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

Explanation

The relationship between the numbers in the set (44, 24, 132) follows the pattern where the product of the first two numbers divided by 8 equals the third number. This can be expressed by the formula n₃ = (n₁ × n₂)/(8). Applying this to the given set, we have (44 × 24)/(8) = 44 × 3 = 132.

Applying the same logic to the numbers in the set (56, 26, 182), we take n₁ = 56 and n₂ = 26. Calculating the third number gives (56 × 26)/(8) = 7 × 26 = 182. Since the result matches the third number of the set, the relationship is consistent.

Explanation

To find the day of the week on 15 June 2012, we first calculate the total number of odd days between 19 July 2000 and 19 July 2012.

The total number of years is 2012 - 2000 = 12 years. Each ordinary year has 1 odd day, and each leap year has 2 odd days. Between 19 July 2000 and 19 July 2012, the leap years are 2004, 2008, and 2012 (since the month of February 2012 is included in this period, whereas February 2000 is not).

Total odd days from years = 12 years + 3 leap days = 15 days. 15 7 = 1 odd day. Since 19 July 2000 was a Wednesday, 19 July 2012 would be Wednesday + 1 day = Thursday.

Next, we calculate the number of days to go back from 19 July 2012 to 15 June 2012: Days in July = 19 Days in June = 30 - 15 = 15 Total days = 19 + 15 = 34 days.

Now, find the odd days in 34 days: 34 7 = 6 odd days. Counting back 6 days from Thursday (or forward 1 day, since 7 - 6 = 1) gives Friday.

Explanation

To arrange words in dictionary order, we compare them letter by letter from left to right. All six words begin with the letters Ca. Comparing the third letters, Callous (5) has l, while the others have r. Since l comes before r in the alphabet, Callous (5) is the first word in the sequence.

Among the remaining words, we examine the fourth letters. Cardinal (1) and Cardiac (3) both have d, Careless (6) has e, Carrot (4) has r, and Cartography (2) has t. In alphabetical order, d comes before e, e comes before r, and r comes before t.

To determine the order between Cardiac (3) and Cardinal (1), we look at the seventh letter. Cardiac (3) has c, and Cardinal (1) has n. Since c precedes n, Cardiac (3) comes before Cardinal (1).

Following the fourth-letter alphabetical sequence, Careless (6) follows the d-words, then Carrot (4) follows with r, and Cartography (2) is last with t. This gives the final dictionary order: 5, 3, 1, 6, 4, 2.

Explanation

Pedology is the branch of science that deals with the study of soil, including its formation, physical and chemical properties, and classification. Similarly, Pomology is the branch of botany and agriculture that focuses on the scientific study of fruits and their cultivation. Both pairs establish a relationship between a specific field of scientific study and the subject matter it investigates.

Explanation

Timid is the odd one out because it represents a personality trait or a character disposition, specifically indicating a lack of courage or self-confidence. In contrast, Excited, Nostalgic, and Energised are adjectives that describe specific emotional states or transient feelings that an individual experiences. While the other three words refer to temporary psychological or physiological responses, Timid identifies an inherent quality or a behavioral characteristic of a person.

Explanation

The series follows a consistent pattern for each position of the letter-clusters based on alphabetical order.

For the first letter, there is a constant decrement of 1: Y(25) - 1 = X(24), X(24) - 1 = W(23), W(23) - 1 = V(22), and V(22) - 1 = U(21).

For the second letter, there is a constant increment of 2: T(20) + 2 = V(22), V(22) + 2 = X(24), X(24) + 2 = Z(26), and Z(26) + 2 = B(2).

For the third letter, there is a constant decrement of 3: U(21) - 3 = R(18), R(18) - 3 = O(15), O(15) - 3 = L(12), and L(12) - 3 = I(9).

For the fourth letter, there is a constant increment of 4: Q(17) + 4 = U(21), U(21) + 4 = Y(25), Y(25) + 4 = C(3), and C(3) + 4 = G(7).

Combining these transformations from the second cluster XVRU, the missing cluster is found by calculating X-1, V+2, R-3, and U+4, which yields WXOY.

