SSC CGL Tier 1 2022 General Intelligence & Reasoning Questions with Solutions

Explanation

By substituting the given symbols with their respective mathematical operators, the expression 126 7 % 3 @ 19 # 21 becomes 126 ÷ 7 × 3 + 19 - 21. Applying the BODMAS rule, the operations are performed in the order of Division, Multiplication, Addition, and then Subtraction.

First, perform the division: 126 ÷ 7 = 18. The expression now is 18 × 3 + 19 - 21.

Next, perform the multiplication: 18 × 3 = 54. The expression becomes 54 + 19 - 21.

Then, perform the addition: 54 + 19 = 73. Finally, perform the subtraction: 73 - 21 = 52$.

Explanation

The numerical series follows the mathematical pattern where each subsequent term is obtained by multiplying the previous term by 3 and adding 2 to the product. The logic can be expressed by the formula Tₙ = (Tₙ₋₁ × 3) + 2.

Applying this rule to the given sequence: The second term is 12 × 3 + 2 = 36 + 2 = 38 The third term is 38 × 3 + 2 = 114 + 2 = 116 The fourth term is 116 × 3 + 2 = 348 + 2 = 350

Following this consistent pattern, the missing number is calculated by applying the same operation to the fourth term: 350 × 3 + 2 = 1050 + 2 = 1052

Explanation

The letter-clusters in the series follow a consistent mathematical pattern based on the positions of the letters in the English alphabet.

The first letter of each cluster increases by 1 in each step: P (16) + 1 = Q (17), Q + 1 = R (18), R + 1 = S (19), and S + 1 = T (20).

The second letter of each cluster increases by 3 in each step: G (7) + 3 = J (10), J + 3 = M (13), M + 3 = P (16), and P + 3 = S (19).

The third letter of each cluster increases by 5 in each step: F (6) + 5 = K (11), K + 5 = P (16), P + 5 = U (21), and U + 5 = Z (26).

Combining these results, the next cluster in the sequence is TSZ.

Explanation

Swati's father is the maternal grandfather of Divya, which means he is the father of Divya's mother. Since it is given that Divya is the daughter of Manya, Manya is the mother of Divya. Manya's husband is therefore the father of Divya. The relationship in question is between Manya's husband's father and Divya. The father of an individual's father is their paternal grandfather. In general kinship terms, this relationship is classified as a grandfather.

Explanation

The given sequence follows a pattern where each subsequent number is obtained by subtracting a constant value of 38 from the preceding number. This is an arithmetic progression with a common difference of -38.

Calculating the differences between consecutive terms: 361 - 323 = 38 323 - 285 = 38 285 - 247 = 38

To find the missing number in the series, subtract 38 from the last known term: 247 - 38 = 209

Explanation

The arrangement of words in an English dictionary follows alphabetical order by comparing letters at each position sequentially from left to right. Among the given words, Southern (3) and Sovereignty (6) start with the prefix So, which alphabetically precedes words starting with Sp or St. Between these two, Southern comes first because the third letter u appears before v. Next, the words Spacious (5) and Speaking (1) both begin with Sp; Spacious precedes Speaking because its third letter a comes before e. Finally, Stampede (4) and Standardize (2) both begin with the letters Sta. Comparing the fourth letters m and n, Stampede comes before Standardize because m precedes n in the alphabet. Following this systematic comparison results in the sequence 3, 6, 5, 1, 4, 2.

Explanation

The given series follows a repeating pattern where a specific five-letter block is repeated four times. By dividing the total 20 characters of the series into groups of five, the pattern becomes clear:

P Q _ Q P | P Q R _ P | P Q R Q _ | P Q R Q _

By sequentially placing the letters from the correct option (R, Q, P, P) into the blanks, the series becomes:

P Q R Q P | P Q R Q P | P Q R Q P | P Q R Q P

In the first group, R completes the block P Q R Q P. In the second group, Q completes the block P Q R Q P. In the third group, P completes the block P Q R Q P. In the fourth group, the final P completes the block P Q R Q P. The sequence is formed by the constant repetition of the five-letter unit P-Q-R-Q-P.

