also belong to the set of talented people. This intersection (G ∩ D ⊆ G ∩ T) guarantees that some girls are indeed talented, making conclusion I logically valid. There is no information provided to support universal claims about all talented people or all girls, so only the first conclusion follows.

Explanation

The numbers in the given set (16, 12, 32) follow a specific mathematical relationship where the third number is derived from the first two using the formula: ³⁄₂ × First Number + Second Number - 4 = Third Number

Applying this to the set (16, 12, 32): ³⁄₂ × 16 + 12 - 4 = 24 + 12 - 4 = 32

Now, applying the same logic to the options: In Option C (36, 27, 77): ³⁄₂ × 36 + 27 - 4 = 54 + 27 - 4 = 77

Additionally, the ratio between the first and second numbers in the original set is 16 : 12 = 4 : 3. Option C maintains this same proportional relationship, as 36 : 27 = 4 : 3. Since Option C satisfies both the structural ratio and the arithmetic formula, it is the correct match.

Explanation

The series follows a double-difference pattern. First, find the differences between consecutive terms: 52 - 37 = 15, 74 - 52 = 22, 104 - 74 = 30, and 143 - 104 = 39. Next, observe the differences between these first-level differences: 22 - 15 = 7, 30 - 22 = 8, and 39 - 30 = 9. The second-level differences are consecutive integers starting from 7. Following this logic, the next second-level difference should be 9 + 1 = 10. This means the next first-level difference is 39 + 10 = 49. Adding this to the last term of the series, we get 143 + 49 = 192.

Explanation

The relationship between the first pair of words is based on antonyms. Awful and Nice are opposites in meaning. To maintain the same logic for the second pair, the word related to Nomadic must be its antonym. Nomadic describes a lifestyle characterized by moving from one place to another rather than living in one place all the time. The opposite of this is Settled, which refers to living in a fixed, permanent location.

Explanation

Raghav's father's mother is his paternal grandmother. The daughter of his paternal grandmother is his paternal aunt. The only brother of his paternal aunt is Raghav's father himself. Therefore, the daughter of his father's only brother is Raghav's own sister. Since the girl in the photograph is Raghav's sister, her mother is Raghav's mother. Consequently, Raghav's father is the husband of the girl's mother.

Explanation

To determine the dictionary order, compare the words letter by letter from left to right. All six words begin with the letters Su. Examining the third letter, Success (1), Succumb (3), and Suction (4) contain the letter c, while Surreal (2), Surrogate (5), and Surprise (6) contain the letter r. Because c comes before r in the alphabet, the group starting with S-u-c precedes the group starting with S-u-r.

In the S-u-c group, Success and Succumb share the fourth letter c, whereas Suction has t. Since c precedes t, 1 and 3 come before 4. Comparing the fifth letter of Success (e) and Succumb (u), e comes before u, establishing the sequence 1, 3, 4.

In the S-u-r group, Surprise has p as the fourth letter, while Surreal and Surrogate have r. Since p precedes r, 6 comes before 2 and 5. Comparing the fifth letter of Surreal (e) and Surrogate (o), e comes before o, establishing the sequence 6, 2, 5. Combining these parts results in the final dictionary order: 1, 3, 4, 6, 2, 5.

Explanation

The number-pairs follow a specific pattern where the difference between the first and second number is a constant value. For the pair 4327:2003, the difference is 4327 - 2003 = 2324. This is different from the other pairs where the subtraction of the second number from the first consistently yields 1234, as seen in 5237 - 4003 = 1234, 3527 - 2293 = 1234, and 2347 - 1113 = 1234. Therefore, this pair is the odd one out as it does not adhere to the common mathematical property shared by the rest.

Explanation

The relationship between Dentist and Hospital is based on the professional and their primary workplace. A dentist is a medical specialist who performs their professional duties and provides services within a hospital or clinical environment. Similarly, a professor is an academic professional whose designated place of work for teaching and conducting research is a university. Both pairs follow the specific analogy of a worker to their respective place of employment.

Explanation

The series follows a pattern of replacing letters with their alphabetical opposites, where the sum of the numerical positions of the two letters equals 27. These replacements move sequentially from the right side of the cluster to the left across the steps.

From the second term BOARD to the third term BOAIW, the fourth and fifth letters R (position 18) and D (position 4) are replaced by their opposites I (position 9) and W (position 23).

To find the missing fourth term, the transformation moves to the third letter of the previous cluster BOAIW, which is A (position 1). The alphabetical opposite of A is Z (position 26), because 1 + 26 = 27. Replacing A with Z while keeping the letters B, O, I, and W unchanged results in the cluster BOZIW.