Explanation

The statement all cupboards are windows implies that the entire set of cupboards is contained within the set of windows (C ⊆ W). The statement no door is a window establishes that there is no intersection between the set of doors and the set of windows (D ∩ W = ∅). Since every cupboard is a window and no window is a door, it logically follows that no cupboard can be a door (C ∩ D = ∅). This makes conclusion II valid. There is no logical connection provided in the premises to establish a definite relationship between cupboards and racks or between racks and windows, meaning conclusions I and III do not necessarily follow from the given information.

Explanation

The relationship between the numbers follows the pattern x = (y - 3)² + 1, where y is the second number and x is the first number in each pair. In the first pair 485:25, the calculation is (25 - 3)² + 1 = 22² + 1 = 484 + 1 = 485. In the third pair 401:23, the logic holds as (23 - 3)² + 1 = 20² + 1 = 400 + 1 = 401. Following this consistent mathematical pattern for the second pair where y = 21, the missing first number is calculated as (21 - 3)² + 1 = 18² + 1 = 324 + 1 = 325.

Explanation

The coding pattern alternates between the opposite alphabetical rank and the direct alphabetical rank of each letter. The opposite rank of a letter is calculated using the formula 27 - n, where n is the standard position of the letter in the alphabet (A=1, B=2, …, Z=26).

For TERMITE, the positions are calculated as follows: T is the 20th letter; its opposite rank is 27 - 20 = 7. E is the 5th letter; its direct rank is 5. R is the 18th letter; its opposite rank is 27 - 18 = 9. M is the 13th letter; its direct rank is 13. I is the 9th letter; its opposite rank is 27 - 9 = 18. T is the 20th letter; its direct rank is 20. E is the 5th letter; its opposite rank is 27 - 5 = 22.

Combining these numerical values in sequence results in the code 75913182022.

Explanation

The equation is balanced by applying the BODMAS rule to the sequence of signs provided in option c), which are ×, +, -, ÷, =.

Substituting these signs into the equation gives: 14 × 7 + 39 - 133 ÷ 19 = 130

Following the order of operations: First, perform the division: 133 ÷ 19 = 7 Next, perform the multiplication: 14 × 7 = 98 Then, perform the addition and subtraction: 98 + 39 - 7 137 - 7 = 130

The calculation results in 130 = 130, which balances the equation.

Explanation

The series is formed by four repeating blocks of five letters each. The pattern for each block is J P C X D, where X represents a variable letter that increments alphabetically in each successive block.

Block 1: J P (C) L D Block 2: (J) P (C) M D Block 3: J (P) C (N) D Block 4: (J) P C (O) D

By aligning these blocks, we can observe that the letters J, P, C, and D are constants in their respective positions (1st, 2nd, 3rd, and 5th), while the 4th position follows the sequence L → M → N → O.

The missing letters required to complete these blocks are: 1st blank: C (from Block 1) 2nd and 3rd blanks: J, C (from Block 2) 4th and 5th blanks: P, N (from Block 3) 6th and 7th blanks: J, O (from Block 4)

Combining these sequentially results in the letter combination: C, J, C, P, N, J, O.

Explanation

The given expression W # Q @ T | Y @ M % K establishes a sequence of familial relationships. The segment T | Y indicates that T is the husband of Y. The segment Y @ M indicates that Y is the daughter of M. The segment M % K indicates that M is the wife of K, which implies that K is the husband of M and therefore the father of Y. Since K is the father of Y and T is the husband of Y, K is the father-in-law of T.

Explanation

The numbers in the given set (47, 64, 55) follow a specific mathematical relationship where the third number is the sum of the first number and the square root of the second number. Using the formula n₃ = n₁ + √(n₂), the calculation for the set is 47 + √(64) = 47 + 8 = 55.

In the set (46, 49, 53), the same pattern is applied. The second number 49 is a perfect square with a square root of 7. Adding this value to the first number, 46, results in the third number: 46 + √(49) = 46 + 7 = 53.

