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

Explanation

The series consists of the squares of prime numbers where every alternate prime number is selected starting from the first prime number. The sequence of prime numbers is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and so on.

The terms in the given series are: 2² = 4 (the square of the 1st prime) 5² = 25 (the square of the 3rd prime) 11² = 121 (the square of the 5th prime) 17² = 289 (the square of the 7th prime) 23² = 529 (the square of the 9th prime) 31² = 961 (the square of the 11th prime)

By following the pattern of squaring the 1st, 3rd, 5th, 7th, 9th, and 11th prime numbers, the missing value is found by squaring the 7th prime number, which is 17. The square of 17 is 289.

Explanation

The coding logic follows the square of the numerical position of each letter in the English alphabet. For the word GUM, the alphabetical positions are G = 7, U = 21, and M = 13. Squaring these numbers gives 7² = 49, 21² = 441, and 13² = 169. When these squares are written consecutively, they form the code 49441169. Applying this same pattern to the word WAX, the alphabetical positions are W = 23, A = 1, and X = 24. Calculating the squares of these positions results in 23² = 529, 1² = 1, and 24² = 576. Combining these results in order produces the code 5291576.

Explanation

The pattern followed in the given matrix is that the third number in each row is twice the difference between the first and second numbers. The logic can be represented by the formula Rₙ C₃ = 2 × (Rₙ C₁ - Rₙ C₂).

Applying this to the first row: 2 × (10 - 3) = 2 × 7 = 14. Applying this to the second row: 2 × (49 - 15) = 2 × 34 = 68. Applying this to the third row: 2 × (33 - 19) = 2 × 14 = 28.

Explanation

The series follows a pattern of decreasing numerical gaps between consecutive letters based on their positions in the English alphabet. The positional values are W = 23, Q = 17, H = 8, E = 5, and C = 3. Calculating the differences between the known terms reveals a sequence: 23 - 17 = 6, 8 - 5 = 3, and 5 - 3 = 2. This indicates that the differences are decreasing by 1 for each step in the series. Following this logic, the gap after Q (17) should be 5, and the gap after the missing letter should be 4. Subtracting 5 from the position of Q gives 17 - 5 = 12. The 12th letter of the alphabet is L. This fits the pattern perfectly, as the next difference would be 12 - 8 = 4, leading to H.

Explanation

Let the price of product B be x. Since product A is costlier than product B by ₹2, the price of product A is represented as x + 2. The problem states that when the price of product A is increased by twice the price of product B, the resulting price is ₹17. This can be expressed using the following linear equation:

(x + 2) + 2x = 17

Combining the terms containing x gives:

3x + 2 = 17

Subtracting 2 from both sides of the equation:

3x = 15

Dividing both sides by 3:

x = 5

The price of product B is ₹5.

Explanation

The words represent units of length that are arranged in a logical ascending order based on their physical magnitude. Converting all units to metres for comparison, a Micron (1) is 10⁻⁶ m, a Millimetre (4) is 10⁻³ m, and a Centimetre (6) is 10⁻² m. These are followed by the Metre (2), which is 1 m. Among the larger units, a Kilometre (5) is 10³ m or 1000 m, and a Mile (3) is approximately 1609.34 m. Arranging these from the smallest to the largest value yields the sequence 1-4-6-2-5-3.

Explanation

The relationship established in the first pair is that of an item and its broader category, where grapes are a specific type of fruit. Following this same logic, pepper is a dried seed or berry used primarily for seasoning, flavoring, and adding heat to food, which classifies it under the category of spices. As grapes are to fruits, pepper is to spices.

Explanation

The coding logic involves reversing the order of the letters in the word and then shifting each letter two positions backward in the alphabetical sequence (n - 2).

For the word PYTHON: Reverse the string: NOHTYP Shift each letter by -2: N (14) - 2 = 12 (L) O (15) - 2 = 13 (M) H (8) - 2 = 6 (F) T (20) - 2 = 18 (R) Y (25) - 2 = 23 (W) P (16) - 2 = 14 (N) The code is LMFRWN.

Applying the same logic to RHYTHM: Reverse the string: MHTYHR Shift each letter by -2: M (13) - 2 = 11 (K) H (8) - 2 = 6 (F) T (20) - 2 = 18 (R) Y (25) - 2 = 23 (W) H (8) - 2 = 6 (F) R (18) - 2 = 16 (P) The resulting code is KFRWFP.