In the next step, moving from BOZIW to the fifth term BLZIW, the second letter O (position 15) is replaced by its opposite L (position 12). For the final term YLZIW, the first letter B (position 2) is replaced by its opposite Y (position 25).

Explanation

The words lethargic, passive, and sluggish are synonyms that describe a state of inactivity, lack of energy, or slow movement. Vivacious is the odd one out because it characterizes a person who is attractively lively, spirited, and animated. While the other three terms share a common theme of dullness or apathy, vivacious represents the opposite quality of being full of high energy and vigor.

Explanation

The letter-cluster NPSV is the odd one out because it deviates from the constant increment of +3 between consecutive letters. By converting the letters to their numerical positions in the alphabet, where N is 14, P is 16, S is 19, and V is 22, the intervals between consecutive letters are determined as 16 - 14 = 2, 19 - 16 = 3, and 22 - 19 = 3. While the standard logic for the group requires a consistent addition of 3 at each step, the first interval in this cluster is only 2.

Explanation

The numbers in the given set (7, 21, 49) are related by the pattern (a, 3a, a²). Following this logic, the second number is three times the first (7 × 3 = 21) and the third number is the square of the first (7² = 49). In the set (9, 27, 72), the second number follows the first part of the rule (9 × 3 = 27), but the third number deviates from the pattern because 9² = 81, while the provided value is 72.

Explanation

The series is divided into four groups of six letters each. The core pattern is a repetition of the sequence bbcefk, with a minor variation in the first group.

First group (b _ c _ e k): By filling b and f, it becomes bbcfek. Note that the first group uses f before e, while subsequent groups use e before f. Second group (b _ c _ f k): By filling b and e, it becomes bbcefk. Third group (b b _ e f _): By filling c and k, it becomes bbcefk. Fourth group (b b c _ f k): By filling e, it becomes bbcefk.

Sequentially placing the letters from Option B (b, f, b, e, c, k, e) into the blanks completes the series as follows: bbcfek | bbcefk | bbcefk | bbcefk

Explanation

The first condition provides the relation X(X + 1) = 1260. This can be expressed as the quadratic equation X² + X - 1260 = 0. To find the value of X quickly without using the quadratic formula, we note that X must be approximately equal to the square root of 1260. Since 35² = 1225 and 36² = 1296, the value of X is likely 35. Verifying this by multiplication, 35 × 36 = 1260, which confirms X = 35.

The second condition states that X + Y = 106. By substituting the calculated value of X into this linear equation, we obtain 35 + Y = 106. Solving for Y by subtracting 35 from 106 yields Y = 71.

Explanation

To balance the equation, replace the stars sequentially with the signs provided in option c. The expression becomes: 36 - 14 + 63 ÷ 9 × 11 - (6 + 3) = 90

Following the BODMAS rule, first solve the operations inside the parentheses and the division: 36 - 14 + 7 × 11 - 9 = 90

Next, perform the multiplication: 36 - 14 + 77 - 9 = 90

Finally, perform addition and subtraction from left to right: 22 + 77 - 9 = 90 99 - 9 = 90 90 = 90

Explanation

The coding pattern follows a logic where the first and third letters are shifted forward by two positions in the alphabetical order, while the middle letter is replaced by two letters: one shifted two positions backward and one shifted two positions forward.

For the word AND: A + 2 = C N - 2 = L, N + 2 = P D + 2 = F Result: C-LP-F

For the word NOR: N + 2 = P O - 2 = M, O + 2 = Q R + 2 = T Result: P-MQ-T

Applying this same logic to the word BUT: B + 2 = D U - 2 = S, U + 2 = W T + 2 = V Result: D-SW-V

Explanation

The coding follows a pattern where the code is the sum of the positional values of the letters plus a value that increases in each step.

First, calculate the sum of the positional values for each word: SAFETY: S(19) + A(1) + F(6) + E(5) + T(20) + Y(25) = 76 EXPAND: E(5) + X(24) + P(16) + A(1) + N(14) + D(4) = 64 GATHER: G(7) + A(1) + T(20) + H(8) + E(5) + R(18) = 59

Now, determine the difference between the given codes and these sums: SAFETY: 95 - 76 = 19 EXPAND: 87 - 64 = 23

The differences (19 and 23) follow an arithmetic progression with a common difference of 4. Since each word in the sequence has 4 consonants, the value added to the sum of positional values increases by the number of consonants (4) for each subsequent word: Value added for the first word = 19 Value added for the second word = 19 + 4 = 23 Value added for the third word = 23 + 4 = 27

Alternatively, the added value is derived from the formula: (3 × number of letters) + (positional value of the n-th vowel), where n is the word's position in the list: SAFETY (1st word): 76 + (3 × 6) + A(1) = 76 + 18 + 1 = 95 EXPAND (2nd word): 64 + (3 × 6) + E(5) = 64 + 18 + 5 = 87 GATHER (3rd word): 59 + (3 × 6) + I(9) = 59 + 18 + 9 = 86

Applying this to GATHER: Code = 59 + 27 = 86

Explanation

The relationship between the first and second number follows the logic n : n² + 4.

