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

Explanation

The relationship between the given words is that of a biological subject and its scientific field of study. Histology is the branch of biology concerned with the microscopic anatomy and study of tissues. Similarly, Herpetology is the specific branch of zoology that deals with the study of amphibians and reptiles. In both pairs, the second term denotes the scientific discipline dedicated to researching the entities mentioned in the first term.

Explanation

The given sequence is a geometric series where each term is obtained by dividing the previous term by a constant factor of 4. The calculations for the terms are as follows:

4096 ÷ 4 = 1024 1024 ÷ 4 = 256 256 ÷ 4 = 64

To find the missing value, we apply the same rule to the last known term: 64 ÷ 4 = 16

The pattern can also be expressed as powers of 4 in descending order, starting from 4⁶: 4⁶ = 4096 4⁵ = 1024 4⁴ = 256 4³ = 64 4² = 16

Explanation

The relationship between the first and second words is that of a country and its capital city. Tripoli is the capital of Libya. Applying the same logic to the second pair, Dublin is the capital city of Ireland.

Explanation

The series follows a repeating pattern of the six-letter sequence "dqtpln". By dividing the 24-character series into four groups of six (dqtpln | dqtpln | dqtpln | dqtpln), we can identify the missing letters as t, d, p, q, n, t, and l. Filling these into the blanks sequentially confirms that Option A is the correct choice.

Explanation

The relationship between the numbers in the first pair is determined by multiplying the first number by 33 to get the second number, as 21 × 33 = 693. Applying the same logic to the second pair, let the missing number be x. The equation becomes x × 33 = 792. Solving for x gives x = 792 / 33 = 24.

Explanation

The coding logic follows a two-step process: reversing the word and then applying an alternating sequence of addition and subtraction of 5 to the alphabetical positions of the letters.

For the word MONTHLY, the reverse order is Y, L, H, T, N, O, M. Applying the pattern (+5, -5, +5, -5, +5, -5, +5): Y(25) + 5 = 30 → 4 (D) L(12) - 5 = 7 (G) H(8) + 5 = 13 (M) T(20) - 5 = 15 (O) N(14) + 5 = 19 (S) O(15) - 5 = 10 (J) M(13) + 5 = 18 (R) This yields the code DGMOSJR.

Applying the same logic to HEADING, the reverse order is G, N, I, D, A, E, H. Applying the pattern: G(7) + 5 = 12 (L) N(14) - 5 = 9 (I) I(9) + 5 = 14 (N) D(4) - 5 = -1 ≡ 25 (Y) A(1) + 5 = 6 (F) E(5) - 5 = 0 ≡ 26 (Z) H(8) + 5 = 13 (M) The resulting code is LINYFZM.

Explanation

Regard represents a feeling of respect, admiration, or positive consideration. It is the different item because it carries a positive connotation, whereas the other items in the group are negative terms that describe disrespectful treatment or harmful behavior.

Explanation

Regard is the only word in the set that conveys a positive or neutral sentiment, referring to respect, esteem, or the act of considering someone with attention and care. The remaining words all share a common theme of negative or hostile behavior directed toward another person. While Taunt, Snub, and Abuse are synonymous with disrespect, mockery, or ill-treatment, Regard signifies a favorable or attentive stance, making it the semantic outlier in the group.

Explanation

Substitute the mathematical signs from the sequence ÷ , × , - , + , = , × into the given equation:

512 ÷ 32 × 9 - 100 + 6 = 25 × 2

Following the BODMAS rule, first solve the division and multiplication on the left-hand side (LHS):

512 ÷ 32 = 16 16 × 9 = 144

The LHS becomes: 144 - 100 + 6 = 44 + 6 = 50

Now solve the right-hand side (RHS): 25 × 2 = 50

Since 50 = 50, the LHS equals the RHS, and the equation is balanced.

Explanation

The relationship established in the pair Handwriting : Graphology is that of a subject and its scientific study. Graphology is the branch of knowledge that involves the analysis and study of handwriting. Following this logic, Physics is the branch of science that deals with the study of matter, energy, and the fundamental laws of nature. Both pairs identify a specific area of inquiry and the formal discipline associated with it.

Explanation

Let the incomes of Aswath, Sunita, and Ramdin be 12x, 9x, and 7x respectively, and let their expenditures be 15y, 9y, and 8y.

