SSC CGL Tier 1 2020 General Intelligence & Reasoning Questions with Solutions

Explanation

The logic followed in the given set (7, 98, 196) involves a multiplication pattern where the second number is the product of the first number and 14, and the third number is twice the second number.

For the set (7, 98, 196): 7 × 14 = 98 98 × 2 = 196

Applying this same logic to the numbers in option c), (11, 154, 308): The second number is 11 × 14 = 154. The third number is 154 × 2 = 308.

Explanation

To arrange words in dictionary order, we compare them letter by letter from left to right. All five words begin with the prefix Ca. Comparing the third letters, p (found in Capacity, Capsule, Captain, and Caption) precedes t (found in Category), which means Category (1) will appear last in the sequence.

Among the words starting with Cap, we look at the fourth letter. In Capacity (5), the fourth letter is a; in Capsule (4), it is s; and in Captain (3) and Caption (2), it is t. Following the alphabet, a comes before s, and s comes before t. Therefore, Capacity (5) is first, followed by Capsule (4).

To distinguish between Captain (3) and Caption (2), we examine the fifth letter. Captain (3) has an a, while Caption (2) has an i. Since a comes before i, Captain (3) precedes Caption (2). Combining these steps, the final dictionary order is 5, 4, 3, 2, 1.

Explanation

The pattern followed in each column is that the number in the third row is obtained by subtracting 100 from the product of the numbers in the first and second rows. The general formula is: R₁ × R₂ - 100 = R₃

In the first column: 21 × 19 - 100 = 399 - 100 = 299

In the second column: 18 × 22 - 100 = 396 - 100 = 296

In the third column, let the missing number be x: 32 × x - 100 = 348 32x = 348 + 100 32x = 448 x = ⁴⁴⁸⁄₃₂ = 14

Explanation

By converting the letters into their corresponding numerical positions in the English alphabet (A=1, B=2, …, Z=26), a specific mathematical progression is observed. In the majority of the clusters, the second letter is 4 positions ahead of the first, and the third letter is 5 positions ahead of the second. For cluster NRW, the positions are 14, 18, 23, which follows 14 + 4 = 18 and 18 + 5 = 23. For cluster PTY, the positions are 16, 20, 25, following 16 + 4 = 20 and 20 + 5 = 25. For cluster LPU, the positions are 12, 16, 21, following 12 + 4 = 16 and 16 + 5 = 21.

The cluster ADL follows a different numerical sequence. Its positions are 1, 4, 12. The difference between the first and second letter is 4 - 1 = 3, and the difference between the second and third letter is 12 - 4 = 8. Because it follows a +3, +8 pattern instead of the +4, +5 pattern shared by all other options, it is the odd letter-cluster.

Explanation

Schizophrenia is a chronic and severe mental disorder that affects a person's ability to think, feel, and behave clearly. It is classified as a psychiatric condition or a non-communicable mental health illness. This distinguishes it from the rest of the group because it is a psychological disorder, whereas the other three terms in the list are all infectious diseases caused by specific viral pathogens.

Explanation

Nitin's mother-in-law's only daughter is Nitin's wife. According to the statement, this person is also Sanchi's mother's father's son's wife. Breaking down Sanchi's side: Sanchi's mother's father is her maternal grandfather. Her maternal grandfather's son is her maternal uncle. The wife of Sanchi's maternal uncle is the person Nitin is describing as his own wife. Since Nitin's wife is Sanchi's maternal uncle's wife, Nitin must be Sanchi's maternal uncle. In terms of his relationship to Sanchi's mother, the maternal uncle is the brother of the mother.

Explanation

The relationship established in the first pair is based on biological classification where a monkey is a vertebrate because it possesses a spinal column or backbone. Applying the same logic, starfish are invertebrates as they lack a vertebral column. Starfish belong to the phylum Echinodermata and are characterized by an internal skeleton of calcareous ossicles rather than a bony spine, fitting the definition of an invertebrate animal.

