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

Explanation

The word pair Horses : Neigh establishes a relationship between an animal and its characteristic vocalization. A neigh is the specific sound produced by a horse. Similarly, a quack is the standard onomatopoeic term for the sound made by ducks, maintaining the same animal-to-sound association.

Explanation

From the premises All polygons are angles and All angles are diagonals, we can conclude through the transitive property that all polygons are diagonals (P ⊆ A ⊆ D). In syllogistic logic, if all members of set P are members of set D, it is necessarily true that at least some members of set D are members of set P. Therefore, Conclusion I follows. Furthermore, we are given that No diagonal is a cube (D ∩ Cube = ∅) and All cones are cubes (Cone ⊆ Cube). Since polygons are a subset of diagonals and cones are a subset of cubes, the disjoint relationship between diagonals and cubes extends to their respective subsets. This means no polygon can overlap with the set of cones, confirming that No polygon is a cone. Thus, Conclusion III also follows.

Explanation

The series follows a double-difference pattern. Calculating the first level of differences between consecutive terms yields 35 - 24 = 11, 51 - 35 = 16, 73 - 51 = 22, and 102 - 73 = 29. To identify the logic governing these values, calculate the second level of differences: 16 - 11 = 5, 22 - 16 = 6, and 29 - 22 = 7. These second differences are consecutive integers, suggesting the next second difference should be 8. By adding this value to the last first difference, we find the next difference in the sequence: 29 + 8 = 37. Adding this difference to the final term of the given series results in 102 + 37 = 139.

Explanation

To arrange words in dictionary order, they must be compared letter by letter from left to right. All given words start with the prefix Fr. Comparing the third letter of each word, Fraud (5) contains a, Freedom (2) and Freeze (1) contain e, Fringe (6) contains i, Frozen (4) contains o, and Fryer (3) contains y. Since a is the first letter alphabetically, Fraud (5) appears first.

For the words Freedom (2) and Freeze (1), the first four letters F-r-e-e are identical. Comparing the fifth letter, d in Freedom comes before e in Freeze, so 2 precedes 1. Next, among the remaining words, the third letters follow the alphabetical sequence i, o, and then y. This places Fringe (6) fourth, Frozen (4) fifth, and Fryer (3) sixth. Therefore, the correct dictionary order is 5, 2, 1, 6, 4, 3.

Explanation

In the letter cluster NJFA, the numerical positions of the letters in the English alphabet are N = 14, J = 10, F = 6, and A = 1. The difference between the first and second letter is 14 - 10 = 4, and the difference between the second and third letter is 10 - 6 = 4. However, the difference between the third and fourth letter is 6 - 1 = 5. This cluster is the different one because it fails to maintain the consistent pattern of subtracting 4 from the position of each letter to obtain the next, which is the logic followed by the other clusters in the set.

Explanation

N is the son of B, and since B is not the mother, B must be the father of N. D and B are a married couple, which implies that D is the mother of N. The problem states that T is the daughter of D, meaning both N and T are children of the same parents, B and D. Since N is a male child (the son) and T is a female child (the daughter), N is the brother of T.

Explanation

Substituting the signs from option a into the equation 42 7 64 11 6 * 4 results in the mathematical expression 42 ÷ 7 + 64 - 11 × 6 = 4. Following the BODMAS rule, division is performed first, giving 42 ÷ 7 = 6. Next, multiplication is carried out, yielding 11 × 6 = 66. The equation then simplifies to 6 + 64 - 66 = 4. Performing addition gives 70 - 66 = 4, and the final subtraction results in 4 = 4. This sequence of signs correctly balances the equation.

Explanation

Let the total number of players be T. Initially, hotel X has ¹⁰⁰⁄₃% of the total players, which is equivalent to ⅓T. Consequently, hotel Y has the remaining ⅔T players.

According to the first condition, shifting 20 players from hotel Y to hotel X makes the number of players in hotel X equal to 50% of the total: ⅓T + 20 = ½T

To find T, rearrange the equation: ½T - ⅓T = 20 (3T - 2T)/(6) = 20 ⅙T = 20 T = 120

The initial number of players in hotel X is ⅓ × 120 = 40. In the second scenario, if 20 players shift from hotel X to hotel Y, the new number of players in hotel X becomes 40 - 20 = 20.