According to the problem, Aswath saves 25% of his income. Savings is the difference between income and expenditure, so for Aswath: 12x - 15y = 25% of 12x 12x - 15y = ¼ × 12x 12x - 15y = 3x 9x = 15y x = ¹⁵⁄₉y = ⁵⁄₃y

Now, calculate the savings for each person in terms of y: Aswath savings: 12(⁵⁄₃y) - 15y = 20y - 15y = 5y Sunita savings: 9(⁵⁄₃y) - 9y = 15y - 9y = 6y Ramdin savings: 7(⁵⁄₃y) - 8y = ³⁵⁄₃y - 8y = (35 - 24)/(3)y = ¹¹⁄₃y

The ratio of their savings is: 5y : 6y : ¹¹⁄₃y Multiplying the entire ratio by 3 to remove the denominator: 15 : 18 : 11

Explanation

The series follows an alternating logic where in one step, the first and third letters are modified, and in the next step, the second and fourth letters are modified.

In the first transition (CLAP to HLVP), the changes are: C + 5 = H (3 + 5 = 8) L + 0 = L A - 5 = V (1 - 5 = -4, which is 22 in a cyclic alphabet where 27 is A) P + 0 = P

In the second transition (HLVP to HQVK), the changes are: H + 0 = H L + 5 = Q (12 + 5 = 17) V + 0 = V P - 5 = K (16 - 5 = 11)

In the third transition (HQVK to MQQK), the changes revert to the first pattern: H + 5 = M (8 + 5 = 13) Q + 0 = Q V - 5 = Q (22 - 5 = 17) K + 0 = K

To find the next cluster (MQQK to ?), we apply the second pattern of changes to the second and fourth letters: M + 0 = M Q + 5 = V (17 + 5 = 22) Q + 0 = Q K - 5 = F (11 - 5 = 6)

The resulting cluster is MVQF.

Explanation

The statements "All lemons are plums" and "All plums are dates" establish a hierarchical relationship where the set of lemons is a subset of plums, and plums is a subset of dates. By the transitive property of inclusion, all lemons are contained within the set of dates, which makes Conclusion III logically certain. Additionally, the statement "Some dates are mangoes" indicates an intersection between the set of dates and the set of mangoes. In categorical logic, the relation "Some" is reciprocal; if a portion of the set of dates consists of mangoes, then a portion of the set of mangoes must also consist of dates. This validates Conclusion IV, "Some mangoes are dates".

Explanation

The relationship established in the given pair is Sport : Playing Venue. Golf is an outdoor sport played on a specially designed area of land known as a course. Similarly, cycling, specifically track cycling, is conducted on a purpose-built banked track known as a velodrome. Both pairs follow the logical pattern of naming a competitive physical activity followed by the specific location or arena dedicated to its practice.

Explanation

The coding logic involves calculating the sum of the reverse positional values of the letters in a word and multiplying that sum by the total number of vowels present in the word. The reverse positional value is determined by subtracting the letter's position from 27.

For LABOUR, the reverse positions are L=15, A=26, B=25, O=12, U=6, and R=9. Sum of reverse positions = 15 + 26 + 25 + 12 + 6 + 9 = 93. There are 3 vowels in LABOUR (A, O, U). The code is 93 × 3 = 279.

For EXHALE, the reverse positions are E=22, X=3, H=19, A=26, L=15, and E=22. Sum of reverse positions = 22 + 3 + 19 + 26 + 15 + 22 = 107. There are 3 vowels in EXHALE (E, A, E). The code is 107 × 3 = 321.

For CAUTIOUS, the reverse positions are C=24, A=26, U=6, T=7, I=18, O=12, U=6, and S=8. Sum of reverse positions = 24 + 26 + 6 + 7 + 18 + 12 + 6 + 8 = 107. There are 5 vowels in CAUTIOUS (A, U, I, O, U). The code is 107 × 5 = 535.

Explanation

To arrange the words in dictionary order, we compare the letters of each word from left to right. All five words begin with the letter P. Moving to the second letter, we have Perturb (e), Pneumonia (n), Precision (r), Publicity (u), and Puberty (u). Since e comes before n, n comes before r, and r comes before u in the alphabet, the first three words in the sequence are 5, 4, and 2.

Next, we compare the words starting with the same first two letters, Publicity (1) and Puberty (3). Both share the third letter b. Comparing the fourth letter, Puberty has e while Publicity has l. In alphabetical order, e precedes l, so Puberty (3) comes before Publicity (1). Combining these steps, the complete chronological dictionary order is 5, 4, 2, 3, 1.