Explanation

In a circular seating arrangement of six people facing the centre, being third to the left is equivalent to being seated diametrically opposite. Let the positions be numbered 1 to 6 in a clockwise direction. If Prakrit is at position 1, Raghav sits second to his left at position 3. The condition that an equal number of people sit between Raghav and Manpreet from both ends implies they are opposite each other, placing Manpreet at position 6. Manpreet is to the immediate left of Sunaina, which means Sunaina is at position 5. The remaining seats are 2 and 4. Arwa is second to the right of Vedika; by moving anticlockwise from position 4, the second seat is position 2. Therefore, Vedika is at position 4 and Arwa is at position 2. The person sitting third to the left of Sunaina at position 5 is the one seated at position 2, which is Arwa.

Explanation

To find the code for love, we compare the two given statements. The first statement jig fig vic translates to I love India, and the second statement re dig fig lic vic translates to I like culture of India. The words I and India appear in both English phrases. Correspondingly, the codes fig and vic appear in both sets of coded instructions. This means that fig and vic represent I and India in some order. In the first statement jig fig vic, after accounting for the codes for I and India, the only remaining word is love and the only remaining code is jig. Thus, love is represented by jig.

Explanation

The letter-cluster HLP is the odd one out because it deviates from the logic shared by the other three clusters. In the clusters LQJ, FKP, and SXC, the second letter is obtained by adding 5 to the alphabetical positional value of the first letter: L(12) + 5 = Q(17), F(6) + 5 = K(11), and S(19) + 5 = X(24). Furthermore, the second and third letters in these three groups are alphabetical opposites, meaning the sum of their positional values is exactly 27: Q(17) + J(10) = 27, K(11) + P(16) = 27, and X(24) + C(3) = 27.

In contrast, the cluster HLP follows a different progression. The difference between the first letter H (8) and the second letter L (12) is only +4. Additionally, the second and third letters, L (12) and P (16), are not alphabetical opposites because their positional values sum to 28 instead of 27.

Explanation

The coding logic follows the positional values of letters in the English alphabet (A=1, B=2, ..., Z=26). Most letters are represented by their positional value multiplied by 2, with specific exceptions for the first occurrence of the letters A and L.

For the word GALLERY: G (7): 7 × 2 = 14 A (1st instance): (1 + 10) × 2 = 22 L (1st instance): (12 - 10) × 2 = 4 L (2nd instance): 12 × 2 = 24 E (5): 5 × 2 = 10 R (18): 18 × 2 = 36 Y (25): 25 × 2 = 50 Concatenated: 1422424103650.

Applying the same logic to NOSTALGIA: N (14): 14 × 2 = 28 O (15): 15 × 2 = 30 S (19): 19 × 2 = 38 T (20): 20 × 2 = 40 A (1st instance): (1 + 10) × 2 = 22 L (1st instance): (12 - 10) × 2 = 4 G (7): 7 × 2 = 14 I (9): 9 × 2 = 18 A (2nd instance): 1 × 2 = 2

Combining these values results in the code: 2830384022414182.

Explanation

The relationship followed in the given number-pair 25:343 is that the second number is the cube of the sum of the digits of the first number.

Calculation for 25:343: Sum of digits of 25 = 2 + 5 = 7 Cube of the sum = 7³ = 343

Applying the same logic to the pair 24:216: Sum of digits of 24 = 2 + 4 = 6 Cube of the sum = 6³ = 216

Explanation

Let the amount received by Vineet be V. Based on the given conditions, Mayank gets twice the amount Vineet gets, so Mayank's share M = 2V. Prateek gets ₹25,000 less than Vineet, so Prateek's share P = V - 25000.

The total amount distributed is the sum of the individual shares: V + P + M = 295000

Substituting the expressions for P and M in terms of V: V + (V - 25000) + 2V = 295000 4V - 25000 = 295000 4V = 295000 + 25000 4V = 320000 V = ³²⁰⁰⁰⁰⁄₄ = 80000

Thus, Vineet receives an amount of ₹80,000.