Explanation

The relationship between the numbers follows the mathematical logic n³ + n², where n represents the first number in each pair.

For the first pair, 6 : 252, the calculation is: 6³ + 6² = 216 + 36 = 252

Applying the same logic to the third number, 5, we get: 5³ + 5² = 125 + 25 = 150

Alternatively, this pattern can be identified as n² × (n + 1). Using this formula for the number 5: 5² × (5 + 1) = 25 × 6 = 150

Explanation

The letter-cluster HFE is the odd one out because it is the only cluster in the set that contains a vowel and follows a strictly decreasing alphabetical sequence. In HFE, the letter E is a vowel, whereas all other clusters are composed exclusively of consonants. Furthermore, when mapping the letters to their numerical positions in the English alphabet (A=1, B=2, ..., Z=26), the letters H, F, and E correspond to 8, 6, and 5 respectively. This sequence is strictly decreasing (8 > 6 > 5), which distinguishes it from the other clusters where the middle letter consistently has a higher numerical value than both the first and the third letters.

Explanation

According to the first statement, the set of cars is a subset of the set of trucks, represented as C ⊆ T. The second statement establishes that there is an intersection between the set of buses and the set of cars, meaning B ∩ C ≠ ∅. Since every car is also a truck, any element that belongs to the intersection of buses and cars must also belong to the set of trucks. Therefore, the intersection of buses and trucks B ∩ T is guaranteed to be non-empty, which logically validates conclusion II.

Explanation

The expression E ÷ F - H + J × G + D defines the family relationships as follows. E ÷ F indicates that F is the husband of E. F - H states that F is the father of H, which makes H the child of F and E. H + J means that J is the sister of H. J × G establishes that G is the son of J. Finally, G + D signifies that D is the sister of G.

From these connections, we can determine that D is the daughter of J, as D and G are siblings and G is the son of J. Since J is the sister of H, D is the daughter of H's sister. In kinship terminology, the daughter of one's sister is a niece. Thus, D is the niece of H.

Explanation

Rajkot, Ahmedabad, and Surat are all major cities located in the state of Gujarat. Jhalrapatan, known as the City of Bells, is situated in the Jhalawar district of the state of Rajasthan. Thus, the classification is based on the geographical location of the cities within Indian states.

Explanation

The relationship between the numbers in the pairs is based on divisibility. In the pairs 6-174, 5-155, and 11-143, the second number is exactly divisible by the first number. Specifically, 174 ÷ 6 = 29, 155 ÷ 5 = 31, and 143 ÷ 11 = 13. In the pair 8-138, the second number 138 is not a multiple of 8, as 138 ÷ 8 = 17.25. This makes the second pair the odd one out.

Explanation

By interchanging the digits 6 and 2, every occurrence of the digit 2 is replaced by 6 and every occurrence of the digit 6 is replaced by 2. The original equation 32 ÷ 6 + 26 - 13 × 6 = 54 is transformed into 36 ÷ 2 + 62 - 13 × 2 = 54. Following the BODMAS rule, we first perform the division 36 ÷ 2 = 18 and the multiplication 13 × 2 = 26. The equation then becomes 18 + 62 - 26 = 54. Summing the first two terms gives 80 - 26 = 54, which results in 54 = 54. This confirms the equation is balanced.

Explanation

The coding logic follows the alphabetical position of each letter in the word, written in reverse order starting from the last letter to the first. In the word EARTH, the positions are E = 5, A = 1, R = 18, T = 20, and H = 8. Reversing the sequence of these numerical values gives 8, 20, 18, 1, and 5, which results in the code 8201815.

Applying this pattern to the word ORBIT, the alphabetical positions of the letters are O = 15, R = 18, B = 2, I = 9, and T = 20. When these positions are arranged in reverse order, the sequence becomes 20, 9, 2, 18, and 15. Concatenating these values yields the code 20921815.

Explanation

The relationship followed in each pair is that the second number is the product of the digits of the first number. In the first pair, 72 : 14, the digits of 72 are 7 and 2, and their product is 7 × 2 = 14. Similarly, in the third pair, 96 : 54, the digits of 96 are 9 and 6, and their product is 9 × 6 = 54. Applying the same logic to the middle pair with the number 87, the product of its digits is 8 × 7 = 56.