Explanation

The given sequence is an alternating series consisting of two distinct patterns. The terms at the odd positions (1st, 3rd, 5th, 7th, 9th, and 11th) follow a decreasing pattern with an increasing difference: 68, 63, 57, 50, 42, 33. The differences are -5, -6, -7, -8, and -9 respectively.

The terms at the even positions (2nd, 4th, 6th, 8th, 10th, and 12th) determine the missing number. Let these terms be b₁, b₂, b₃, b₄, b₅, b₆. The sequence is 3, 3, 9, 15, 33, ?. The pattern for this sub-series is bₙ = bₙ₋₁ + 2 × bₙ₋₂ starting from the third term (b₃):

b₁ = 3 b₂ = 3 b₃ = 3 + 2(3) = 9 b₄ = 9 + 2(3) = 15 b₅ = 15 + 2(9) = 33 b₆ = 33 + 2(15) = 63

Applying the formula to the final term, the result is 63.

Explanation

The letter-cluster NRIP is the odd one out because it deviates from the consistent positional logic shared by the other three clusters. In the standard pattern for this group, the first letter and second letter have a difference of +4 positions in the alphabet. The second and third letters are alphabetical opposites, meaning the sum of their numerical positions equals 27. Finally, the third and fourth letters have a difference of +6 positions.

In the case of NRIP, the first letter N (14) to R (18) correctly follows the +4 rule, and the middle pair R (18) and I (9) are alphabetical opposites since 18 + 9 = 27. However, the transition from the third letter I (9) to the fourth letter P (16) involves an increase of +7 positions, whereas the established pattern requires an increase of only +6 positions. This discrepancy also makes the total sum of the positional values for NRIP equal to 57, while the clusters that follow the pattern have a constant sum of 56.

Explanation

Based on the given symbols, the expression Y + Z H % C D + S can be decoded to determine the family relationships. Y + Z indicates that Y is the husband of Z, making Y male and Z female. Z H means Z is the mother of H, which implies Y is the father of H. H % C indicates that H is the father of C, which makes H the son of Y and Z. C D means C is the mother of D. Finally, D + S indicates that D is the husband of S.

In the relationship between Z and C, Z is the mother of H, and H is the father of C. This establishes that Z is the paternal grandmother of C. The statement in option d asserts that Z is the maternal grandmother of C, which is incorrect because a maternal grandmother must be the mother of the person's mother, while Z is the mother of C's father.

Explanation

The first statement establishes that the set of rugs is a subset of blankets, and the second statement establishes that the set of blankets is a subset of pillows. By the transitive property of inclusion, all rugs are necessarily pillows. In syllogistic logic, the statement all rugs are pillows implies the subaltern and converse relation that some pillows are rugs. Therefore, conclusion II follows directly from the premises. Conclusion I does not follow because a universal affirmative statement does not imply its simple converse. Conclusion III does not follow because while some blankets are frames, there is no information provided to confirm that this overlap includes the specific subset of blankets that are rugs.

Explanation

The series follows a specific mathematical pattern for each letter position based on the English alphabetical order where A=1, B=2, ..., Z=26.

For the first letter of each cluster, the value decreases by 4: U (21) - 4 = Q (17) Q (17) - 4 = M (13) M (13) - 4 = I (9) I (9) - 4 = E (5)

For the second letter of each cluster, the value increases by 4: T (20) + 4 = X (24) X (24) + 4 = B (28 ≡ 2) B (2) + 4 = F (6) F (6) + 4 = J (10)

For the third letter of each cluster, the value decreases by 4: M (13) - 4 = I (9) I (9) - 4 = E (5) E (5) - 4 = A (1) A (1) - 4 = W (23)

For the fourth letter of each cluster, the value increases by 4 (starting from the second cluster as the first cluster provided is shorter): H (8) + 4 = L (12) L (12) + 4 = P (16) P (16) + 4 = T (20)

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

Explanation

The series follows a pattern where each term is increased by the sequence of every second prime number. The differences between consecutive terms are 3, 7, 13, 19, and 29, which correspond to the 2nd, 4th, 6th, 8th, and 10th prime numbers respectively.