Explanation

The letter-clusters are analyzed by converting each letter to its corresponding numerical position in the English alphabet, where A=1, B=2, …, Z=26. In the clusters TXDL and BFLT, the difference between consecutive letters follows an increasing sequence of +4, +6, and +8. For the cluster BFLT, the positions are B(2), F(6), L(12), and T(20). The gaps are 2+4=6, 6+6=12, and 12+8=20. For the cluster TXDL, the positions are T(20), X(24), D(4 or 30), and L(12 or 38). The gaps are 20+4=24, 24+6=30, and 30+8=38.

The cluster LOUC is the different one because it fails to follow this specific increment pattern. Its positional values are L(12), O(15), U(21), and C(3 or 29). The gaps in this cluster are 12+3=15, 15+6=21, and 21+8=29. While the second and third gaps match the sequence, the first gap is +3 instead of +4. Additionally, LOUC is the only cluster among the options that contains vowels (O and U), whereas the others consist entirely of consonants.

Explanation

The relationship between the words in the first pair is based on degrees of intensity and method. To coerce means to compel or persuade someone through the use of force or threats, representing a more extreme and assertive form of persuasion. To maintain a similar relationship for the second pair, the required word must represent an extreme or high-intensity state of the base word. Furious is defined as being extremely angry or full of intense rage, thus serving as the high-intensity counterpart to the word angry.

Explanation

The coding logic follows a pattern based on whether the letter is a vowel or a consonant. Consonants are replaced by the letter immediately preceding them in the English alphabet (-1), while vowels (A, E, I, O, U) are replaced by the letter immediately succeeding them (+1).

In DARK, the consonant D becomes 4 - 1 = 3 (C), the vowel A becomes 1 + 1 = 2 (B), the consonant R becomes 18 - 1 = 17 (Q), and the consonant K becomes 11 - 1 = 10 (J), resulting in CBQJ.

In SOUND, the consonant S becomes 19 - 1 = 18 (R), the vowel O becomes 15 + 1 = 16 (P), the vowel U becomes 21 + 1 = 22 (V), the consonant N becomes 14 - 1 = 13 (M), and the consonant D becomes 4 - 1 = 3 (C), resulting in RPVMC.

Applying this logic to TOXIC: T (Consonant) → 20 - 1 = 19 (S) O (Vowel) → 15 + 1 = 16 (P) X (Consonant) → 24 - 1 = 23 (W) I (Vowel) → 9 + 1 = 10 (J) C (Consonant) → 3 - 1 = 2 (B)

The coded word is SPWJB.

Explanation

The series is formed by applying a specific mathematical operation to the alphabetical position of each letter in the clusters. For the first letter of each cluster, there is a constant increment of 3: M (13) + 3 = P (16), P (16) + 3 = S (19), S (19) + 3 = V (22), and V (22) + 3 = 25 (Y). For the second letter, the pattern also involves a constant increment of 3: E (5) + 3 = H (8), H (8) + 3 = K (11), K (11) + 3 = N (14), and N (14) + 3 = 17 (Q).

For the third letter, the pattern follows a constant decrement of 4: N (14) - 4 = J (10), J (10) - 4 = F (6), F (6) - 4 = B (2), and B (2) - 4 in cyclic order results in 24 (X). Similarly, the fourth letter follows a constant decrement of 4: D (4) - 4 = Z (26), Z (26) - 4 = V (22), V (22) - 4 = R (18), and R (18) - 4 = 14 (N). Combining these derived letters results in the cluster YQXN.

Explanation

PROPOSED: [a]

Sripad's father's mother is his paternal grandmother. The only daughter of his paternal grandmother is his father's sister, who is Sripad's paternal aunt.

The elder daughter of Sripad's paternal aunt is Sripad's cousin. According to the statement, the baby girl is the daughter of this elder daughter.

Since the baby girl's mother is the elder daughter of Sripad's aunt, she is Sripad's cousin.

Explanation

The relation for the number-pairs is defined by the formula y = 6x - 5. When the first number 27 is substituted into this formula, the result is 27 × 6 - 5 = 162 - 5 = 157. Because the second number provided in this pair is 82, it does not conform to the established mathematical logic.

Explanation

The relationship between the numbers in the set (12, 14, 143) follows the logic where the product of the first number minus one and the second number minus one equals the third number. Applying this formula (n₁ - 1) × (n₂ - 1) = n₃ to the given set, we get (12 - 1) × (14 - 1) = 11 × 13 = 143.