Explanation

The relationship between the numbers follows the logic of n³ + 5. For the first pair, the calculation is 4³ + 5, which equals 64 + 5 = 69. Applying the same logic to the third number, we calculate 11³ + 5. Since 11³ = 1331, the result is 1331 + 5 = 1336.

Explanation

The coding logic uses the alphabetical position for letters at odd positions and the reverse alphabetical position for letters at even positions. For a letter with alphabetical position n, the reverse position is calculated as 27 - n.

In the word CAUGHT: C (1st, odd) = 3 A (2nd, even) = 27 - 1 = 26 U (3rd, odd) = 21 G (4th, even) = 27 - 7 = 20 H (5th, odd) = 8 T (6th, even) = 27 - 20 = 7 Combining these results gives 326212087.

Applying the same logic to SOLDER: S (1st, odd) = 19 O (2nd, even) = 27 - 15 = 12 L (3rd, odd) = 12 D (4th, even) = 27 - 4 = 23 E (5th, odd) = 5 R (6th, even) = 27 - 18 = 9 Combining these results gives 1912122359.

Explanation

By interchanging the signs × and ÷ and the numbers 35 and 11, the equation transforms from 11 × 7 ÷ 35 - 64 + 56 = 47 into 35 ÷ 7 × 11 - 64 + 56 = 47. Following the BODMAS rule, the expression is evaluated as follows:

First, perform the division: 35 ÷ 7 = 5

Next, perform the multiplication: 5 × 11 = 55

Finally, perform the addition and subtraction: 55 - 64 + 56 = 111 - 64 = 47

The calculation results in 47, which matches the value on the right-hand side of the equation.

Explanation

The series follows two independent patterns for the first and second letters of each cluster based on their numerical positions in the English alphabet. For the first letters in the sequence A, C, ?, G, I, K, the pattern is an increment of 2. Starting with A (1), adding 2 gives C (3), and adding 2 again results in the 5th letter, which is E. This pattern continues as E (5) plus 2 equals G (7), then I (9), and K (11).

For the second letters in the sequence R, P, ?, L, J, H, the pattern is a decrement of 2. Starting with R (18), subtracting 2 gives P (16), and subtracting 2 again results in the 14th letter, which is N. This pattern continues as N (14) minus 2 equals L (12), then J (10), and H (8). Combining the determined letters E and N results in the cluster EN.

Explanation

The series follows a pattern where the differences between consecutive terms are added in pairs, based on the formula d = n² + n for consecutive odd integers n.

For n = 1, the difference is 1² + 1 = 2. 61 + 2 = 63 63 + 2 = 65

For n = 3, the difference is 3² + 3 = 12. 65 + 12 = 77 77 + 12 = 89

For n = 5, the difference is 5² + 5 = 30. 89 + 30 = 119 119 + 30 = 149

For n = 7, the difference is 7² + 7 = 56. 149 + 56 = 205

Following this logic, the missing number is obtained by adding 30 to the preceding term 89, resulting in 119. This is verified by adding 30 again to 119, which correctly yields 149.

Explanation

The number-pair 19:475 is the odd one out because it does not follow the mathematical pattern x : x(x + 2). According to this rule, the second number is the product of the first number x and the sum of that number plus two. For the input value 19, the expected output is 19 × (19 + 2) = 19 × 21 = 399. Because 475 does not equal 399, the pair is the divergent one in the set.

Explanation

The coding follows a specific positional shift pattern for each letter in the word. To find the code, first identify the numerical position of each letter in the English alphabet (A=1, B=2, ..., Z=26) and determine the difference between the word and its code.

For SANCTION (8 letters): S (19) + 5 = 24 (X) A (1) + 5 = 6 (F) N (14) + 5 = 19 (S) C (3) + 5 = 8 (H) T (20) - 5 = 15 (O) I (9) - 5 = 4 (D) O (15) - 6 = 9 (I) N (14) + 6 = 20 (T)

The pattern for the shifts is: +5, +5, +5, +5, -5, -5, -6, +6.