Explanation

The coding logic follows a pattern where the first and the last letters of the word remain unchanged. For the intermediate letters, the pattern alternates between moving one position forward (+1) and one position backward (-1) in the English alphabetical order. In the word JUPITER, the first letter J and last letter R are fixed, while the middle letters transform as U + 1 = V, P - 1 = O, I + 1 = J, T - 1 = S, and E + 1 = F, resulting in JVOJSFR. Applying this logic to NEPTUNE, the first letter N and the last letter E remain constant. The intermediate letters undergo the same alternating shifts: E + 1 = F, P - 1 = O, T + 1 = U, U - 1 = T, and N + 1 = O. Concatenating these letters results in the coded form NFOUTOE.

Explanation

Let the printed price of the product be x. The label price is a 20% discount on the printed price, so the Label Price = x × (100 - 20)/(100) = 0.8x. An additional 10% discount is then applied to the label price during the sale, making the final selling price 0.8x × (100 - 10)/(100) = 0.8x × 0.9 = 0.72x.

Given that the final selling price is ₹468, we can equate: 0.72x = 468 x = (468)/(0.72) x = ⁴⁶⁸⁰⁰⁄₇₂

Simplifying the fraction by dividing both the numerator and denominator by 9: x = ⁵²⁰⁰⁄₈ x = 650

Explanation

From the expression P + R× T - Q + S ÷ U, we decode the relationships step by step. S ÷ U indicates S is the father of U. Q + S denotes Q is the wife of S, which makes Q the mother of U. T - Q means Q is the daughter of T. R× T tells us T is the brother of R, which implies R and T are brothers. Finally, P + R establishes that P is the wife of R.

Since T is the father of Q and R is the brother of T, R is the paternal uncle of Q. As P is the wife of R, P is the paternal aunt-in-law of Q. In standard kinship terms, the wife of one's father's brother is referred to as an Aunt. Therefore, P is the aunt of Q, who is the mother of U.

Explanation

Based on the 2011 Census and the reorganization of states as of 2014, the states are arranged in descending order of population. Uttar Pradesh (4) is the most populous state in India with approximately 19.98 crore people. Madhya Pradesh (2) ranks as the fifth most populous state with a population of approximately 7.26 crore. After the separation of Telangana, the population of Andhra Pradesh (1) is approximately 4.93 crore. Among the smaller states, Himachal Pradesh (5) has a population of approximately 68.6 lakh, and Arunachal Pradesh (3) is one of the least populated states with approximately 13.8 lakh residents.

Explanation

The relationship between the words is that of a sub-category to its primary category. A dentist is a specific type of medical professional who belongs to the broader classification of a doctor. Similarly, chemistry is a specific branch of knowledge that falls under the overarching domain of science.

Explanation

By interchanging the signs ÷ and ×, the given equation 121 + 11 - 42 × 6 ÷ 7 = 83 is rewritten as 121 + 11 - 42 ÷ 6 × 7 = 83. Following the BODMAS rule, we first perform the division operation, then multiplication, and finally addition and subtraction.

Step 1: Division 121 + 11 - (42 ÷ 6) × 7 = 121 + 11 - 7 × 7

Step 2: Multiplication 121 + 11 - (7 × 7) = 121 + 11 - 49

Step 3: Addition and Subtraction 132 - 49 = 83

Since 83 = 83, the equation is satisfied.

Explanation

The logic followed by the number-pairs is (n + 1)² + 2 = second number, where n is the first number. In option b, the first number is 17. Following the established pattern, the second number should be (17 + 1)² + 2 = 18² + 2 = 324 + 2 = 326. However, the given value is 290, which instead satisfies the relationship n² + 1 = 17² + 1 = 290. This pair deviates from the consistent pattern applied to the other sets, which all satisfy the logic: (10 + 1)² + 2 = 123, (14 + 1)² + 2 = 227, and (11 + 1)² + 2 = 146.

Explanation

In the set (17, 24, 45), the relationship between the numbers is defined by the differences between consecutive terms. The difference between the first and second number is 24 - 17 = 7. The difference between the second and third number is 45 - 24 = 21.

Applying the same logic to the set (12, 19, 40): The difference between the first and second number is 19 - 12 = 7. The difference between the second and third number is 40 - 19 = 21.

The pattern follows the addition of 7 and 21 respectively to obtain the subsequent numbers in the set.