Following the same logic for the set in option d, we subtract one from the first two numbers and multiply them: (15 - 1) × (19 - 1) = 14 × 18. Calculating this product, 14 × 18 = 252, which matches the third number in the set.

Explanation

The numbers in the given set (64, 91, 118) follow an arithmetic progression with a constant common difference of 27. This is shown by the calculations 91 - 64 = 27 and 118 - 91 = 27. In the set provided in option a), the difference between the first two numbers is 73 - 46 = 27, which matches the pattern. However, the difference between the second and third numbers is 101 - 73 = 28. Because this second difference does not equal 27, the set in option a) is not related in the same way as the numbers in the original set.

Explanation

To make the equation 156 - 13 + 9 × 18 ÷ 5 = 169 correct, the signs ÷ and - are interchanged. The modified equation becomes 156 ÷ 13 + 9 × 18 - 5 = 169. Following the BODMAS rule, the division is performed first, which gives 156 ÷ 13 = 12. Then, the multiplication is performed, resulting in 9 × 18 = 162. Substituting these values into the expression yields 12 + 162 - 5. Finally, performing addition and subtraction results in 174 - 5 = 169, which satisfies the given equation.

Explanation

Let x be the number of years after marriage when Sanju was born. A silver wedding anniversary marks 25 years of marriage, while a golden wedding anniversary marks 50 years of marriage.

According to the question, Sanju's age 18 years after his parents' marriage was (18 - x). His age at their golden anniversary, which is 50 years after the marriage, was (50 - x). The ratio of these ages is given as 5:21.

We can set up the equation: (18 - x)/(50 - x) = ⁵⁄₂₁

Cross-multiplying to solve for x: 21(18 - x) = 5(50 - x) 378 - 21x = 250 - 5x 378 - 250 = 21x - 5x 128 = 16x x = ¹²⁸⁄₁₆ = 8

Sanju was born 8 years after his parents' marriage.

Explanation

The series consists of 20 characters that follow a repetitive pattern when divided into four equal groups of five letters each. By observing the distribution of the letters r, m, v, q, and l, it is evident that the sequence rmvql repeats throughout the series. Dividing the given string into blocks of five results in the segments r_vql, mv_l, rm_q, and rm_ql. To maintain the consistent unit rmvql in every block, the blanks must be filled with the letters m, r, q, v, l, and v in that specific order. This results in the complete string rmvqlrmvqlrmvqlrmvql.

Explanation

A tintometer is a specialized instrument used to measure the intensity and quality of color by comparing it against standard scales. This establishes a relationship between a measuring device and the specific physical property it quantifies. Similarly, a protractor is the standard mathematical tool designed specifically for measuring the magnitude of angles in degrees.

Explanation

The relationship established in the first pair is Country: Capital, as Ottawa is the capital city of Canada. Following this same logic, Havana is the capital city of Cuba, serving as its political, economic, and cultural center.

Explanation

The coding logic follows two steps: first, the order of the letters in the word is reversed, and second, each letter is shifted forward by 3 positions in the English alphabet.

In the case of COW: Reverse the letters to get W-O-C. Apply the +3 shift to each letter's position: W (23) + 3 = 26, which is Z. O (15) + 3 = 18, which is R. C (3) + 3 = 6, which is F. This gives the code ZRF.

To find the code for RAT: Reverse the letters to get T-A-R. Apply the +3 shift to each letter's position: T (20) + 3 = 23, which is W. A (1) + 3 = 4, which is D. R (18) + 3 = 21, which is U. Following this transformation, RAT is written as WDU.

Explanation

Dictionary order is determined by comparing words character by character from left to right. All five words begin with the letters To. Comparing the third letters of each word, g in Together (4) comes first in alphabetical order. This is followed by l in Tolerance (3), and then m in Tomorrow (5). The remaining two words, Topology (1) and Topper (2), both have p as their third letter, requiring a comparison of their fourth letters. Since o in Topology (1) precedes p in Topper (2) in the alphabet, Topology comes before Topper. Arranging these based on these alphabetical priorities results in the sequence 4, 3, 5, 1, 2.