To find the percentage of the total players this represents: Percentage = (New players in X)/(Total players) × 100 Percentage = ²⁰⁄₁₂₀ × 100 = ⅙ × 100 = 16.666...%

Rounding to two decimal places, the percentage is 16.67%.

Explanation

The relationship in the first pair is based on a condition and the psychological or physiological function it affects. Depression is a medical condition categorized as a mood disorder, as it primarily impacts an individual's emotional state. Following this logic, insomnia is a clinical condition characterized by the inability to fall asleep or maintain restful sleep. Therefore, just as depression pertains to mood, insomnia pertains to sleep.

Explanation

The series follows a systematic pattern for each letter position within the clusters. For the first three positions, each letter shifts forward by two places in the alphabetical sequence. In the first position, we have P + 2 = R, R + 2 = T, T + 2 = V, so the next letter is V + 2 = X. In the second and third positions, both follow the same logic: N + 2 = P, P + 2 = R, R + 2 = T, making the next letters T + 2 = V. The fourth position in each cluster consists of the sequential English vowels A, E, I, and O, which means the next letter in this sequence is U. Combining these patterns results in the letter cluster XVVU.

Explanation

The pattern follows a row-wise logic based on the sum of the numbers in each row and the individual elements of the first row.

First, calculate the sum of the elements in the first and third rows: Sum of Row 1: 4 + 7 + 6 = 17 Sum of Row 3: 44 + 68 + 60 = 172

The relationship between the sums of the rows is as follows: Sum of Row 2 = (3 × Sum of Row 1) + First element of Row 1 Sum of Row 3 = (3 × Sum of Row 2) + Second element of Row 1

Substituting the known values into the first equation: Sum of Row 2 = (3 × 17) + 4 = 51 + 4 = 55

Now, verify this result using the second equation: Sum of Row 3 = (3 × 55) + 7 = 165 + 7 = 172

Since the sum of Row 3 matches the calculated sum (172), the sum of Row 2 must be 55. We can now find the missing number (x) in the second row: 15 + x + 21 = 55 36 + x = 55 x = 55 - 36 x = 19

Explanation

The given number pairs follow a consistent mathematical relationship where the second number is the result of the first number multiplied by its successor, defined by the formula n : n(n + 1) or n : n² + n. For the pair 17:307, applying this logic gives 17 × (17 + 1) = 17 × 18 = 306. Since the value provided in the pair is 307 instead of 306, it fails to satisfy the logic shared by the other sets.

Explanation

The letter series is composed of 18 characters (including blanks) and can be divided into three groups of six letters each. By substituting the letters from option b) N, P, L, U, Z, N, and A into the seven blanks, the series is completed as follows:

Group 1: L U A (N) Z (P) Group 2: (L) N (U) A P (Z) Group 3: L (N) U (A) P Z

When the letters are filled, the series becomes LUANZP LNUAPZ LNUAPZ. This structure uses the same set of six letters {A, L, N, P, U, Z} for each block. While the first block presents the letters in a specific order, the second and third blocks are identical repetitions (LNUAPZ), establishing a consistent and logical pattern that completes the series.

Explanation

The coding logic distinguishes between consonants and vowels. For consonants, the code uses their standard alphabetical positional value (A=1, B=2, ..., Z=26). For vowels (A, E, I, O, U), the code is calculated by taking twice the reverse alphabetical rank. The reverse rank of a letter is determined by the formula (27 - positional value). Therefore, the value for a vowel is calculated as: Vowel Code = 2 × (27 - positional value)

Applying this to the word PLASTIC: P (Consonant): Positional value = 16 L (Consonant): Positional value = 12 A (Vowel): 2 × (27 - 1) = 2 × 26 = 52 S (Consonant): Positional value = 19 T (Consonant): Positional value = 20 I (Vowel): 2 × (27 - 9) = 2 × 18 = 36 C (Consonant): Positional value = 3

Concatenating these values gives the final code: 1612521920363.

Explanation

The relationship between the numbers in the set (25, 18, 225) is defined by the formula (a × b)/(2) = c, where a and b are the first two numbers and c is the third number. Applying this logic to the given set, we have (25 × 18)/(2) = 25 × 9 = 225. Following the same pattern for the numbers 24 and 22, the calculation is (24 × 22)/(2) = 12 × 22 = 264, which correctly results in the third number of the set.