Explanation

Based on the first statement, the set of singers is entirely contained within the set of dancers. The second statement establishes that the set of dancers and the set of plumbers are completely disjoint, meaning they have no elements in common. Since all singers are dancers, and no dancer is a plumber, it logically follows that no singer can be a plumber. Consequently, no plumber can be a singer, which validates Conclusion I.

Regarding Conclusion III, the statement that all singers are dancers implies that every individual in the singer category is also in the dancer category. This creates an overlap where at least some members of the dancer group are singers. In categorical logic, the universal affirmative statement All A are B supports the particular affirmative inference Some B are A. Therefore, Conclusion III is also logically valid.

Explanation

Aurangabad is not a state capital, which distinguishes it from the other three cities that serve as administrative capitals. Hyderabad is the capital of Telangana, Chennai is the capital of Tamil Nadu, and Gangtok is the capital of Sikkim. While Aurangabad is a major city in Maharashtra, Mumbai serves as the capital of that state.

Explanation

The series follows a pattern where each letter in a cluster is moved forward by two positions in the English alphabetical order to form the next cluster. For the first letter of each cluster, the progression is D+2=F, F+2=H, H+2=J, and J+2=L. For the second letter, the sequence is A+2=C, C+2=E, E+2=G, and G+2=I. For the third letter, the pattern is G+2=I, I+2=K, K+2=M, and M+2=O. Applying these increments to the second cluster FCI, the first letter F becomes H, the second letter C becomes E, and the third letter I becomes K, forming the cluster HEK.

Explanation

The relationship established in the first pair is that of raw material and its derived product. Wheat is the primary raw material used in the production of bread. Similarly, sugarcane serves as the essential raw material for producing jaggery, which is created by boiling and concentrating sugarcane juice until it solidifies.

Explanation

Mapping the letters of the cluster FGL to their numerical positions in the English alphabet where A=1, B=2, …, Z=26, the values are F=6, G=7, and L=12. The sequence follows an increment of 1 from the first to the second letter (6+1=7), while the increment from the second to the third letter is 5 (7+5=12). The established logic for the set requires an increment of 1 followed by an increment of 4 (+1, +4).

Explanation

The series follows a pattern based on the numerical positions of the letters in the English alphabet. The first letter A is at position 1. The second letter E is at position 5, which is an increase of +4 from the previous letter (1 + 4 = 5). The third letter J is at position 10, which is an increase of +5 from the previous letter (5 + 5 = 10). The increments between successive letters are increasing by 1 each time (+4, +5, …). Therefore, the next increment in the series should be +6. Adding 6 to the current position of 10 results in 10 + 6 = 16. The 16th letter of the English alphabet is P.

Explanation

The numerical analogy follows a constant ratio of 2:3 between the numbers in each pair. This can be expressed as multiplying the first number by 1.5 or ³⁄₂ to obtain the second number.

In the first pair, 72 × 1.5 = 108.

In the third pair, 102 × 1.5 = 153.

Following the same logic for the second pair, the missing number is calculated by multiplying 84 by 1.5: 84 × ³⁄₂ = 42 × 3 = 126.

Explanation

Shaan starts with ₹5,500 and buys product Z for ₹5,000, leaving him with ₹500 in cash. The selling price of product Z with a 15% profit is calculated as: Selling Price of Z = 5000 × (1 + ¹⁵⁄₁₀₀) = 5000 × 1.15 = 5,750

The total money Shaan has after selling product Z is the sum of the selling price and the remaining cash: Total Money = 5750 + 500 = 6,250

He then uses this entire amount of ₹6,250 to buy product X and sells it at a 25% profit. The final total money is calculated as: Final Money = 6250 × (1 + ²⁵⁄₁₀₀) = 6250 × 1.25 = 7,812.50

Explanation

The series follows a specific positional pattern for each letter in the cluster. For the first letter (lowercase), the sequence is a (1), f (6), k (11), and p (16). The pattern is n + 5, meaning the next letter is 16 + 5 = 21, which corresponds to u.

For the second letter (uppercase), the sequence is Y (25), T (20), O (15), and J (10). The pattern is n - 5, so the next letter is 10 - 5 = 5, which corresponds to E.

For the third letter (lowercase), the sequence is d (4), i (9), n (14), and s (19). The pattern is n + 5, so the next letter is 19 + 5 = 24, which corresponds to x. Combining these results, the next cluster in the series is uEx.