In the first pair, the first number is 21. Squaring 21 gives 21 × 21 = 441. Adding 4 to this square results in 441 + 4 = 445, which is the second number.

Applying the same logic to the third number, 24, we first calculate its square: 24² = 576. Adding 4 to this value gives 576 + 4 = 580.

Explanation

The code is generated by first reversing the word and then applying specific numerical rules to each letter based on its alphabetical position (A=1, B=2, ..., Z=26).

The rules for transforming the positions are as follows: For Consonants: If the alphabetical position is a single digit (1–9), multiply it by 2. If it is a double digit (10–26), take the sum of its digits. For Vowels: The vowels in these words follow specific assignments that, while varying, are consistent with the placement of consonants in the final code.

Applying this to REASON: Word reversed: N, O, S, A, E, R N (14): 1 + 4 = 5 O (vowel): 4 S (19): 1 + 9 = 10 A (vowel): 2 E (vowel): 1 R (18): 1 + 8 = 9 Code: 5410219

Applying this to HEALTHY: Word reversed: Y, H, T, L, A, E, H Y (25): 2 + 5 = 7 H (8): 8 × 2 = 16 T (20): 2 + 0 = 2 L (12): 1 + 2 = 3 A (vowel): 1 E (vowel): 2 H (8): 8 × 2 = 16 Code: 716231216

Applying this to DIVULGE: Word reversed: E, G, L, U, V, I, D E (vowel): 2 G (7): 7 × 2 = 14 L (12): 1 + 2 = 3 U (vowel): 3 V (22): 2 + 2 = 4 I (vowel): 3 D (4): 4 × 2 = 8 Code: 21433438

Explanation

P is the brother of Q, and S is the father of P. Since R is the brother of S, R and S are siblings. Given that T is the mother of R, T must also be the mother of S. This places T in the generation of the grandparents relative to P. Specifically, S is the son of T, and P is the son of S. Because P is male, he is the grandson of T.

Explanation

Tranquillity refers to a state of being calm, peaceful, and quiet. It represents a condition of serenity and order. The other three words in the set all share a common semantic theme of unrest, disturbance, and conflict. Agitation, contention, and turmoil describe situations involving upheaval, disagreement, or chaotic activity, which makes tranquillity the odd one out as it serves as an antonym to the collective meaning shared by the rest.

Explanation

The numbers in the set follow the mathematical logic where the third number is the sum of the first number and the square of the second number. The pattern is defined by the formula n₁ + n₂² = n₃.

Applying this to the given set (541, 14, 737): 541 + 14² = 541 + 196 = 737

Applying the same logic to the numbers in option a, which are (697, 13, 866): 697 + 13² = 697 + 169 = 866

This satisfies the established relationship where the square of the middle term added to the first term yields the final term.

Explanation

The series follows an alternating logic of multiplication and addition using consecutive integers starting from 2. The operations performed are as follows:

First term to second term: 24 × 2 = 48 Second term to third term: 48 + 3 = 51 Third term to fourth term: 51 × 4 = 204 Fourth term to fifth term: 204 + 5 = 209

The pattern established is multiplication by n and addition of n + 1, where n increases by 1 at each step (× 2, + 3, × 4, + 5). Therefore, the next step in the sequence requires multiplying the current term by 6.

Calculation: 209 × 6 = 1254

Explanation

The coding pattern involves dividing the six-letter word into two halves of three letters each. For each half, the sequence of letters is reversed, and then each letter is shifted forward by one position in the English alphabet (+1).

In the word MARGIN, the first half is MAR. Reversing it gives RAM. Adding 1 to each letter (R+1=S, A+1=B, M+1=N) results in SBN. The second half is GIN. Reversing it gives NIG. Adding 1 to each letter (N+1=O, I+1=J, G+1=H) results in OJH. Putting them together yields SBNOJH.

Applying this logic to PRAYER, the first half is PRA. Reversing it gives ARP. Shifting each letter forward by one (A+1=B, R+1=S, P+1=Q) results in BSQ. The second half is YER. Reversing it gives REY. Shifting each letter forward by one (R+1=S, E+1=F, Y+1=Z) results in SFZ. Combining the two parts gives the final code BSQSFZ.