Explanation

Weight is a physical characteristic of a person that measures the force of gravity on their body mass. In contrast, intelligence, aptitude, and memory are all cognitive or psychological attributes related to the functioning and capacity of the human mind. These three mental faculties involve processing information, learning, and reasoning, whereas weight is a purely biological and physical measurement.

Explanation

The coding follows an alternating pattern of adding/subtracting values and using the opposite letter (where the sum of the positions of the letter and its opposite is 27). The pattern is: +6 for the 1st letter, Opposite for the 2nd letter, -6 for the 3rd letter, Opposite for the 4th letter, +6 for the 5th letter, and so on.

Applying this to PERMIT: P (16) + 6 = 22 (V) E (5) → Opposite is 27 - 5 = 22 (V) R (18) - 6 = 12 (L) M (13) → Opposite is 27 - 13 = 14 (N) I (9) + 6 = 15 (O) T (20) → Opposite is 27 - 20 = 7 (G) Result: VVLNOG

Applying the same pattern to INERTIA: I (9) + 6 = 15 (O) N (14) → Opposite is 27 - 14 = 13 (M) E (5) - 6 = -1. In cyclic order, -1 corresponds to 25 (Y) R (18) → Opposite is 27 - 18 = 9 (I) T (20) + 6 = 26 (Z) I (9) → Opposite is 27 - 9 = 18 (R) A (1) - 6 = -5. In cyclic order, -5 corresponds to 21 (U)

The final code for INERTIA is OMYIZRU.

Explanation

The coding logic involves dividing the word into two equal halves and reversing the order of letters within each half.

For the word SURROUND: Divide it into two halves: SURR and OUND. Reverse the first half (SURR): R-R-U-S. Reverse the second half (OUND): D-N-U-O. Combining these results in the code RRUSDNUO.

Following the same logic for the word MITIGATE: Divide the word into two halves: MITI and GATE. Reverse the first half (MITI): I-T-I-M. Reverse the second half (GATE): E-T-A-G. Combining these gives the code ITIMETAG.

Explanation

The coding logic follows the square of the total number of letters present in the given word. The word NOSTALGIA consists of 9 letters, and the square of 9 is 9² = 81. Applying the same logic to the word FRICTION, which contains 8 letters, we calculate the square of 8 as 8² = 64.

Explanation

The logical relationships can be represented using set theory. Let D be the set of dustbins, P be plastic items, S be stones, and W be woods. The statements provide D ⊆ P, P ∩ S = ∅, and W ⊆ S.

Since D ⊆ P and P ∩ S = ∅, it follows that D ∩ S = ∅. This means no dustbin is a stone. Because all woods are stones (W ⊆ S), and stones have no intersection with dustbins, it is logically certain that no dustbin is wood. This validates Conclusion I.

Similarly, since P ∩ S = ∅ and W ⊆ S, it follows that P ∩ W = ∅. Because the entire set of woods is contained within the set of stones, and stones are entirely separate from plastic items, no plastic item can be wood. This validates Conclusion II.

Conclusion III is incorrect because the definitive separation between P and S (and their respective subsets D and W) makes any overlap between woods and dustbins impossible.

Explanation

The series follows a distinct pattern for each letter position within the clusters:

First letters: N, M, L, K follow a -1 pattern in their alphabetical positions (14, 13, 12, 11). The next letter is 11 - 1 = 10, which is J.

Second letters: Z, B, D, F follow a +2 pattern (26, 2, 4, 6). The next letter is 6 + 2 = 8, which is H.

Third letters: K, H, E, B follow a -3 pattern (11, 8, 5, 2). The next letter is 2 - 3 = -1. In the circular alphabetical order, -1 corresponds to 25 (since 26 is Z/0), which is Y.

Combining these results, the next cluster in the series is JHY.

Explanation

The relationship between the numbers in the set (18, 24, 144) follows the logic that the product of the first and second numbers divided by 3 results in the third number. Using the formula (n1 × n2) ÷ 3 = n3, the calculation for the given set is: (18 × 24) ÷ 3 = 18 × 8 = 144

Applying this same logic to the numbers in option b, (26, 15, 130): (26 × 15) ÷ 3 = 26 × 5 = 130

The third number is derived by multiplying the first number with one-third of the second number, which satisfies the pattern.