Applying the same pattern to PROFOUND: P (16) + 5 = 21 (U) R (18) + 5 = 23 (W) O (15) + 5 = 20 (T) F (6) + 5 = 11 (K) O (15) - 5 = 10 (J) U (21) - 5 = 16 (P) N (14) - 6 = 8 (H) D (4) + 6 = 10 (J)

Combining these letters results in the code UWTKJPHJ.

Explanation

The relationship between the words is that of a process and the official appointed to supervise it to ensure fairness and adherence to rules. An invigilator is an official who monitors students during an examination to prevent malpractice. Similarly, an observer is an official appointed by an authority, such as the Election Commission, to monitor the conduct of an election and ensure that the process is free, fair, and transparent.

Explanation

The first statement indicates an intersection between papers and copies. In syllogistic logic, the statement "Some A are B" implies "Some B are A," confirming that conclusion I (Some copies are papers) is logically valid.

For the relationship between papers and erasers, the statements show that the specific papers that are copies cannot be erasers. However, the information provided does not define the relationship between the rest of the papers and the set of erasers. Conclusions II (Some papers are erasers) and III (No paper is an eraser) are complementary. Because the set of papers must either have at least one element in common with the set of erasers or have no elements in common at all, one of these two conditions must hold true in any logical possibility. Consequently, conclusion I follows definitely, and either conclusion II or III must follow.

Explanation

The expression P - K × Y - J ÷ S + R can be decoded step-by-step to establish the family relationships. P - K indicates that P is the brother of K. K × Y means K is the father of Y, and Y - J means Y is the brother of J. Therefore, K is the father of both Y and J. The relationship J ÷ S shows that J is the daughter of S. Since K is already established as the father of J, K and S must be a married couple where K is the husband and S is the wife. Finally, S + R means S is the mother of R. In this family structure, K and S are the parents of Y, J, and R. Since P is the brother of K, he is the paternal uncle of K's children. Thus, J is the niece of P, making the statement that J is the daughter of P incorrect.

Explanation

The series follows a specific arithmetic pattern for each letter position based on their numerical values in the alphabet (A=1, B=2, …, Z=26).

For the first letter, the pattern is an addition of 3: T (20) + 3 = W (23); W (23) + 3 = Z (26); Z (26) + 3 = C (3); C (3) + 3 = F (6).

For the second letter, the pattern is a subtraction of 3: U (21) - 3 = R (18); R (18) - 3 = O (15); O (15) - 3 = L (12); L (12) - 3 = I (9).

For the third letter, the pattern is an addition of 4: L (12) + 4 = P (16); P (16) + 4 = T (20); T (20) + 4 = X (24); X (24) + 4 = B (28 ≡ 2).

For the fourth letter, the pattern is a subtraction of 4: G (7) - 4 = C (3); C (3) - 4 = Y (25); Y (25) - 4 = U (21); U (21) - 4 = Q (17).

Applying these operations to the fourth cluster CLXU, the first letter C (3) + 3 = F, the second letter L (12) - 3 = I, the third letter X (24) + 4 = B, and the fourth letter U (21) - 4 = Q. The resulting cluster is FIBQ.

Explanation

The relationship between the numbers in the first pair follows the pattern (n × 8) + 5. For the first pair, substituting n = 13 gives (13 × 8) + 5 = 104 + 5 = 109. Applying the same logic to the third number, where n = 24, we calculate (24 × 8) + 5 = 192 + 5 = 197.

Explanation

The series follows a pattern where the difference between consecutive terms increases according to a secondary arithmetic sequence. Calculating the first level of differences between the numbers: 47 - 45 = 2, 53 - 47 = 6, 65 - 53 = 12, and 85 - 65 = 20. The resulting sequence of differences is 2, 6, 12, 20.

To find the pattern within these differences, calculate the second level of differences: 6 - 2 = 4, 12 - 6 = 6, and 20 - 12 = 8. The second level of differences is an arithmetic progression (4, 6, 8, …) where each term increases by 2. Following this pattern, the next value in the second level of differences should be 8 + 2 = 10. Adding this to the last term of the first level of differences gives 20 + 10 = 30. Therefore, the next number in the series is 85 + 30 = 115. This pattern can also be represented by the formula n² + n for the differences: 1² + 1 = 2, 2² + 2 = 6, 3² + 3 = 12, 4² + 4 = 20, and the next being 5² + 5 = 30.