Explanation

The given numbers are organized into a grid structure where each row contains four numbers. The logic governing the pattern is the difference between the sum of the two middle numbers and the sum of the first and last numbers in each row.

For the first row: (55 + 56) - (8 + 91) = 111 - 99 = 12 For the second row: (2 + 68) - (28 + 20) = 70 - 48 = 22

The results of these operations, 12 and 22, follow a progression where the difference between consecutive results increases by 1 in each step. The difference between 22 and 12 is 10. Therefore, the difference for the next step is 10 + 1 = 11, which makes the required result for the third row 22 + 11 = 33.

Applying this to the third row: (27 + x) - (11 + 7) = 33 (27 + x) - 18 = 33 27 + x = 51 x = 24

By following this mathematical pattern, the missing number is determined to be 24.

Explanation

To find the shortest distance between the office and the bank, we determine the net displacement in the north-south and east-west directions. Shweta first walks 150 m South, then 80 m West (right turn from South), then 60 m South (left turn from West), and finally 280 m East (left turn from South).

The total vertical displacement in the South direction is 150 + 60 = 210 m. The net horizontal displacement is the difference between the eastward and westward movements, which is 280 - 80 = 200 m East.

Using the Pythagorean theorem, the shortest distance D is the hypotenuse of a right-angled triangle with sides of 210 m and 200 m:

D = √(210²⁾⁺²⁰⁰^^^² D = √(44100 + 40000) D = √(84100) D = 290 m

Explanation

The first statement, All rabbits are cows, is a universal affirmative proposition (A-type). According to the rules of syllogism, a universal affirmative statement can be converted into a particular affirmative statement (I-type). Therefore, All rabbits are cows logically implies that Some cows are rabbits, which makes Conclusion II valid. Conclusion I does not logically follow because the statement Some rabbits are cats only establishes a partial intersection between rabbits and cats, which does not guarantee that the entire set of cats is contained within the set of rabbits.

Explanation

The series follows a specific pattern for each letter position within the clusters.

For the first letter of each cluster, the positional values increase by consecutive odd numbers: B (2) + 1 = C (3) C (3) + 3 = F (6) F (6) + 5 = K (11) Following the sequence +1, +3, +5, the next increment is +7. K (11) + 7 = R (18)

For the second letter of each cluster, the letters follow the sequence of English vowels: E, I, O, and U. Following the cyclic order of vowels (A, E, I, O, U), the next vowel after U is A.

For the third letter of each cluster, the positional values also increase by consecutive odd numbers: C (3) + 1 = D (4) D (4) + 3 = G (7) G (7) + 5 = L (12) Following the sequence +1, +3, +5, the next increment is +7. L (12) + 7 = S (19)

Combining these positions gives the cluster RAS.

Explanation

The difference between two people's ages remains constant throughout their lives. Since the difference between the ages of Ravish and Kailash was 18 years three years ago, it remains 18 years at any point in time. Let the present age of Kailash be K and the present age of Ravish be R. We establish the relationship R - K = 18, which means R = K + 18.

Three years from today, Ravish's age will be R + 3 and Kailash's age will be K + 3. According to the problem, at that time, Ravish will be three times as old as Kailash, leading to the equation R + 3 = 3(K + 3). Substituting the first relationship into this equation gives (K + 18) + 3 = 3K + 9. Simplifying the expression, we get K + 21 = 3K + 9, which leads to 2K = 12, and thus K = 6. By substituting the value of K back into the first relation, the present age of Ravish is R = 6 + 18 = 24.

Explanation

The series follows a pattern where consecutive prime numbers are added to each term to obtain the next term. Calculating the differences between the given numbers reveals the following sequence of additions:

54 - 35 = 19 77 - 54 = 23 106 - 77 = 29 137 - 106 = 31

The numbers added are 19, 23, 29, and 31, which are consecutive prime numbers. The next prime number following 31 is 37. By adding this value to the last term in the series, we find the missing number:

137 + 37 = 174

Explanation

The series follows a specific addition and subtraction pattern for each position in the letter-clusters.