Explanation

In the letter-clusters FHJ, LNP, and DFH, the letters follow a consistent pattern of increasing by 2 in alphabetical position. Specifically, F (6) + 2 = H (8) and H (8) + 2 = J (10); L (12) + 2 = N (14) and N (14) + 2 = P (16); D (4) + 2 = F (6) and F (6) + 2 = H (8). In contrast, the cluster TWV follows a different pattern: T (20) + 3 = W (23) and W (23) - 1 = V (22). Since TWV does not follow the uniform +2 increment, it is the odd one out.

Explanation

The relationship between the words in the given pair is based on the degree of intensity among synonyms. A blunder is defined as a gross, الانتقام, or particularly significant error. Similarly, euphoria represents a state of intense, extreme, or overwhelming happiness. In both instances, the first word acts as an augmented or more powerful version of the second word, preserving both the synonymic connection and the specific order of increasing magnitude.

Explanation

The logical sequence follows the physical size and body mass of the organisms in ascending order. The housefly (4) is a small insect and the smallest in the list. The lizard (2) is a reptile that is larger than a housefly but smaller than the other mammals and reptiles mentioned. The monkey (5) is a primate that generally possesses greater body mass and dimensions than a common lizard. The crocodile (1) is a large predatory reptile that grows significantly larger than a monkey. Finally, the whale (3) is the largest mammal on Earth, representing the maximum size in this sequence. This progression from 4 to 2 to 5 to 1 to 3 correctly represents the transition from the smallest to the largest creature.

Explanation

The words indigence and destitution are synonyms that refer to a state of extreme poverty and the lack of basic necessities. Similarly, a penny represents the smallest unit of currency and is often used metaphorically to signify a lack of wealth or a condition of being poor. In contrast, plenty denotes a large or sufficient amount, abundance, or prosperity. While the other three words are associated with financial hardship or minimal resources, plenty describes a state of having more than enough, making it the odd word in the group.

Explanation

The numbers in the set (13, 65, 117) follow a pattern where the second and third numbers are specific multiples of the first number. Specifically, the second number is 5 times the first number (13 × 5 = 65) and the third number is 9 times the first number (13 × 9 = 117).

Applying this logic to the set (15, 75, 135), we see that the same relationship holds true. The second number is 5 times the first (15 × 5 = 75) and the third number is 9 times the first (15 × 9 = 135). Alternatively, the set can be viewed as an arithmetic progression where the common difference between consecutive terms is 4 times the first number (65 - 13 = 52 = 4 × 13; 117 - 65 = 52 = 4 × 13). In the chosen set, the common difference is similarly 4 times the first number (75 - 15 = 60 = 4 × 15; 135 - 75 = 60 = 4 × 15).

Explanation

The logical relationship between the groups follows a transitive hierarchy based on the provided statements: Parakeets ⊂ Cuckoos ⊂ Rabbits ⊂ Snakes.

Conclusion I states that all parakeets are snakes. Since the set of parakeets is entirely contained within the set of cuckoos, and cuckoos are entirely contained within snakes via the rabbit category, the transitive property of inclusion ensures that every member of the parakeet group is also a member of the snake group.

Conclusion IV states that all cuckoos are snakes. This follows directly from the statements as well. Since all cuckoos are rabbits and all rabbits are snakes, the entire set of cuckoos is subsumed by the set of snakes. In categorical logic, if all A are B and all B are C, then it is a valid deduction that all A are C. Therefore, conclusions I and IV are the only logically sound deductions.

Explanation

The pattern followed by the number pairs is n² : (n + 1)² + 1, where n is the square root of the first number. In the pair 225-241, the first number is 15², which means n = 15. According to this logic, the second number should be (15 + 1)² + 1 = 16² + 1 = 256 + 1 = 257. The value of 241 provided in the pair does not satisfy this relationship.

Explanation

The numerical value of each letter is determined by the formula V = 2n - 1, where n represents the position of the letter in the English alphabet (A=1, B=2, …, Z=26).

For the word HONEY: The letter H is the 8th letter, so its value is 2(8) - 1 = 15. The letter O is the 15th letter, so its value is 2(15) - 1 = 29. The letter N is the 14th letter, so its value is 2(14) - 1 = 27. The letter E is the 5th letter, so its value is 2(5) - 1 = 9. The letter Y is the 25th letter, so its value is 2(25) - 1 = 49.