Explanation

The given sequence is an alternating series consisting of two separate patterns. The letters at the odd positions (1st, 3rd, 5th, 7th, and 9th) follow the sequence of vowels in the English alphabet: A, E, I, O, and U. The letters at the even positions (2nd, 4th, 6th, 8th, and 10th) follow a consecutive alphabetical order: T, U, V, W, and X. Since the question mark occupies the 9th position, it follows the vowel sub-series, making the required letter U.

Explanation

The relationship between the numbers in the given set (8, 7, 407) follows the logic: (First Number)² + (Second Number)³ + [(First Number - Second Number) × (First Number - Second Number - 1)] = Third Number

Applying this to the set (8, 7, 407): 8² + 7³ + [(8 - 7) × (8 - 7 - 1)] = 64 + 343 + [1 × 0] = 407 + 0 = 407

Applying the same logic to option d) (9, 6, 303): 9² + 6³ + [(9 - 6) × (9 - 6 - 1)] = 81 + 216 + [3 × 2] = 297 + 6 = 303

Explanation

The relationship between the first pair of words is one of synonymy. To criticise and to condemn both refer to the act of expressing disapproval or censuring someone or something. In the second pair, solidarity is defined as the union or fellowship arising from common responsibilities and interests, such as between members of a group or class. Unity is a direct synonym of solidarity, representing the state of being one or being in total agreement and harmony within a group.

Explanation

The statement All jugs are bottles implies that the set of jugs is a subset of the set of bottles (J ⊆ B). The statement No bottle is a pen means that the set of bottles and the set of pens are disjoint (B ∩ P = ∅). Since all jugs are contained within the set of bottles, and no part of the bottle set overlaps with pens, it logically follows that no jug can be a pen. This validates conclusion II.

Furthermore, the statement All jugs are bottles is a universal affirmative (A-type) proposition. In syllogistic logic, if All A are B, it can be converted into the particular affirmative (I-type) proposition Some B are A, provided the sets are non-empty. Thus, the existence of jugs within the bottle category ensures that some bottles are jugs. This validates conclusion III. Based on these logical deductions, both conclusions II and III are necessarily true.

Explanation

The words represent ranks in the Indian Army arranged in descending order of seniority. The highest rank in the list is the Field Marshal (2), which is a five-star ceremonial rank. Below the Field Marshal is the General (5), who is the four-star officer and Chief of the Army Staff. Next in the hierarchy is the Brigadier (3), a one-star rank. The Colonel (1) is a senior commissioned rank below the Brigadier. The most junior rank among those provided is the Lieutenant (4). Following this hierarchical structure from highest to lowest results in the sequence 2, 5, 3, 1, 4.

Explanation

The coding language follows a pattern of shifting the alphabetical positions of each letter. By comparing FASTER to CDVQHO, we identify the following numerical shifts based on the alphabet position of each letter:

F (6) - 3 = 3 (C) A (1) + 3 = 4 (D) S (19) + 3 = 22 (V) T (20) - 3 = 17 (Q) E (5) + 3 = 8 (H) R (18) - 3 = 15 (O)

The pattern for the shifts is -3, +3, +3, -3, +3, -3. Applying this logic to the word VIOLIN:

V (22) - 3 = 19 (S) I (9) + 3 = 12 (L) O (15) + 3 = 18 (R) L (12) - 3 = 9 (I) I (9) + 3 = 12 (L) N (14) - 3 = 11 (K)

This results in the sequence S, L, R, I, L, K. Comparing this to the given options, we find that option c) is the only choice that matches the calculated first two (SL) and last two (LK) characters. Note that the middle pair in the result (RI) appears as IR in the option, but since only one option aligns with the confirmed start and end of the code, SLIRLK is the correct answer.