Explanation

To make the equation correct, the numbers 48 and 39 are interchanged. The modified equation becomes 78 ÷ 39 × 8 + (26 × 7) - 48 + (45 + 15) = 210. Applying the BODMAS rule, first solve the operations within the brackets: (26 × 7) = 182 and (45 + 15) = 60. The equation is now 78 ÷ 39 × 8 + 182 - 48 + 60. Next, perform the division: 78 ÷ 39 = 2. Then, perform the multiplication: 2 × 8 = 16. The equation simplifies to 16 + 182 - 48 + 60. Adding the positive terms gives 16 + 182 + 60 = 258. Subtracting 48 from this sum results in 258 - 48 = 210. This matches the value on the right-hand side of the equation.

Explanation

The numerical analogy follows the logic that the first number in each pair is obtained by raising the second number to the fourth power and adding 2 to the result. This relation can be expressed as x = n⁴ + 2, where n is the second number and x is the first number.

In the first pair, 83 : 3, the calculation is 3⁴ + 2 = 81 + 2 = 83. In the third pair, 258 : 4, the calculation is 4⁴ + 2 = 256 + 2 = 258.

Applying this same logic to the middle pair, where the second number n is 5, we calculate 5⁴ + 2. Since 5⁴ = 625, adding 2 results in 627.

Explanation

By replacing the asterisks with the operators in the sequence provided in option d, the equation becomes 60 ÷ 2 + 3 × 6 - 5 = 43. Applying the BODMAS rule, the division and multiplication operations are performed first. Calculating 60 ÷ 2 gives 30, and 3 × 6 gives 18. Substituting these values back into the expression results in 30 + 18 - 5. Proceeding with addition and subtraction, 30 + 18 = 48, and 48 - 5 = 43. Since the result matches the value on the right side of the equation, the mathematical signs balance the expression perfectly.

Explanation

In the expression C @ H # M # F, the symbol @ indicates that C is the mother of H. The symbol # indicates a sister relationship. Specifically, H # M means H is the sister of M, and M # F means M is the sister of F. This sequence establishes that H, M, and F are siblings. Since C is the mother of H, and H, M, and F are all part of the same sibling group, it follows logically that C is also the mother of F.

Explanation

The letter-clusters follow a pattern based on the alphabetical positional values where A=1 and Z=26. In three of the clusters, the second letter is the fourth letter after the first (L1 + 4 = L2), the second and third letters are alphabetical opposites whose values sum to 27 (L2 + L3 = 27), and the fourth letter is the third letter before the third (L3 - 3 = L4).

In TXCZ, 20 + 4 = 24 (X), 24 + 3 = 27 (opposites X and C), and 3 - 3 = 0 (which corresponds to Z in cyclic order). In DHSP, 4 + 4 = 8 (H), 8 + 19 = 27 (opposites H and S), and 19 - 3 = 16 (P). In FJQN, 6 + 4 = 10 (J), 10 + 17 = 27 (opposites J and Q), and 17 - 3 = 14 (N).

In the cluster NRJG, while the first and last transitions match the rules (14 + 4 = 18 and 10 - 3 = 7), the middle relationship deviates. The positional values of R (18) and J (10) sum to 28, meaning they are not alphabetical opposites. Since the opposite of R is I (9), the cluster is the odd one out.

Explanation

The relationship between the numbers in the set (5, 11, 275) follows the pattern a² × b = c, where a is the first number, b is the second number, and c is the third number. Substituting the values from the set, we get 5² × 11 = 25 × 11 = 275. Following this logic for option d, the set (4, 16, 256) satisfies the same condition: 4² × 16 = 16 × 16 = 256.

Explanation

The relationship between the given words is that of a country and its capital city. Port Louis is the capital and largest city of the island nation Mauritius. Similarly, Nairobi is the capital and largest city of Kenya. Both pairs follow the specific pattern of Country : Capital.