For the first letter, the pattern is an increase of 2: L(12) + 2 = N(14), N(14) + 2 = P(16), P(16) + 2 = R(18). Following this, R(18) + 2 = 20, which corresponds to the letter T.

For the second letter, the pattern is an increase of 3: J(10) + 3 = M(13), M(13) + 3 = P(16), P(16) + 3 = S(19). Following this, S(19) + 3 = 22, which corresponds to the letter V.

For the third letter, the pattern is a decrease of 4: V(22) - 4 = R(18), R(18) - 4 = N(14), N(14) - 4 = J(10). Following this, J(10) - 4 = 6, which corresponds to the letter F.

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

Explanation

The coding logic follows an alternating addition pattern where +3 and +2 are added to the alphabetical positions of successive letters. In the word COLOUR, the transformations are C + 3 = F, O + 2 = Q, L + 3 = O, O + 2 = Q, U + 3 = X, and R + 2 = T. This same pattern is observed in VIOLET, where V + 3 = Y, I + 2 = K, O + 3 = R, L + 2 = N, E + 3 = H, and T + 2 = V.

Applying this +3, +2 alternating rule to PURPLE: P + 3 = S U + 2 = W R + 3 = U P + 2 = R L + 3 = O E + 2 = G

By calculating the forward shifts for each letter, the resulting code is SWUROG.

Explanation

The coding logic follows a two-step process: first, the positional values of the letters in the English alphabet (A = 1, B = 2, ..., Z = 26) are added together, and second, the resulting sum is multiplied by 2.

For the word LILY, the positional values are L = 12, I = 9, L = 12, and Y = 25. The sum is 12 + 9 + 12 + 25 = 58. Multiplying this sum by 2 gives 58 × 2 = 116.

For the word LOTUS, the positional values are L = 12, O = 15, T = 20, U = 21, and S = 19. The sum is 12 + 15 + 20 + 21 + 19 = 87. Multiplying this sum by 2 gives 87 × 2 = 174.

Applying this logic to the word TULIP, the positional values are T = 20, U = 21, L = 12, I = 9, and P = 16. The sum of these values is 20 + 21 + 12 + 9 + 16 = 78. Multiplying the sum by 2 results in 78 × 2 = 156.

Explanation

The letter-cluster GZTNK is the different cluster because it fails to follow the consistent decreasing subtraction pattern of -7, -6, -5, and -4 applied to the alphabetical positions of the letters. The numerical positions for the letters in this cluster are G = 7, Z = 26, T = 20, N = 14, and K = 11. The mathematical transitions are 7 - 7 = 26 (Z), 26 - 6 = 20 (T), 20 - 6 = 14 (N), and 14 - 3 = 11 (K). This results in a shift sequence of -7, -6, -6, and -3. The deviation occurs at the third and fourth transitions, which fail to adhere to the -5 and -4 sequence required by the common logic of the set.

Explanation

Substituting the given symbols with their corresponding mathematical operators, the expression becomes: 9 + 114 ÷ 19 × 5 - 21

Following the BODMAS rule, perform the operations in the order of Division, Multiplication, Addition, and Subtraction.

First, perform the division: 114 ÷ 19 = 6 The expression simplifies to: 9 + 6 × 5 - 21

Next, perform the multiplication: 6 × 5 = 30 The expression simplifies to: 9 + 30 - 21

Then, perform the addition: 9 + 30 = 39

Finally, perform the subtraction: 39 - 21 = 18

Explanation

The relationship between the letter-clusters follows a pattern of increasing addition to the positional values of the letters. For the first pair, L (12), G (7), and S (19) are transformed into P (16), L (12), and Y (25) respectively.