Explanation

Based on the first statement, all pencils are contained within the category of erasers (P ⊆ E). The second statement establishes that there is an intersection between sharpeners and pencils (S ∩ P ≠ ∅). Since every pencil is an eraser, the portion of sharpeners that are pencils must also belong to the set of erasers (S ∩ P ⊆ S ∩ E). Therefore, the conclusion that some sharpeners are erasers logically follows. Regarding conclusion II, the premise that some sharpeners are pencils does not provide sufficient information to assert that the entire set of pencils is contained within sharpeners.

Explanation

The coding logic is defined by the formula: (Sum of the numerical positions of the letters in the English alphabet) × (Total number of letters in the word). For the word MINT, the positional values are M=13, I=9, N=14, and T=20. The sum of these values is 13 + 9 + 14 + 20 = 56. Since the word contains 4 letters, the code is 56 × 4 = 224. For the word FANCY, the positional values are F=6, A=1, N=14, C=3, and Y=25. The sum is 6 + 1 + 14 + 3 + 25 = 49. Multiplying this by the 5 letters in the word gives 49 × 5 = 245.

Applying this same logic to the word CONTOUR, the positional values are C=3, O=15, N=14, T=20, O=15, U=21, and R=18. The sum of these numerical positions is 3 + 15 + 14 + 20 + 15 + 21 + 18 = 106. As the word CONTOUR consists of 7 letters, the final code is calculated as 106 × 7 = 742.

Explanation

In the given letter-clusters, the first and fourth letters are alphabetical opposites, meaning the sum of their positional values is 27. In the cluster FHWU, F = 6 and U = 21, so 6 + 21 = 27. While all four options follow this rule for the first and fourth letters, a secondary pattern exists for the second and third letters. In the other three clusters, the sum of the positional values of the second and third letters is always 17. For example, in TFKG, F(6) + K(11) = 17; in RDMI, D(4) + M(13) = 17; and in JNCQ, N(14) + C(3) = 17. In contrast, for the cluster FHWU, the positional values of the second letter H (8) and the third letter W (23) sum to 8 + 23 = 31. Because it deviates from the consistent sum of 17 for the middle pair, FHWU is the different cluster.

Explanation

The relationship follows the pattern n : (n² + 2). For the first pair, the square of 23 is 529, and adding 2 results in 529 + 2 = 531. Applying the same logic to the third number, the square of 27 is 729. Adding 2 to this value gives 729 + 2 = 731.

Explanation

Ecology is the branch of biology that deals with the relations of organisms to one another and to their physical surroundings. It focus on ecosystems and environmental interactions. The other three terms are specific branches of medical science or anatomy dedicated to the study of particular organs or systems within the human body. Because ecology pertains to environmental relationships rather than specific human anatomical specializations, it is the different word in the group.

Explanation

The provided sequence is an alternating series consisting of two interleaved sub-sequences. The first sub-sequence consists of the terms at the odd positions: 3, 38, 75, and 114. These terms follow a pattern of adding increasing odd numbers where 3 + 35 = 38, 38 + 37 = 75, and 75 + 39 = 114.

The second sub-sequence consists of the terms at the even positions: 20, 52, 82, and the required term. The terms in this sub-sequence follow a pattern where the value added to each term decreases by 2 at each step. The difference between 20 and 52 is 32, and the difference between 52 and 82 is 30. Following this decreasing pattern, the next difference to be added is 30 - 2 = 28. Thus, the missing number is determined by the calculation 82 + 28 = 110.

Explanation

By substituting the signs from option d sequentially into the given expression, the equation becomes 135 ÷ 15 × 3 + 2 - 13 = 16. To solve this, apply the BODMAS rule, which prioritizes division and multiplication before addition and subtraction.

First, perform the division: 135 ÷ 15 = 9. The equation simplifies to 9 × 3 + 2 - 13 = 16.

Next, perform the multiplication: 9 × 3 = 27. The equation simplifies to 27 + 2 - 13 = 16.

Finally, perform the addition and subtraction: 29 - 13 = 16. Since 16 = 16, the mathematical signs in option d correctly balance the equation.