Starting from the first term, 27 + 3 = 30 using the 2nd prime. Next, 30 + 7 = 37 using the 4th prime, followed by 37 + 13 = 50 using the 6th prime. To find the missing term, we add the 8th prime number, which is 19, to the fourth term: 50 + 19 = 69. This logic is verified by the final step, where adding the 10th prime number, 29, to 69 results in 69 + 29 = 98.

Explanation

The relationship follows the pattern (First Number - 1) / 3 = Second Number. Applying this logic, (13 - 1) / 3 = 4 and (16 - 1) / 3 = 5, so for the third pair, (19 - 1) / 3 = 6.

Explanation

The relationship between the numbers in the set follows the mathematical pattern (x, x² + 3, x³ + 3), where x represents the first number. Applying this logic to the first number 8, the second number is calculated as 8² + 3, which equals 64 + 3 = 67. The third number is then calculated as 8³ + 3, which results in 512 + 3 = 515. This derivation consistently produces the triplet (8, 67, 515).

Explanation

Ahmedabad is not the capital city of an Indian state. Although it is a prominent metropolitan area and the largest city in Gujarat, the official seat of government for the state is located in Gandhinagar. The city functions as a major commercial and industrial hub rather than an administrative capital. This lack of capital status differentiates it from the other cities in the group.

Explanation

The coding logic follows the mathematical rule where the code is the cube of the number of letters in the word. In the word CROW, there are 4 letters, and 4³ = 64. For the word EAGLE, there are 5 letters, and 5³ = 125. The word PARROT consists of 6 letters, so the code is calculated as 6³ = 216.

Explanation

The pattern in the grid follows a column-wise logic where the third row is calculated using the formula R₃ = R₂ - √(R₁). In the first column, substituting the values gives 23 - √(25) = 23 - 5 = 18. In the second column, the formula yields 41 - √(64) = 41 - 8 = 33. Using this same logic for the third column, the missing value is found by calculating 38 - √(81), which simplifies to 38 - 9 = 29.

Explanation

The relationship between the first pair of words is based on synonymy. Nascent describes something that is just coming into existence or beginning to display signs of future potential, which is synonymous with being young or in an early stage. Following this logic, an adjunct is something added to another thing as a supplementary or auxiliary part rather than an essential one. In a functional or organizational context, an adjunct serves a supportive role, acting as an addition that assists or complements the primary element.

Explanation

Let the total number of students be 100.

The number of students who received cricket training is 14% of 100, which is 14. The remaining number of students is 100 - 14 = 86.

The number of students who received hockey training is 22% of the remaining 86 students: Hockey trainees = 0.22 × 86 = 18.92

The number of students remaining after hockey training is 86 - 18.92 = 67.08.

The problem states that half of these remaining students received training for badminton. Therefore, the other half did not receive training in any of the three games. Students without training = ½ × 67.08 = 33.54

As a percentage of the total 100 students, the students who did not receive training is 33.54%.

Explanation

Dictionary arrangement follows alphabetical order character by character. Comparing Tamarind (4) and Tame (5), the first three letters are identical, but at the fourth position, a in Tamarind appears before e in Tame, placing 4 before 5. For the remaining words starting with Te, Temperature (3) comes next as its third letter m precedes the r found in Terminal (1), Terminology (2), and Tertiary (6). Among those starting with Ter, Terminal (1) and Terminology (2) come before Tertiary (6) because their fourth letter m precedes t. Finally, comparing Terminal (1) and Terminology (2), they share the first seven letters, but at the eighth position, a in Terminal precedes o in Terminology, placing 1 before 2. The final sequence in dictionary order is 4, 5, 3, 1, 2, 6.

Explanation

In the given number-pairs, the relationship is based on a constant difference between the second number and the first number. For the pairs a, b, and c, the difference is consistently 123, calculated as 338 - 215 = 123, 134 - 11 = 123, and 292 - 169 = 123. In contrast, for the pair d, the difference between the numbers is 308 - 178 = 130. Because this pair does not follow the common difference of 123 shared by the other three pairs, it is the odd one out.

Explanation

The series consists of 24 positions, which can be divided into four equal groups of six letters each. By analyzing the frequency and placement of the letters Q, K, A, D, P, and R, it is evident that each group follows the same repeating pattern: QKADPR.