L (12) + 4 = P (16) G (7) + 5 = L (12) S (19) + 6 = Y (25)

Applying the same logic of +4, +5, and +6 to the third letter-cluster MKB:

M (13) + 4 = Q (17) K (11) + 5 = P (16) B (2) + 6 = H (8)

Thus, the resulting letter-cluster is QPH.

Explanation

The pattern followed in the given table is based on the relationship: (First Number + 1) × (Second Number + 1)/(2) = Third Number

Applying this formula to the first row: (14 + 1) × (21 + 1)/(2) = 15 × ²²⁄₂ = 15 × 11 = 165

Applying the same logic to the third row: (10 + 1) × (17 + 1)/(2) = 11 × ¹⁸⁄₂ = 11 × 9 = 99

To find the missing number in the second row, we use the same formula with the given numbers 13 and 19: (13 + 1) × (19 + 1)/(2) = 14 × ²⁰⁄₂ = 14 × 10 = 140

Explanation

The pattern involves adding 1 to each individual digit of the first number to obtain the second number (3+1=4, 8+1=9, 2+1=3, 4+1=5). Applying this logic to 5716, each digit is increased by 1 to get 6827.

Explanation

The series follows a pattern where each term is generated by multiplying the preceding term by 4 and adding 2. The recursive formula for the nth term is aₙ = (aₙ₋₁ × 4) + 2.

Applying this rule to the series: For the second term: (9 × 4) + 2 = 36 + 2 = 38 For the third term: (38 × 4) + 2 = 152 + 2 = 154 For the fourth term: (154 × 4) + 2 = 616 + 2 = 618

To find the missing term, we apply the same operation to the fourth term: (618 × 4) + 2 = 2472 + 2 = 2474

Explanation

To find the code for take medicines, we compare the given phrases to isolate the digits corresponding to each word. Comparing she needs some medicines (1542) and take some water (849), the common word is some and the common digit is 4, so some = 4. Comparing she needs some medicines (1542) and he needs rest (713), the common word is needs and the common digit is 1, so needs = 1. Comparing she needs some medicines (1542) and she is water (269), the common word is she and the common digit is 2, so she = 2. In the first sentence, since she, needs, and some are assigned 2, 1, and 4 respectively, the remaining digit 5 represents medicines.

Next, comparing take some water (849) and she is water (269), the common word is water and the common digit is 9, so water = 9. In the second sentence, since some is 4 and water is 9, the remaining digit 8 must represent take. Combining the codes for take (8) and medicines (5) gives the code 85.

Explanation

When the signs ÷ and + are interchanged, the given equation becomes 45 + 15 × 5 ÷ 15 - 11 = 39. Following the BODMAS rule, the operations are performed in the order of Division, Multiplication, Addition, and then Subtraction.

First, perform the division: 5 ÷ 15 = ⅓. The equation now reads: 45 + 15 × ⅓ - 11 = 39.

Next, perform the multiplication: 15 × ⅓ = 5. The equation simplifies to: 45 + 5 - 11 = 39.

Then, perform the addition: 45 + 5 = 50. The equation becomes: 50 - 11 = 39.

Finally, perform the subtraction: 50 - 11 = 39. Since 39 = 39, the equation is balanced.

Explanation

Niraj is the father of Rinku. Since Ruby is the only sister of Rinku, Niraj must also be the father of Ruby. Tiya is the daughter of Ruby, which makes Ruby the mother of Tiya. Consequently, Niraj is the father of Tiya's mother. In kinship terms, the father of one's mother is the maternal grandfather.

Explanation

The logical sequence of video production begins with the Script (4), which serves as the written plan for the project. Once the script is ready, the cast and crew perform a Rehearsal (2) to prepare for the shoot. Following the practice sessions, the actual Recording (1) of the footage takes place. After the raw footage is captured, it undergoes Video Editing (5) to assemble the final product. Finally, the completed video is released to the Viewers (3) for consumption. This chronological order represents the standard workflow from pre-production to post-production and distribution.