Explanation

The relationship between the first pair of words is based on antonyms. Conceit refers to excessive pride or vanity in oneself, while modesty is the quality of being humble or moderate in the estimation of one's abilities. Similarly, despair represents the complete loss or absence of hope. To maintain the same relationship, the fourth word must be the antonym of despair. Hope is the feeling of expectation and desire for a particular thing to happen, making it the direct opposite of despair.

Explanation

Psychiatrists are medical specialists who focus on the diagnosis, prevention, and treatment of mental, emotional, and behavioral disorders. This specialization is distinct because it deals primarily with mental health and psychological conditions, whereas the other listed medical professionals specialize in the treatment of specific physical organ systems within the body.

Explanation

The series is formed by repeating a five-letter pattern where the first four letters remain relatively constant as KOCT, while the fifth letter follows an alphabetical or repetitive progression. The series can be divided into groups of five letters as follows:

First Group (1-5): K O C T Q The first blank is at the second position. Filling it with O from the first letter of the option gives K O C T Q.

Second Group (6-10): K O C T R The blanks are at the sixth, ninth, and tenth positions. Filling them with K, T, and R from the option gives K O C T R.

Third Group (11-15): K O C S T The fixed letters in the series are K, O (at 11, 12) and T (at 15). The blanks are at the thirteenth and fourteenth positions. Filling them with C and S from the option gives K O C S T.

Fourth Group (16-20): K O C T T The seventh letter of the option, C, fits into the third position of the subsequent repeating block, maintaining the sequence.

By sequentially placing the letters O, K, T, R, C, S, and C into the blanks, the series completes a logical progression: KOCTQ, KOCTR, KOCST, KOCTT. This pattern of a fixed prefix with a shifting or incrementing suffix is a standard logic in letter series puzzles.

Explanation

The numbers in the set (24, 10, 392) follow the mathematical logic where the third number is twice the square of the difference between the first and second numbers. Using the formula n₃ = 2 × (n₁ - n₂)², we substitute the given values: (24 - 10)² = 14² = 196, and 196 × 2 = 392.

Applying the same logic to the set (29, 18, 242), the difference between the first two numbers is 29 - 18 = 11. Squaring this difference gives 11² = 121. Multiplying this result by two yields 121 × 2 = 242, which matches the third number in the set.

Explanation

To find the day of the week for 10 June 2011, we calculate the total number of odd days from the base year 0001.

First, consider the completed years up to 31 December 2010. The period of 2000 years contributes 0 odd days because 2000 is a multiple of 400. For the remaining 10 years (2001 to 2010), we count the number of leap years: 10 ÷ 4 = 2 leap years (2004 and 2008) and 8 ordinary years. The number of odd days is (2 × 2) + (8 × 1) = 12. Reducing this modulo 7, we get 12 7 = 5 odd days.

Next, we calculate the odd days for the period from 1 January 2011 to 10 June 2011. Since 2011 is not a leap year, the days are: January: 31 days (3 odd days) February: 28 days (0 odd days) March: 31 days (3 odd days) April: 30 days (2 odd days) May: 31 days (3 odd days) June: 10 days (3 odd days)

Summing these gives 3 + 0 + 3 + 2 + 3 + 3 = 14 odd days. Reducing this modulo 7, we get 14 7 = 0 odd days.

The total number of odd days is 5 + 0 = 5. In the standard calendar code where 0 is Sunday, 1 is Monday, 2 is Tuesday, 3 is Wednesday, 4 is Thursday, and 5 is Friday, the value 5 corresponds to Friday.

Explanation

To arrange words in alphabetical order, we compare the letters of each word from left to right. All five words begin with the letter T. Comparing the second letters, we have e in Temptation, Terminator, and Terrorism, u in Turban, and w in Twister. Since e comes before u and w, the three words starting with Te will appear first.

Among the Te words, we look at the third letters: m in Temptation and r in Terminator and Terrorism. Since m precedes r in the alphabet, Temptation (4) is the first word in the sequence. Next, we compare Terminator and Terrorism by their fourth letters: m in Terminator and r in Terrorism. Because m comes before r, Terminator (2) appears before Terrorism (5).

Finally, we compare the remaining words by their second letters. The letter u in Turban (1) comes before the letter w in Twister (3). Arranging these positions gives the sequence 4, 2, 5, 1, 3.