Dividing the series into these segments reveals the missing letters: First segment: Q (K) A D (P) R Second segment: (Q) K A D P (R) Third segment: Q K A (D) P R Fourth segment: Q K (A) D (P) R

By filling the blanks sequentially with the letters K, P, Q, R, D, A, and P, the series becomes a perfect repetition of the cluster QKADPR four times. This sequence matches the order of letters provided in the first option.

Explanation

In the letter-cluster ZEJP, the numerical positions of the letters in the English alphabet are Z(26), E(5), J(10), and P(16). The gaps between the consecutive letters are 26 + 5 = 31 ≡ 5 (E), 5 + 5 = 10 (J), and 10 + 6 = 16 (P). This cluster is different because it follows an inconsistent addition pattern of +5, +5, and +6, whereas the other clusters in the set maintain a constant addition of +5 between all consecutive letters.

Explanation

The code is determined by reversing the word and then applying an alternating addition and subtraction of 3 to the numerical value of each letter.

For the word COUNTRY: Reverse the word: Y R T N U O C Apply the pattern +3, -3, +3, -3, +3, -3, +3: Y (25) + 3 = 28 → B (2) R (18) - 3 = 15 → O T (20) + 3 = 23 → W N (14) - 3 = 11 → K U (21) + 3 = 24 → X O (15) - 3 = 12 → L C (3) + 3 = 6 → F The resulting code is BOWKXLF.

For the word DESPAIR: Reverse the word: R I A P S E D Apply the same pattern +3, -3, +3, -3, +3, -3, +3: R (18) + 3 = 21 → U I (9) - 3 = 6 → F A (1) + 3 = 4 → D P (16) - 3 = 13 → M S (19) + 3 = 22 → V E (5) - 3 = 2 → B D (4) + 3 = 7 → G The resulting code is UFDMVBG.

Explanation

By interchanging the numbers 36 and 14 in the given equation, the expression becomes: 14 × 81 ÷ 9 - (88 ÷ 4) + 36 + (22 + 7) = 169

To verify this, we apply the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction). First, solve the operations inside the parentheses: 88 ÷ 4 = 22 22 + 7 = 29

Substitute these values back into the equation: 14 × 81 ÷ 9 - 22 + 36 + 29

Next, perform the division: 81 ÷ 9 = 9 The equation now looks like: 14 × 9 - 22 + 36 + 29

Perform the multiplication: 14 × 9 = 126

Finally, solve the addition and subtraction from left to right: 126 - 22 + 36 + 29 = 104 + 36 + 29 140 + 29 = 169

The Left Hand Side (LHS) equals the Right Hand Side (RHS), which confirms that interchanging 36 and 14 makes the equation correct.

Explanation

The statement all offices are stalls is a universal affirmative proposition, which can be represented in set notation as O ⊆ S. This means that the entire set of offices is contained within the set of stalls. In logic, the conversion of a universal affirmative proposition (All A are B) yields a particular affirmative proposition (Some B are A). Since every office is a stall, it naturally follows that any area occupied by offices is also occupied by stalls. Therefore, the conclusion that some stalls are offices is a direct logical consequence of the second statement. This inference remains valid regardless of the relationship between banks and offices, as it describes the inherent overlap between the sets of stalls and offices.

Explanation

Empathy is the only positive and prosocial emotion among the group. It involves the ability to understand, share, and resonate with the feelings and perspectives of another person, fostering connection and compassion. The other three terms represent negative or hostile emotional states that are generally associated with resentment, insecurity, or intense dislike toward others. Therefore, empathy is the odd one out based on its positive psychological and social nature.

Explanation

The given series is an alternating series where the missing value corresponds to the 7th term. We can determine this by examining the sub-series formed by the terms at the odd positions: 10, 35, 72, and ?.

First, we calculate the differences between these consecutive odd-positioned terms: 35 - 10 = 25 72 - 35 = 37

The difference between these first-order differences (the second-order difference) is 37 - 25 = 12. In this pattern, the second-order difference doubles in each subsequent step. Applying this logic to find the next gap: Next second-order difference = 12 × 2 = 24 Next first-order difference = 37 + 24 = 61 7th term = 72 + 61 = 133

This calculation is further supported by a cube-based pattern that applies to the odd-positioned terms from the 3rd term onwards, using the formula n³ + 8. For the 3rd term, 3³ + 8 = 35; for the 5th term, 4³ + 8 = 72. Following this sequence, the 7th term is 5³ + 8 = 125 + 8 = 133.