Explanation

In a circular arrangement where six children face the centre, immediate left corresponds to the clockwise direction and immediate right corresponds to the anti-clockwise direction. Starting with G, we place J to his immediate left (one position clockwise) and K to his immediate right (one position anti-clockwise). Since L is sitting to the immediate left of J, L is placed two positions clockwise from G. This leaves two consecutive empty seats between L and K.

The condition states that L is not to the immediate right of H. Because the immediate right is the anti-clockwise direction, if H were placed in the seat immediately following L in the clockwise direction, L would be to the immediate right of H. To avoid this, H must occupy the other available seat, which is the one located to the immediate right (anti-clockwise) of K. This placement leaves the remaining seat between L and H for I. Consequently, H is the person sitting to the immediate right of K.

Explanation

The relationship between the numbers in the pair 24:648 is defined by the formula x : x × (x + 3). Substituting 24 for x, we get 24 × (24 + 3) = 24 × 27 = 648. Applying this same logic to the first number in option b, we substitute 22 for x to get 22 × (22 + 3) = 22 × 25 = 550, which matches the second number of the pair.

Explanation

The given sequence 5, 25, 125, 625, ... is a geometric progression where the first term a = 5 and the common ratio r = 5, calculated as 25/5 = 5. The formula for the n-th term of a geometric progression is Tₙ = a · rⁿ⁻¹. To find the position of 390625, we substitute the values into the formula: 390625 = 5 · 5ⁿ⁻¹.

This equation simplifies to 390625 = 5ⁿ. To solve for n, we express 390625 as a power of 5. We know that 5⁴ = 625. Squaring both sides gives (5⁴)² = 625², which results in 5⁸ = 390625. By comparing the exponents in 5ⁿ = 5⁸, we determine that n = 8. Thus, 390625 is the 8th term in the series.

Explanation

To determine the initial direction, we calculate the net change in orientation by treating clockwise (CW) turns as positive and anticlockwise (ACW) turns as negative.

Net rotation = +90° (CW) - 180° (ACW) - 135° (ACW) + 180° (CW) Net rotation = +90° - 135° = -45°

A net rotation of -45° indicates that the final direction is 45° anticlockwise from the initial direction. To find the starting point, we must perform the inverse operation by moving 45° clockwise from the final direction.

Initial Direction = Final Direction + 45° (CW) Initial Direction = North-East + 45° (CW)

On a standard compass, North-East is located at 45° from North. Moving 45° clockwise from North-East reaches the 90° mark, which corresponds to the East direction.

Explanation

To determine if the first equation is balanced, we interchange the positions of the numbers 18 and 30. The original equation is 35 ÷ 5 × 5 + 30 - 18 = 23. By swapping 18 and 30, the left-hand side (LHS) of the equation becomes 35 ÷ 5 × 5 + 18 - 30.

Applying the BODMAS rule, we first perform the division operation: 35 ÷ 5 = 7 The expression now reads: 7 × 5 + 18 - 30

Next, we perform the multiplication: 7 × 5 = 35 The expression now reads: 35 + 18 - 30

Following this, we perform the addition: 35 + 18 = 53 The expression now reads: 53 - 30

Finally, we perform the subtraction: 53 - 30 = 23

Since the calculated LHS is 23 and the right-hand side (RHS) is also 23, the equation is correctly balanced after the interchange.

Explanation

Let the number of students in class 12 be y. The number of students in class 10 is 1/3 more than class 12, which can be expressed as y + ⅓y = ⁴⁄₃y. The sum of the students in both classes is given as 112, leading to the linear equation ⁴⁄₃y + y = 112. Combining the terms on the left side gives ⁷⁄₃y = 112. Multiplying both sides by 3/7 results in y = (112 × 3)/(7) = 16 × 3 = 48. To find the number of students in class 10, substitute y back into the expression ⁴⁄₃y, which yields ⁴⁄₃ × 48 = 4 × 16 = 64.