By concatenating these values, the code for HONEY is 152927949.

Explanation

The series is composed of two interleaved sequences alternating at each position. The first sequence involves the terms at the first, third, and fifth positions: 40, 43, and 46. This sequence follows an addition pattern where each term increases by 3, as seen in 40 + 3 = 43 and 43 + 3 = 46. The second sequence involves the terms at the second, fourth, and sixth positions: 37, 34, and the question mark. This sequence follows a subtraction pattern where each term decreases by 3, as seen in 37 - 3 = 34. To find the missing number at the sixth position, we apply the same rule to the fourth term: 34 - 3 = 31.

Explanation

The relationship in this analogy is based on a group and its collective designation. A group of Ministers forms a Council, specifically referred to as the Council of Ministers in a governmental context. Similarly, the collective group of Sailors who operate and work on a ship or vessel is known as a Crew.

Explanation

The logic followed in each row of the pattern is that the product of the first and third numbers divided by the second number equals the fourth number. This relationship is expressed as (Column 1 × Column 3)/(Column 2) = Column 4.

In the first row, (10 × 14)/(4) = ¹⁴⁰⁄₄ = 35. In the second row, (15 × 5)/(3) = ⁷⁵⁄₃ = 25. In the third row, (14 × 6)/(7) = ⁸⁴⁄₇ = 12.

For the fourth row, the same formula applies: (18 × 8)/(?) = 16. Solving for the missing value, we calculate (144)/(?) = 16, which gives ? = ¹⁴⁴⁄₁₆ = 9.

Explanation

To solve this, evaluate the expressions using the BODMAS rule. The initial value of the left hand side is 3 + 5 × 4 - 24 ÷ 3 = 3 + 20 - 8 = 15, and the initial value of the right hand side is 7 × 4 - 3 + 36 ÷ 6 = 28 - 3 + 6 = 31. By interchanging the numbers 5 and 7, the left hand side becomes 3 + 7 × 4 - 24 ÷ 3, which calculates to 3 + 28 - 8 = 23. Simultaneously, the right hand side becomes 5 × 4 - 3 + 36 ÷ 6, which calculates to 20 - 3 + 6 = 23. Since both sides of the equation result in the same value of 23 after the swap, the interchange of 5 and 7 satisfies the condition.

Explanation

The letter series follows a cyclic pattern based on groups of three letters. The total number of characters in the series, including the blanks, is 18. This can be divided into six groups of three letters each: fgh, ghf, hfg, fgh, ghf, and hfg.

In this pattern, the letters f, g, and h rotate their positions in each successive group. The first group is fgh. In the second group, the first letter of the previous group moves to the end, resulting in ghf. In the third group, the g moves to the end, resulting in hfg. This three-group cycle then repeats itself for the remainder of the series. By placing the letters g, h, f, g, h, and f into the blanks sequentially, the series perfectly maintains this periodic and cyclic rotation of f, g, and h.

Explanation

The code for KNUCKLES is found by substituting each of its letters with the corresponding character assigned in the provided language rules. Based on those rules, K is written as H, N is written as E, U is written as C, C is written as N, the second K is written as H, L is written as U, E is written as K, and S is written as L. Placing these substitutions in the original sequence of the word results in HECHNUKL.

Explanation

Let the amount of money with Vineet be x. According to the problem, Rajesh has double the amount of Vineet, which is 2x. Kriti has 6 more than Vineet, so her amount is x + 6.

The total amount with Rajesh and Kriti is given as 147. We can set up the following equation: 2x + (x + 6) = 147 3x + 6 = 147 3x = 141 x = 47

Vineet has 47. Therefore, the amount of money Kriti has is x + 6 = 47 + 6 = 53.

Explanation

The series follows specific alphabetical patterns for each letter position in the clusters. In the first position, the letters increase by 3 in their alphabetical order: S (19) + 3 = V (22), V (22) + 3 = Y (25), Y (25) + 3 = B (2 or 28), and B (2) + 3 = E (5). In the second position, the letters follow the sequence of English vowels: A, E, I, O, and U. In the third position, the letters again increase by 3 in their alphabetical order: T (20) + 3 = W (23), W (23) + 3 = Z (26), Z (26) + 3 = C (3 or 29), and C (3) + 3 = F (6). Following these independent patterns for the missing cluster results in B for the first letter, O for the second, and C for the third, which forms the cluster BOC.