Explanation

The coding pattern involves reversing the word and applying alternating transformations to the alphabetical ranks of the letters. For a word with letters W₁ W₂ W₃ W₄ W₅, the code C₁ C₂ C₃ C₄ C₅ is determined as follows:

For positions i = 1, 3, 5: Cᵢ = W₆₋ᵢ + 5 For positions i = 2, 4: Cᵢ = 27 - W₆₋ᵢ (the opposite letter)

Applying this to PRINT (P=16, R=18, I=9, N=14, T=20): C₁ = T(20) + 5 = 25 (Y) C₂ = 27 - N(14) = 13 (M) C₃ = I(9) + 5 = 14 (N) C₄ = 27 - R(18) = 9 (I) C₅ = P(16) + 5 = 21 (U) The code is YMNIU.

Applying the same logic to MAGIC (M=13, A=1, G=7, I=9, C=3): C₁ = C(3) + 5 = 8 (H) C₂ = 27 - I(9) = 18 (R) C₃ = G(7) + 5 = 12 (L) C₄ = 27 - A(1) = 26 (Z) C₅ = M(13) + 5 = 18 (R)

The resulting code for MAGIC is HRLZR.

Explanation

To arrange the words in dictionary order, they must be compared letter by letter from left to right. All five words begin with the prefix So. Examining the third letter of each word, we find l in Solitary, Solution, and Solvent, p in Sophisticate, and r in Sorting. In alphabetical order, l precedes p, and p precedes r.

Among the words starting with Sol, we compare the fourth letters: i in Solitary, u in Solution, and v in Solvent. Since i comes before u, and u comes before v, the relative order is Solitary (2), Solution (3), and then Solvent (5). Following the Sol group, the next word is Sophisticate (4) because its third letter p comes after l but before r. The last word is Sorting (1) as its third letter r appears latest in the alphabet. Therefore, the alphabetical sequence is 2, 3, 5, 4, 1.

Explanation

The series consists of 24 characters that follow a repetitive logical pattern. By dividing the sequence into four equal blocks of six letters each, the repeating unit is identified as UACBDT. The segments formed by this division are UA_B_T, U_CBD_, _ACB_T, and UAC__T. To complete the pattern uniformly across all blocks, the blanks must be filled sequentially with the letters C, D, A, T, U, D, B, and D.

The first blank at the third position receives C and the second blank at the fifth position receives D, completing the first group as UACBDT. The third blank at the eighth position receives A and the fourth blank at the twelfth position receives T, completing the second group as UACBDT. The fifth blank at the thirteenth position receives U and the sixth blank at the seventeenth position receives D, completing the third group as UACBDT. Finally, the seventh blank at the twenty-second position receives B and the eighth blank at the twenty-third position receives D, completing the fourth group as UACBDT. This results in the continuous sequence UACBDT UACBDT UACBDT UACBDT.

Explanation

The relationship established in the first pair is between an object and the specific sound it produces. Leaves are known to make a rattling or rustling sound when they move. Following the same logic for the second pair, the characteristic vocalization or sound made by an owl is known as hooting, which is phonetically represented as hoooho.

Explanation

The letters in the clusters follow a specific arithmetic pattern based on their numerical positions in the alphabet, where A=1, B=2, …, Z=26. The logic governing three of the clusters is L₂ = L₁ + 2, L₃ = L₂ - 4, and L₄ = L₃ - 1. Applying this to DFBA (4, 6, 2, 1), RTPO (18, 20, 16, 15), and LNJI (12, 14, 10, 9) confirms these transitions. However, for the cluster FHDB, the numerical values are 6, 8, 4, 2. Substituting these values into the pattern: L₂ = 6 + 2 = 8, L₃ = 8 - 4 = 4, but L₄ = 4 - 2 = 2. Because the final step involves a subtraction of 2 instead of 1, FHDB does not follow the same rule as the others and is the different cluster.

Explanation

The relationship between the numbers follows the logic x : x × (ˣ⁄₂ + 1). In this pattern, the second number is derived by multiplying the first number by the sum of its half and one.