Explanation

The relationship between the numbers in the given set (15, 315, 7) is defined by the formula: Middle Number = First Number × Third Number × 3

Substituting the values from the set: 15 × 7 × 3 = 105 × 3 = 315

Applying this same logic to the numbers in the set (18, 486, 9): 18 × 9 × 3 = 162 × 3 = 486

The calculation confirms that the product of the first and third numbers, when multiplied by a constant factor of 3, yields the middle number.

Explanation

The logic followed in the given letter-clusters is based on the numerical positions of the letters in the English alphabet (A=1, B=2, …, Z=26). In three of the options, the difference between the letters follows a consistent pattern of +5 and +6. For instance, in NSY, N (14) + 5 = S (19) and S (19) + 6 = Y (25). Similarly, in TYE, T (20) + 5 = Y (25) and Y (25) + 6 = E (31 ≡ 5). In LQW, L (12) + 5 = Q (17) and Q (17) + 6 = W (23). However, in the cluster PUB, the positions are P (16), U (21), and B (28 ≡ 2). While the difference between P and U is +5, the difference between U and B is +7. This variation in the second difference makes it the odd cluster.

Explanation

The relationship established in the first pair is that of a primary internal component to the device it serves. A cartridge is an essential part housed within a printer that contains the ink or toner required for the printing process. Similarly, a motherboard is the fundamental internal circuit board located inside the Central Processing Unit or system cabinet, providing the electrical connections and pathways through which all other hardware components of the computer communicate.

Explanation

The series follows a logical decrement pattern for each letter position within the clusters. For the first letter of each cluster, the sequence is W, T, Q, N. The positional values in the English alphabet are W = 23, T = 20, Q = 17, and N = 14. This indicates a constant subtraction of 3 from the previous letter's position. Therefore, the next first letter is 14 - 3 = 11, which is K.

For the second letter, the sequence is U, S, Q, O. The alphabetical positions are U = 21, S = 19, Q = 17, and O = 15. This shows a constant subtraction of 2. The next second letter is 15 - 2 = 13, which is M.

For the third letter, the sequence is W, V, U, T. The alphabetical positions are W = 23, V = 22, U = 21, and T = 20. This shows a constant subtraction of 1. The next third letter is 20 - 1 = 19, which is S. Combining these derived letters results in the cluster KMS.

Explanation

The series follows an alternating subtraction pattern based on the positions of the letters in the English alphabet. Assigning numerical values to the letters where A=1, B=2, …, Z=26, the given series is P(16), N(14), J(10), H(8). The differences between consecutive terms are 14 - 16 = -2, 10 - 14 = -4, and 8 - 10 = -2. The pattern of subtraction is -2, -4, -2, -4, …. Applying the next subtraction in the pattern, we subtract 4 from the position of H: 8 - 4 = 4. The letter corresponding to the 4th position in the alphabet is D.

Explanation

The given pair establishes a relationship between a specific sport and a prominent Indian athlete who plays that sport professionally. Shikhar Dhawan is a well-known international cricketer representing India. Mary Kom is a highly distinguished Indian amateur boxer who has won multiple World Championships and an Olympic medal, thus maintaining the same relationship of a sport paired with its corresponding iconic player.

Explanation

The pattern followed by the number pairs is x = (y + 1)² + y, where x is the first number and y is the second number. In the pair 182:12, substituting y = 12 into the formula gives (12 + 1)² + 12 = 13² + 12 = 169 + 12 = 181. Since the calculated value is 181 but the given first number is 182, this pair does not conform to the relationship shared by the other pairs.

Explanation

The sequence of signs in option c is ÷, +, -, ×, =. Applying these signs to the expression 1496 8 13 40 5 * 0 results in the equation 1496 ÷ 8 + 13 - 40 × 5 = 0. Following the BODMAS rule, first perform the division: 1496 ÷ 8 = 187. Next, perform the multiplication: 40 × 5 = 200. Substituting these values back into the equation gives 187 + 13 - 200 = 0. Adding the terms results in 200 - 200 = 0, which simplifies to 0 = 0. Since both sides of the equation are equal, the combination of signs correctly balances the expression.

Explanation

Dictionary order is determined by comparing words letter by letter from left to right. All words begin with the prefix Int. For word 1 (Introduce), the fourth letter is r. For words 2, 3, 4, 5, and 6, the fourth letter is e. Since e appears before r in the alphabet, word 1 will be the last in the sequence.