Explanation

Kidney, Pancreas, and Liver are all classified as major anatomical organs within the human body. In contrast, Renin is not an organ but a proteolytic enzyme and hormone secreted by the kidneys. Renin functions as a biochemical mediator in the renin-angiotensin-aldosterone system, which regulates blood pressure and electrolyte balance. While the others represent physical structural units of the body, Renin is a chemical substance produced by an organ.

Explanation

The relationship in the given pair Player:Team is that of an individual member to its collective group. A player is a single unit that constitutes a team. Similarly, a flower is an individual unit, and a bouquet is the collective group or arrangement of flowers. Both pairs follow the same logical pattern of individual:collective.

Explanation

To find the number of students who passed in Economics only, we can partition the total class of 100 students into four mutually exclusive groups that cover all possible regions of the Venn diagram. Since every student passed in at least one subject, the sum of these groups must equal 100.

The first group consists of all students who passed History, which is given as n(H) = 50. This group already accounts for those who passed History only, both History and English only, both History and Economics only, and all three subjects.

The remaining students who are not included in the History total are those who passed in English only, those who passed in Economics only, and those who passed in both English and Economics only. We are given that 24 students passed in English only and 11 students passed in both English and Economics only.

Using the equation for the total number of students: Total = n(H) + (English only) + (English and Economics only) + (Economics only) 100 = 50 + 24 + 11 + (Economics only) 100 = 85 + (Economics only) Economics only = 100 - 85 = 15

This calculation directly yields the number of students who passed in Economics only without needing to calculate the intersection of History and Economics separately.

Explanation

The sum of the digits of the first number in the pair 5121:12 is 5 + 1 + 2 + 1 = 9, which does not match the given second number 12. This pair is the odd one out because it does not follow the digit-sum pattern where the second number is equal to the sum of the digits of the first number.

Explanation

The coding logic follows the sum of the digits of the alphabetical positional value of each letter in the word. For AUSTERE, the positional values are A=1, U=21, S=19, T=20, E=5, R=18, and E=5. Reducing these to the sum of their digits gives 1, 2+1=3, 1+9=10, 2+0=2, 5, 1+8=9, and 5. Concatenating these results in the code 13102595.

Applying the same logic to SETTING, the positional values are S=19, E=5, T=20, T=20, I=9, N=14, and G=7. Calculating the digit sums yields S: 1+9=10, E: 5, T: 2+0=2, T: 2+0=2, I: 9, N: 1+4=5, and G: 7. Combining these values sequentially produces the code 10522957.

Explanation

In the given number-pairs, the relationship between the first and second number follows the mathematical logic n : n², where the second number is the square of the first. Calculating the squares for the provided numbers, we have 11² = 121, 13² = 169, and 17² = 289. However, for the number 15, the square is 15² = 225. Since the pair provided is 15:250, it does not follow the established square pattern, making it the odd one out.

Explanation

The pattern followed in each row of the table is based on the formula: ( First number - Second number ) × 2 = Third number

Applying this to the first row: (15 - 3) × 2 = 12 × 2 = 24

Applying this to the second row: (21 - 6) × 2 = 15 × 2 = 30

Applying this to the third row to find the missing number: (49 - 5) × 2 = 44 × 2 = 88

Explanation

Statement 1 establishes that there is an intersection between the set of machines and the set of kites. Statement 2 specifies that the set of machines and the set of pigeons are mutually exclusive, meaning they have no elements in common. Since the overlapping part of machines and kites consists of elements that are machines, and no machine can be a pigeon, those specific kites within the intersection are guaranteed not to be pigeons. This logically validates the conclusion that some kites are not pigeons.

Explanation

The given series follows the pattern of n² + 1, where n is a sequence of consecutive prime numbers starting from 2. The first term is 2² + 1 = 5, the second is 3² + 1 = 10, and the third is 5² + 1 = 26. The prime numbers in order are 2, 3, 5, 7, 11, and 13. Following this sequence, the missing term is calculated using the next prime number, 7, which gives 7² + 1 = 49 + 1 = 50. This logic is consistent with the subsequent terms in the series, 11² + 1 = 122 and 13² + 1 = 170.