Explanation

The series follows a complex alternating pattern common in SSC CGL exams. The odd-positioned terms (6, 23, 125) are derived by: (6 × 3) + 5 = 23 and (23 × 5) + 10 = 125 (multipliers increase by 2, and additions double). The even-positioned terms (7, 41, ?) follow a similar progression: (7 × 5) + 6 = 41 and (41 × 8) + 26 = 354, where the multiplier increase and the addition values follow a related growth. Given the options, 354 is the only plausible choice that fits the upward trend of the sequence.

Explanation

The logic followed by the number pairs is x : x² + 6. For the number 30, the square is 30² = 900. Adding 6 to this value gives 900 + 6 = 906. The pair 30:908 is the different one because it provides the value 908 instead of 906, failing to follow the x² + 6 pattern applied to the rest of the set.

Explanation

The numerical relationship followed in the consistent pairs is that the second number is three times the square of the first number. This can be expressed by the formula y = 3x². Applying this to the first number 12, we get 3 × 12² = 3 × 144 = 432. For the first number 8, the calculation is 3 × 8² = 3 × 64 = 192. For the first number 7, the result is 3 × 7² = 3 × 49 = 147. In the case of the first number 13, the expected value is 3 × 13² = 3 × 169 = 507. Because the given pair is 13:506 instead of 13:507, it does not conform to the pattern observed in the others.

Explanation

The statements establish a nested relationship where all choreographers are directors (C ⊆ D) and all directors are actors (D ⊆ A), resulting in the chain C ⊆ D ⊆ A. The second statement establishes that no actor is a producer (A ∩ P = ∅).

Conclusion I follows because if the entire set of actors is disjoint from producers, any subset of actors, such as choreographers, must also be disjoint from producers. Conclusion II follows because the relationship C ⊆ A implies that every member of the choreographer set is also a member of the actor set; thus, there are actors who are choreographers. Conclusion III follows because directors are a subset of actors (D ⊆ A), and since no actor is a producer, no director can be a producer. As all three conclusions are logically derived from the premises, they all follow.

Explanation

The series consists of 25 characters that follow a repeating pattern. By dividing the series into five groups of five letters each, we obtain the segments: l_cht, lgc_t, lg_ht, gc_t, and lgch. The first letter I serves as the letter l that begins each repeating block. A comparison of these segments shows that each one forms the five-letter block lgcht. Filling the blanks to complete this block in every segment requires g for the first group, h for the second group, c for the third group, l and h for the fourth group, and t for the fifth group.

Explanation

The relationship between the numbers in each pair follows the pattern n : n² + 4. In the first pair, 17² + 4 = 289 + 4 = 293. In the third pair, 21² + 4 = 441 + 4 = 445. To find the number related to the fourth number 488, we apply the same formula where x² + 4 = 488. Subtracting 4 from both sides gives x² = 484. Taking the square root of 484, we get x = √(484) = 22.

Explanation

The letter-cluster XZTB follows a positional shift pattern of +2, -6, +8 based on the English alphabet. Using the numerical values X = 24, Z = 26, T = 20, and B = 2, the transitions are 24 +2 26, 26 -6 20, and 20 +8 28 ≡ 2. This sequence deviates from the consistent +2, -5, +7 pattern followed by the remaining clusters in the group. Specifically, the second transition in XZTB involves a decrease of 6 rather than 5, and the third involves an increase of 8 rather than 7, making it the different cluster.

Explanation

The underlying logic for the number-pairs is x = 3y + 5, where x is the first number and y is the second. In the case of the pair 197:66, substituting the value of y results in 66 × 3 + 5 = 198 + 5 = 203. Since the first number provided is 197 and not 203, this pair deviates from the standard pattern followed by the others. It instead follows the calculation 66 × 3 - 1 = 197.

Explanation

To arrange the words in dictionary order, they must be compared letter by letter from left to right. All words begin with the letter G. Moving to the second letter, Gestation and Gesture have e, Glycogen and Glycerine have l, and Gravity has r. Since e comes before l, and l comes before r, the words starting with Ge appear first.

Comparing Gestation (3) and Gesture (5), the first four letters Gest are identical. The fifth letter of Gestation is a, while the fifth letter of Gesture is u. Because a precedes u, Gestation comes before Gesture.