Explanation

To arrange the words in dictionary order, we compare them letter by letter from left to right. All five words begin with the prefix In.

Comparing the third letter of each word, word 2 (Independent) has the letter d, while the others (1, 3, 4, 5) have the letter t. Since d precedes t in the alphabet, Independent (2) is the first word in the sequence.

Next, we compare the remaining words which all start with Int. Looking at the fifth letter, word 3 (Intentional) has n, whereas words 1, 4, and 5 have r. As n comes before r, Intentional (3) is the second word in the sequence.

Finally, we compare words 1, 4, and 5, which all share the prefix Inter. We examine the sixth letter: word 5 (Interactive) has a, word 1 (Interchangeable) has c, and word 4 (Interesting) has e. Following alphabetical order where a comes before c, and c comes before e, the words follow the order 5, then 1, and finally 4. This results in the complete sequence 2, 3, 5, 1, 4.

Explanation

The coding logic follows the pattern of multiplying the numerical positional value of each letter in the English alphabet by its position within the specific word. In the word ONE, the first letter O (15) is multiplied by 1 to get 15; the second letter N (14) is multiplied by 2 to get 28; and the third letter E (5) is multiplied by 3 to get 15, yielding the code 15-28-15. Similarly, for the word TWO, T (20) is multiplied by 1 to get 20; W (23) is multiplied by 2 to get 46; and O (15) is multiplied by 3 to get 45, resulting in 20-46-45. Applying this logic to the word SIX, the first letter S (19) is multiplied by 1 to get 19; the second letter I (9) is multiplied by 2 to get 18; and the third letter X (24) is multiplied by 3 to get 72. This produces the code 19-18-72.

Explanation

The number-pairs follow a specific mathematical pattern where the first number is the square of a base integer x, and the second number is the cube of the next consecutive integer (x+1).

In option b, 64 = 8² and 729 = (8+1)³ = 9³. In option c, 49 = 7² and 512 = (7+1)³ = 8³. In option d, 25 = 5² and 216 = (5+1)³ = 6³.

Following this logic for option a, since the first number is 36 = 6², the second number should be (6+1)³ = 7³ = 343. Because the pair is given as (36, 353), it does not satisfy the x² : (x+1)³ relationship shared by the other pairs.

Explanation

The numbers in the set (12, 60, 84) follow the logic (n, n × 5, n × 7). Taking n = 12, the second number is 12 × 5 = 60 and the third number is 12 × 7 = 84. Applying this same pattern to option b where n = 16, we calculate the second number as 16 × 5 = 80 and the third number as 16 × 7 = 112. This consistency in the multiples of 5 and 7 relative to the first number establishes the shared relationship.

Explanation

The series follows a specific arithmetic pattern for each letter position in the clusters. For the first letter, there is a constant increment of +1: R (18) to S (19) to T (20) to U (21), making the next letter 21 + 1 = 22, which is V. For the second letter, there is a constant decrement of -2: O (15) to M (13) to K (11) to I (9), making the next letter 9 - 2 = 7, which is G.

For the third letter, the series follows a constant increment of +3: A (1) to D (4) to G (7) to J (10), making the next letter 10 + 3 = 13, which is M. For the fourth letter, there is a constant decrement of -4: D (4) to Z (26) to V (22) to R (18), making the next letter 18 - 4 = 14, which is N. Combining these results yields the cluster VGMN.

Explanation

The coding scheme uses an alternating shift pattern of +5 and +3 applied to the alphabetical positions of each character.

For the word RITU, the transformation is as follows: R (18) + 5 = 23 (W), I (9) + 3 = 12 (L), T (20) + 5 = 25 (Y), and U (21) + 3 = 24 (X).

Similarly, for AMAN, the letters shift as: A (1) + 5 = 6 (F), M (13) + 3 = 16 (P), A (1) + 5 = 6 (F), and N (14) + 3 = 17 (Q).

Applying this specific +5, +3, +5, +3 pattern to the word MIRA, the calculation is: M (13) + 5 = 18 (R) I (9) + 3 = 12 (L) R (18) + 5 = 23 (W) A (1) + 3 = 4 (D)

By combining these results, the code for MIRA is RLWD.