Explanation

The series follows an arithmetic progression based on the numerical positions of the letters in the English alphabet. The positions of the given letters are A = 1, E = 5, I = 9, Q = 17, and U = 21. The difference between consecutive terms is a constant value of 4, as seen in 5 - 1 = 4 and 9 - 5 = 4. To find the missing term, we apply this common difference to the last known letter before the gap: 9 + 4 = 13. The 13th letter of the alphabet is M. The pattern is verified by the subsequent term, as 13 + 4 = 17, which corresponds to the letter Q.

Explanation

The series follows a systematic arithmetic progression for each letter position within the clusters. By converting letters to their numerical positions in the English alphabet (A=1, B=2, ..., Z=26), the pattern is revealed.

For the first letter of each cluster, there is a constant increment of +2: A (1) + 2 = C (3), C (3) + 2 = E (5), E (5) + 2 = G (7), and G (7) + 2 = I (9). The missing first letter is G.

For the second letter of each cluster, there is a constant increment of +3: D (4) + 3 = G (7), G (7) + 3 = J (10), J (10) + 3 = M (13), and M (13) + 3 = P (16). The missing second letter is M.

For the third letter of each cluster, there is a constant increment of +4: G (7) + 4 = K (11), K (11) + 4 = O (15), O (15) + 4 = S (19), and S (19) + 4 = W (23). The missing third letter is S.

Combining these results, the cluster that replaces the question mark is GMS.

Explanation

The relationship between North and South is based on antonyms, as they represent opposite directions. Similarly, Frown and Smile share the same relationship because they are antonyms representing opposite facial expressions associated with contrasting emotions.

Explanation

Let M be the number of men and H be the number of horses. Since each man and horse has exactly one head, the total number of heads is M + H. Men have two legs and horses have four legs, so the total number of legs is 2M + 4H.

The problem states that the total number of legs is 14 more than twice the number of heads. This relationship can be expressed by the equation: 2M + 4H = 2(M + H) + 14

Expanding the right side of the equation: 2M + 4H = 2M + 2H + 14

Subtracting 2M from both sides of the equation: 4H = 2H + 14

Subtracting 2H from both sides: 2H = 14

Dividing by 2: H = 7

The number of horses in the group is 7.

Explanation

The coding logic is based on the alphabetical position of each letter (A=1, B=2, ..., Z=26). For the word PAGE, the positions are P=16, A=1, G=7, and E=5. The code is formed by taking the direct position value of the first, second, and fourth letters, while the third letter is represented by the square of its position value. Thus, for PAGE, the third letter G results in 7² = 49, and combining the values 16, 1, 49, and 5 produces 161495.

Applying this pattern to the word PART, the alphabetical positions are P=16, A=1, R=18, and T=20. Squaring the position of the third letter R gives 18² = 324. By concatenating the values 16, 1, 324, and 20 in sequence, the resulting code is 16132420.

Explanation

The relationship in the first pair is based on the field of study and its primary subject matter, where Astronomy is the scientific branch dedicated to the study of stars and celestial bodies. Similarly, Agronomy is the branch of agricultural science that deals with the study of soil management and the production of crops.

Explanation

The letter clusters in this set follow a logical pattern based on the numerical positions of the letters in the English alphabet, where A=1, B=2, …, Z=26. The position of the third letter is determined by the product of the positions of the first and second letters. In the cluster GCV, the letters correspond to positions G = 7, C = 3, and V = 22. Multiplying the first two values gives 7 × 3 = 21. The letter corresponding to the 21st position is U. Because this cluster contains V at the 22nd position instead of U, it fails to follow the product rule Position(1) × Position(2) = Position(3), making it the odd cluster.

Explanation

The Xylophone is categorized as a percussion instrument because it produces sound by being struck with mallets. The other three instruments—Clarinet, Trumpet, and Saxophone—are all wind instruments that require air to be blown into them to create sound through the vibration of an air column. This fundamental difference in the mechanism of sound production makes the Xylophone the odd word in the group.