For the first pair 16 : 144: 16 × (¹⁶⁄₂ + 1) = 16 × (8 + 1) = 16 × 9 = 144

Applying the same logic to the third number 28: 28 × (²⁸⁄₂ + 1) = 28 × (14 + 1) = 28 × 15 = 420

Explanation

To determine the day of the week on 17 April 2014, we calculate the total number of odd days starting from the year 2000, which has 0 odd days. From 1 January 2001 to 31 December 2013, there are 13 years. In these 13 years, there are 3 leap years (2004, 2008, 2012) and 10 ordinary years. The number of odd days is calculated as (3 × 2) + (10 × 1) = 16. Dividing 16 by 7 gives a remainder of 2 odd days.

Next, we count the number of days in the year 2014 up to 17 April. 2014 is an ordinary year, so February has 28 days. The days are: January (31), February (28), March (31), and April (17). The sum of these days is 31 + 28 + 31 + 17 = 107. Dividing 107 by 7 gives 107 = (15 × 7) + 2, which results in 2 odd days.

The total number of odd days is the sum of odd days from the period 2001–2013 and the period within 2014, which is 2 + 2 = 4. Using the standard day-to-number mapping where 0 is Sunday, 1 is Monday, 2 is Tuesday, 3 is Wednesday, and 4 is Thursday, the day on 17 April 2014 is Thursday.

Explanation

The expression M @ R % K # G # N | T can be decoded as follows: M is the mother of R, R is the sister of K, and K is the son of G. This establishes that M and G are a married couple where M is the wife and G is the husband, being the parents of R and K. Further, G # N indicates G is the son of N, and N | T indicates N is the wife of T. This means T is the father of G.

Since T is the father of G and M is the wife of G, the relationship between T and M is that of a father-in-law and daughter-in-law. A paternal grandfather is the father of one's father. In this family structure, T is the paternal grandfather of R and K, but he is the father-in-law of M. Therefore, the statement claiming T is the paternal grandfather of M is factually incorrect.

Explanation

The coding logic follows the formula: Code = (Sum of reverse positional values of letters) + (Number of letters in the word). The reverse positional value of a letter is calculated as (27 - actual positional value), where A=1 and Z=26.

For FRENCH: Reverse values: F=21, R=9, E=22, N=13, C=24, H=19 Sum = 21 + 9 + 22 + 13 + 24 + 19 = 108 Number of letters = 6 Total = 108 + 6 = 114

For LOSS: Reverse values: L=15, O=12, S=8, S=8 Sum = 15 + 12 + 8 + 8 = 43 Number of letters = 4 Total = 43 + 4 = 47

For COURSE: Reverse values: C=24, O=12, U=6, R=9, S=8, E=22 Sum = 24 + 12 + 6 + 9 + 8 + 22 = 81 Number of letters = 6 Total = 81 + 6 = 87

Explanation

The series follows a double-difference pattern. First, find the differences between consecutive terms: 13 - 5 = 8 22 - 13 = 9 34 - 22 = 12 51 - 34 = 17 75 - 51 = 24 108 - 75 = 33 152 - 108 = 44

Next, calculate the differences between these resulting values (the second differences): 9 - 8 = 1 12 - 9 = 3 17 - 12 = 5 24 - 17 = 7 33 - 24 = 9 44 - 33 = 11

The second differences are consecutive odd numbers: 1, 3, 5, 7, 9, 11. Following this pattern, the next second difference must be 13. To find the next first difference, add 13 to the previous difference: 44 + 13 = 57. The missing number in the original series is obtained by adding this value to the last term: 152 + 57 = 209.

Explanation

The series follows a specific addition pattern for the numerical positions of the letters in each cluster where A=1, B=2, …, Z=26.

For the first letter of each cluster: G(7) +3 J(10) +3 M(13) +3 P(16). Following this +3 pattern, the next letter is 16 + 3 = 19, which corresponds to S.

For the second letter of each cluster: C(3) +5 H(8) +5 M(13) +5 R(18). Following this +5 pattern, the next letter is 18 + 5 = 23, which corresponds to W.

For the third letter of each cluster: B(2) +3 E(5) +3 H(8) +3 K(11). Following this +3 pattern, the next letter is 11 + 3 = 14, which corresponds to N.

By combining these results, the next cluster in the sequence is SWN.

Explanation

The letter-cluster FJQL is the odd one out because the sum of the positional values of its first and fourth letters, F (6) and L (12), is 18. This deviates from the logic where the sum of the first and fourth letters must be 16. While FJQL shares the common trait of having middle letters J (10) and Q (17) that are alphabetical opposites with a sum of 27, its total positional sum of 45 distinguishes it from the other clusters in the group, which all have a total positional sum of 43.