Explanation

The letter-cluster WRO is the outlier because the numerical gaps between its constituent letters do not align with the -4, -3 pattern observed in the rest of the set. For WRO, the alphabetical positions are W(23), R(18), and O(15). The difference between the first and second letters is 23 - 18 = 5, and the difference between the second and third letters is 18 - 15 = 3. In the common pattern, the first difference should be 4, making this cluster the odd one out.

Explanation

The relationship between the numbers in the first pair follows the logic n² + n + 1 = Result. For the first number 9, the calculation is 9² + 9 + 1, which simplifies to 81 + 9 + 1 = 91.

Applying the same pattern to the third number 13, the result is calculated as 13² + 13 + 1 = 169 + 13 + 1 = 183. This can also be expressed as multiplying the number by its consecutive successor and adding one, represented by the formula n × (n + 1) + 1, where 13 × 14 + 1 = 182 + 1 = 183.

Explanation

Conclusion II logically follows because the statements establish a necessary overlap between cars and cycles. Statement 2 specifies that some scooters are cars, meaning there is at least one element common to both the set of scooters (S) and the set of cars (C). Statement 3 asserts that all scooters are cycles, which can be represented as S ⊆ Cy. Since every scooter is also a cycle, any element that is both a scooter and a car must also be a cycle. This ensures that the intersection between cars and cycles is non-empty (C ∩ Cy ≠ ∅), making the conclusion that some cars are cycles valid.

Explanation

The numbers in the given set (59, 118, 295) follow the pattern of x, 2x, and 5x. Taking the first number x = 59, the second number is calculated as 59 × 2 = 118 and the third number is calculated as 59 × 5 = 295. Applying this same logic to the numbers in option d, where the first number x = 17, the second number is 17 × 2 = 34 and the third number is 17 × 5 = 85.

Explanation

The given series consists of 20 positions including the blanks. Dividing the series into four blocks of five letters each reveals a repeating pattern of the string qpltr. By substituting the letters t, q, r, l, p, and t into the six blanks sequentially, the complete sequence becomes qpltr qpltr qpltr qpltr.

The first block qpl_r is completed with t to form qpltr. The second block plt uses q and r to form qpltr. The third block qp_tr is completed with l to form qpltr. Finally, the fourth block q_l_r uses p and t to form qpltr. This uniform repetition of the five-letter unit satisfies the logical requirement of the letter series.

Explanation

Roshan is the son of Guna, so Roshan's father is Guna. The relationship between Hemanth and Guna is determined by the sibling link: Guna and Manu are siblings. Since Hemanth is the father of Manu, he is also the father of Guna. Thus, Hemanth is the father of Roshan's father.

Explanation

The relationship in the given analogy is between an Indian state and its respective High Court. The Allahabad High Court is the principal judicial body for the state of Uttar Pradesh. Similarly, the Patna High Court is the High Court for the state of Bihar. It was established on 3 February 1916 under the Government of India Act 1915 and is situated in the state capital, Patna.

Explanation

To find the combined ratio of the three numbers N₁, N₂, and N₃, we equate the value of the second number in both given ratios. Given N₁ : N₂ = 3:4 and N₂ : N₃ = 5:6, we multiply the first ratio by 5 and the second by 4 to get N₁ : N₂ = 15:20 and N₂ : N₃ = 20:24. The joint ratio is 15:20:24.

Let the numbers be 15x, 20x, and 24x. The difference between the first and third numbers is 24x - 15x = 9x. Given that this difference is 1125, we solve for x: 9x = 1125 x = ¹¹²⁵⁄₉ = 125

The average of the second and third numbers is calculated as: Average = (20x + 24x)/(2) = ⁴⁴ˣ⁄₂ = 22x

Substituting the value of x: Average = 22 × 125 = 2750

Explanation

A plotter is a hardware device that functions as an output unit by receiving digital data from a computer and rendering it into a physical format, such as vector graphics or architectural designs on paper. It is the odd one out in this group because it is used to display or produce information for the user, whereas the other items listed are input devices used to feed data or control signals into the computer system.