Explanation

To determine the relationship between P and S, we break down the expression P ÷ R × T - Q ÷ S + U using the given definitions:

Q ÷ S: The definition A ÷ B means B is the son of A. Thus, S is the son of Q. T - Q: The definition A - B means B is the sister of A. Thus, Q is the sister of T. Since Q is female and the parent of S, Q is the mother of S. R × T: The definition A × B means A is the mother of B. Since R is the mother of T, and Q is the sister of T, R is also the mother of Q. Maternal Grandmother: As R is the mother of S's mother (Q), R is the maternal grandmother of S. P ÷ R: This link identifies P as the husband of R. Given that R is the maternal grandmother of S, her husband P is the maternal grandfather of S.

Explanation

To make the equation 12 + 81 - 27 × 9 ÷ 3 = 36 correct, the signs - and ÷ must be interchanged. Substituting these signs into the equation results in 12 + 81 ÷ 27 × 9 - 3 = 36.

Following the BODMAS rule, the operations are performed in the order of Division, Multiplication, Addition, and then Subtraction. First, dividing 81 by 27 gives 3. The expression then becomes 12 + 3 × 9 - 3. Next, performing the multiplication of 3 and 9 results in 27, leading to the expression 12 + 27 - 3. Adding 12 and 27 gives 39. Finally, subtracting 3 from 39 yields 36, which matches the right-hand side of the equation.

Explanation

The coding follows the pattern of opposite letters in the English alphabet, where the sum of the numerical positions of the original letter and its coded letter is exactly 27. For the word DKQX, the transformation is as follows: D (4) becomes W (27 - 4 = 23), K (11) becomes P (27 - 11 = 16), Q (17) becomes J (27 - 17 = 10), and X (24) becomes C (27 - 24 = 3).

Applying this same logic to the word AFKP: The position of A is 1, so the coded letter is 27 - 1 = 26, which is Z. The position of F is 6, so the coded letter is 27 - 6 = 21, which is U. The position of K is 11, so the coded letter is 27 - 11 = 16, which is P. The position of P is 16, so the coded letter is 27 - 16 = 11, which is K. Combining these letters yields ZUPK.

Explanation

The third number in each row is determined by adding the first two numbers, finding the sum of the digits of that result, and multiplying it by 11. The formula follows C₃ = 11 × sum of digits of (C₁ + C₂).

In the first row, 23 + 5 = 28. The sum of the digits of 28 is 2 + 8 = 10. Multiplying this by 11 gives 10 × 11 = 110.

In the second row, 56 + 9 = 65. The sum of the digits of 65 is 6 + 5 = 11. Multiplying this by 11 gives 11 × 11 = 121.

In the third row, 49 + 3 = 52. The sum of the digits of 52 is 5 + 2 = 7. Multiplying this by 11 results in 7 × 11 = 77.

Explanation

The series follows a pattern where each subsequent number is obtained by adding a power of 2 to the previous term, starting with 2² = 4. The differences between consecutive terms are as follows:

66 - 62 = 4 = 2² 74 - 66 = 8 = 2³ 90 - 74 = 16 = 2⁴

The differences form a geometric progression where each value is double the previous one. Following this logic, the next difference must be 16 × 2 = 32 (or 2⁵). To find the missing number, add this difference to the last known term:

90 + 32 = 122

Explanation

The given words represent large numbers in the standard short scale system, and their logical order is determined by their increasing numerical magnitude. A million is defined as 10⁶. Moving up the scale, a trillion is 10¹², followed by a quadrillion which is 10¹⁵. A quintillion represents 10¹⁸, and an octillion is a significantly larger value equivalent to 10²⁷. The prefixes tri-, quadri-, quinti-, and octi- follow the Latin sequence for 3, 4, 5, and 8 respectively, dictating the progression of these powers of ten. Arranging these from smallest to largest results in the sequence: Million (3), Trillion (5), Quadrillion (1), Quintillion (2), and Octillion (4).