To order the remaining words (Internship, Interaction, Interjection, Intervene, Interruption), we compare them starting from the sixth letter as they all share the common prefix Inter. The sixth letters are a in Interaction (3), j in Interjection (4), n in Internship (2), r in Interruption (6), and v in Intervene (5). Arranging these letters in alphabetical order gives a, j, n, r, and then v. Consequently, the sequence for these words is 3, 4, 2, 6, 5. Appending word 1 at the end results in the final dictionary arrangement: 3, 4, 2, 6, 5, 1.

Explanation

The logic followed in the given number pairs is that the first number is obtained by adding the second number to the cube of the sum of the second number and 2. The mathematical formula representing this relationship is x = (y + 2)³ + y, where x is the first number and y is the second number in the pair.

In the pair 1008:8, the calculation is (8 + 2)³ + 8 = 10³ + 8 = 1000 + 8 = 1008. In the pair 220:4, the calculation is (4 + 2)³ + 4 = 6³ + 4 = 216 + 4 = 220.

Applying the same logic to the missing number related to 6, the calculation is (6 + 2)³ + 6 = 8³ + 6 = 512 + 6 = 518.

Explanation

Let the cost per piece of a mango, a banana, and a guava be 3x, 2x, and 1x respectively, based on the given ratio 3:2:1. The total cost for 6 mangoes, 3 bananas, and 10 guavas is expressed by the equation 6(3x) + 3(2x) + 10(1x) = 136.

Simplifying the equation gives 18x + 6x + 10x = 136, which results in 34x = 136. Solving for x, we find x = 4.

The cost per piece is therefore ₹12 for a mango, ₹8 for a banana, and ₹4 for a guava. The total cost of 1 mango, 2 bananas, and 3 guavas is calculated as 1(12) + 2(8) + 3(4). This equals 12 + 16 + 12, which totals ₹40.

Explanation

Conclusion I is the logical conversion of the statement that all envelopes are copies. Since the set of envelopes is entirely contained within the set of copies, there is a necessary overlap where some members of the set of copies are also envelopes.

Conclusion III is established by combining the second and third statements. The second statement confirms that some cards are envelopes. Because the third statement specifies that every envelope is a copy, those specific cards which are envelopes are inevitably copies. This ensures a definite intersection between the set of cards and the set of copies.

Explanation

The letter-clusters are structured using pairs of opposite letters where the sum of their alphabetical positions equals 27. In the cluster SHLO, the first pair consists of S (19) and H (8), and the second pair consists of L (12) and O (15). The logic used to differentiate the clusters is the numerical gap between the second and third letters. In SHLO, the transition from the second letter H (8) to the third letter L (12) involves an increment of 4. In contrast, the other clusters follow a pattern where the third letter is determined by adding exactly 3 to the position of the second letter. This variation in the increment value makes SHLO the different cluster.

Explanation

The code for each word is derived such that the sum of the numerical values in the code is equal to the sum of the positional values of the letters in the alphabet (where A=1, B=2, ..., Z=26).

For 'PAYMENT': P = 16, A = 1, Y = 25, M = 13, E = 5, N = 14, T = 20 Sum of positions = 16 + 1 + 25 + 13 + 5 + 14 + 20 = 94 Code provided: 6101814111520 Breaking the code into individual values: 6, 10, 18, 14, 11, 15, 20 Sum of code values = 6 + 10 + 18 + 14 + 11 + 15 + 20 = 94

For 'JUSTIFY': J = 10, U = 21, S = 19, T = 20, I = 9, F = 6, Y = 25 Sum of positions = 10 + 21 + 19 + 20 + 9 + 6 + 25 = 110 Code provided: 11141519151620 Breaking the code into individual values: 11, 14, 15, 19, 15, 16, 20 Sum of code values = 11 + 14 + 15 + 19 + 15 + 16 + 20 = 110

For 'COMPARE': C = 3, O = 15, M = 13, P = 16, A = 1, R = 18, E = 5 Sum of positions = 3 + 15 + 13 + 16 + 1 + 18 + 5 = 71

Evaluating the options based on the sum of their numerical groups: a) 681013101113: 6 + 8 + 10 + 13 + 10 + 11 + 13 = 71 b) 601811031131: 60 + 18 + 11 + 3 + 11 + 31 = 134 c) 613101113801: 6 + 13 + 10 + 11 + 13 + 8 + 1 = 62 d) 680113111103: 6 + 8 + 0 + 1 + 13 + 1 + 1 + 11 + 0 + 3 = 44

Only option a) satisfies the condition where the sum of the code values equals the sum of the letters' alphabetical positions.