Alternatively, the relationship can be viewed as a ratio. If class 12 has 3 parts, class 10 has 3 + 1 = 4 parts. The total number of parts is 4 + 3 = 7. Since 7 parts correspond to 112 students, one part is equal to 112 / 7 = 16. Therefore, the number of students in class 10 is 4 × 16 = 64.

Explanation

By substituting the signs sequentially into the equation 84 ∗ 42 ∗ 7 ∗ 5 ∗ 21 ∗ 93, we get the expression 84 + 42 ÷ 7 × 5 - 21 = 93. Following the BODMAS rule, the operations are performed in the order of Division, Multiplication, Addition, and then Subtraction.

First, perform the division: 42 ÷ 7 = 6. The equation becomes 84 + 6 × 5 - 21 = 93. Next, perform the multiplication: 6 × 5 = 30. This results in 84 + 30 - 21 = 93. Then, perform the addition: 84 + 30 = 114. Finally, perform the subtraction: 114 - 21 = 93.

Since 93 = 93, the equation is perfectly balanced.

Explanation

The relationship can be decoded by breaking down the statement from Shalini's perspective. Shalini's daughter's father is her husband. Her husband's wife refers to Shalini herself. Shalini's father's wife is Shalini's mother. The only son of Shalini's mother is Shalini's brother. Therefore, the boy is Shalini's brother, which makes Shalini the sister of the boy.

Explanation

The series follows a specific pattern of decreasing alphabetical positions for each corresponding letter in the clusters. By converting the letters into their numerical positions in the English alphabet (A=1, B=2, ..., Z=26), the pattern can be calculated as follows:

First letter: T (20), P (16), L (12), H (8), ?, Z (26). The difference is -4. 8 - 4 = 4, which corresponds to the letter D. Verification: 4 - 4 = 0, which corresponds to Z (26) in a circular alphabet.

Second letter: M (13), H (8), C (3), X (24), ?, N (14). The difference is -5. C (3) - 5 = -2; -2 + 26 = 24 (X). X (24) - 5 = 19, which corresponds to the letter S. Verification: 19 - 5 = 14 (N).

Third letter: D (4), X (24), R (18), L (12), ?, Z (26). The difference is -6. D (4) - 6 = -2; -2 + 26 = 24 (X). L (12) - 6 = 6, which corresponds to the letter F. Verification: 6 - 6 = 0, which corresponds to Z (26).

Fourth letter: S (19), L (12), E (5), X (24), ?, J (10). The difference is -7. E (5) - 7 = -2; -2 + 26 = 24 (X). X (24) - 7 = 17, which corresponds to the letter Q. Verification: 17 - 7 = 10 (J).

Combining these results, the missing cluster is DSFQ.

Explanation

The coding pattern follows a specific rule for vowels and consonants: consonants are shifted two places forward (+2) in the alphabetical order, while vowels are shifted two places backward (-2). In the word NAILS, the consonants N, L, and S are coded as P, N, and U (N+2=P, L+2=N, S+2=U), and the vowels A and I are coded as Y and G (A-2=Y, I-2=G). In the word TEXT, the consonants T and X shift to V and Z (T+2=V, X+2=Z), while the vowel E shifts to C (E-2=C).

Applying this logic to FOREST: F (consonant) + 2 = H O (vowel) - 2 = M R (consonant) + 2 = T E (vowel) - 2 = C S (consonant) + 2 = U T (consonant) + 2 = V

The resulting code for FOREST is HMTCUV.

Explanation

To arrange words in dictionary order, we compare letters from left to right. All six words begin with the prefix dis. Comparing the fourth letter, words 1, 2, 4, 5, and 6 have a, while word 3 has c, which places discharge last in the sequence. Among the words starting with disa, we compare the fifth letter: d in disadvantage (5), p in disappear (4) and disappointment (2), r in disarticulate (6), and s in disaster (1). Following the alphabet, d comes first, making disadvantage (5) the first word. To distinguish between disappear (4) and disappointment (2), we look at the seventh letter, as the first six letters are identical; e in disappear comes before o in disappointment, so 4 precedes 2. Next is disarticulate (6) because r follows p. Then comes disaster (1) because s follows r. Finally, discharge (3) completes the list. The final alphabetical order is 5, 4, 2, 6, 1, 3.