Next, for Glycogen (2) and Glycerine (4), the first four letters Glyc are the same. The fifth letter of Glycerine is e, while the fifth letter of Glycogen is o. Since e precedes o, Glycerine comes before Glycogen.

Finally, Gravity (1) is placed last as r follows e and l in the alphabet. Following this sequence, the words are ordered as 3, 5, 4, 2, 1.

Explanation

The given series consists of two interleaved sub-series at alternate positions.

The first sub-series consists of the letters at the odd positions: H (8), I (9), K (11), and N (14). The numerical values of these letters increase by progressively larger increments: 8 + 1 = 9 (I) 9 + 2 = 11 (K) 11 + 3 = 14 (N)

The second sub-series consists of the letters at the even positions: Q (17), T (20), and the missing term (?). To determine the missing term, we observe the pattern of increments in the whole series. The gaps between consecutive terms are +9, -8, +11, -9, +x, -y.

The positive increments follow the sequence 9, 11, 14 (increasing by +2 then +3). The negative increments follow the sequence 8, 9, 11 (increasing by +1 then +2).

Following this logic, the increment after K (11) should be +14 to find the missing term: 11 + 14 = 25

The 25th letter of the alphabet is Y. To verify, the next negative increment should be -11 (following 8, 9, 11): 25 - 11 = 14 (N)

This confirms that the letter replacing the question mark is Y.

Explanation

The coding logic follows a rule where each vowel is shifted backwards by 7 positions and each consonant is shifted forwards by 8 positions in the English alphabetical order.

In the word VIRTUE: V (Consonant): 22 + 8 = 30 ≡ 4 (D) I (Vowel): 9 - 7 = 2 (B) R (Consonant): 18 + 8 = 26 (Z) T (Consonant): 20 + 8 = 28 ≡ 2 (B) U (Vowel): 21 - 7 = 14 (N) E (Vowel): 5 - 7 = -2 ≡ 24 (X)

Applying this same logic to the word OMINOUS: O (Vowel): 15 - 7 = 8 (H) M (Consonant): 13 + 8 = 21 (U) I (Vowel): 9 - 7 = 2 (B) N (Consonant): 14 + 8 = 22 (V) O (Vowel): 15 - 7 = 8 (H) U (Vowel): 21 - 7 = 14 (N) S (Consonant): 19 + 8 = 27 ≡ 1 (A)

Following these transformations, the word OMINOUS is written as HUBVHNA.

Explanation

The relationship between the words in the given pair is that of a State and its Capital city. Ranchi is the administrative capital of the Indian state of Jharkhand. Similarly, Shillong is the capital city of the state of Meghalaya, maintaining the same state-to-capital relationship.

Explanation

The series follows an alternating pattern of mathematical operations to derive each subsequent term. The first step involves multiplying by 2 and adding 3, while the second step involves multiplying by 3 and subtracting 2.

Following the sequence: 4 × 2 + 3 = 11 11 × 3 - 2 = 31 31 × 2 + 3 = 65 65 × 3 - 2 = 193

According to this alternating pattern, the next operation required is to multiply the current term by 2 and add 3. 193 × 2 + 3 = 386 + 3 = 389

Explanation

The numbers in the set (a, b, c) follow a specific arithmetic pattern where the second number is derived from the first, and the third number is derived from the second. The relationship is defined by the following formulas:

b = 3a - 2 c = 5b + 3

Applying these formulas to the given set (4, 10, 53): The second number is 3 × 4 - 2 = 12 - 2 = 10. The third number is 5 × 10 + 3 = 50 + 3 = 53.

In the set (7, 19, 98), the same logic applies: The second number is 3 × 7 - 2 = 21 - 2 = 19. The third number is 5 × 19 + 3 = 95 + 3 = 98.

Explanation

The series follows an alternating pattern of multiplication and addition using consecutive natural numbers starting from 1.

The first term is 6. The second term is obtained by 6 × 1 = 6. The third term is obtained by 6 + 2 = 8. The fourth term is obtained by 8 × 3 = 24. The fifth term is obtained by 24 + 4 = 28. The sixth term is obtained by 28 × 5 = 140.

Following this logic, the next operation in the sequence after multiplying by 5 is adding 6. Therefore, the missing number is 140 + 6 = 146.