Explanation

The pattern follows the logic 5 × First Number + 6 × Second Number = Third Number.

In the first set of numbers: 5 × 8 + 6 × 6 = 40 + 36 = 76

In the third set of numbers: 5 × 7 + 6 × 13 = 35 + 78 = 113

Applying the same logic to the second set to find the missing number: 5 × 12 + 6 × 10 = 60 + 60 = 120

Explanation

The cluster FCXB is different because it fails to follow the consistent pattern where the second letter is three positions behind the first, and the fourth letter is three positions behind the third. In terms of alphabetical positions, the rule applied to the other clusters is L₁ - 3 = L₂ and L₃ - 3 = L₄. For this specific cluster, the first part is correct as F (6) - 3 = 3 (C). However, the second part is incorrect because X (24) - 3 equals 21, which corresponds to the letter U, whereas the cluster provides the letter B (2). This deviation from the required subtraction logic distinguishes this cluster from the rest.

Explanation

The relationship between the letter-clusters is determined by two distinct rules applied to the positions of the letters in the English alphabet. The first two letters of the cluster follow the opposite letter rule, where the sum of the positional values of the original letter and its corresponding letter is 27. The third letter follows a positional shift of +5.

Analyzing the transformation from FPD to UKI: The first letter F (6) corresponds to U (21) because 6 + 21 = 27. The second letter P (16) corresponds to K (11) because 16 + 11 = 27. The third letter D (4) shifts forward by 5 units to become I (9).

Applying this same logic to the letter-cluster LWP: The first letter L (12) corresponds to O (15) because 12 + 15 = 27. The second letter W (23) corresponds to D (4) because 23 + 4 = 27. The third letter P (16) shifts forward by 5 units to become U (21).

Following these steps, the resulting letter-cluster is ODU.

Explanation

The series follows a pattern where the difference between consecutive terms is defined by the expression n³ + 1 for n = 1, 2, 3, 4, ….

Starting from the first term: 32 + (1³ + 1) = 32 + 2 = 34 34 + (2³ + 1) = 34 + 9 = 43 43 + (3³ + 1) = 43 + 28 = 71 71 + (4³ + 1) = 71 + 65 = 136

To find the missing number, the next difference in the sequence must be 5³ + 1, which is 125 + 1 = 126. Adding this value to the previous term gives: 136 + 126 = 262

Explanation

The series T_XTU__UXT_X consists of 12 letters. By dividing the total length into four groups of three letters each, we can identify a repeating pattern. Filling the blanks with the letters from option a (UXTU) results in the sequence T(U)X T U(X) (T)U X T(U)X. When partitioned, this reads as TUX | TUX | TUX | TUX, establishing a consistent repeating unit of TUX throughout the series.

Explanation

The coding logic involves calculating the sum of the positional values of the letters in the English alphabet (where A = 1, B = 2, ..., Z = 26) and then multiplying that sum by 2.

For the word MOST: M = 13, O = 15, S = 19, T = 20 Sum = 13 + 15 + 19 + 20 = 67 Value = 67 × 2 = 134

For the word FUR: F = 6, U = 21, R = 18 Sum = 6 + 21 + 18 = 45 Value = 45 × 2 = 90

Applying the same logic to the word SUCCESS: S = 19, U = 21, C = 3, C = 3, E = 5, S = 19, S = 19 Sum = 19 + 21 + 3 + 3 + 5 + 19 + 19 = 89 Value = 89 × 2 = 178

Explanation

Thermometers conventionally use mercury as the working fluid because it remains in liquid form over a wide range of temperatures and expands linearly with heat. In this coding-decoding problem, the actual substance used in thermometers, which is mercury, is referred to by the code name curd. Therefore, based on the specific mapping provided in the question, curd is the name designated for the substance used in thermometers.