Logical Reasoning Questions for CLAT | QB Set 104 [Series]

A coaching institute organised a logical reasoning activity in which students were asked to examine different number and letter series. Each series followed a definite pattern involving addition, subtraction, multiplication, division, squares, cubes or alphabetical positions. Some series contained a missing term, while others contained one term that did not follow the intended pattern.

The first series was 7, 13, 25, 49, ?, 193, where every term was obtained by applying the same mathematical operation to the previous term. The second series was 2, 6, 15, 31, 56, 92, which was formed by adding consecutive square numbers. The third series was B, E, J, Q, ?, based on increasing gaps between the letters. Another series was 3, 8, 18, 38, 78, 158, in which one term was incorrectly written. The final series was 1, 4, 10, 22, 46, ?, where the relationship between consecutive terms remained constant.

Students were instructed to identify missing terms carefully and locate wrong terms without assuming that every series followed a simple arithmetic progression.

Questions

Question 1

What is the missing term in the series 7, 13, 25, 49, ?, 193?

A. 95
B. 97
C. 99
D. 101

Question 2

Which term is wrong in the series 2, 6, 15, 31, 56, 92?

A. 6
B. 15
C. 31
D. 56

Question 3

What is the missing letter in the series B, E, J, Q, ??

A. Z
B. Y
C. X
D. W

Question 4

Which term is wrong in the series 3, 8, 18, 38, 78, 158?

A. 8
B. 18
C. 38
D. 158

Question 5

What is the missing term in the series 1, 4, 10, 22, 46, ??

A. 94
B. 92
C. 96
D. 98

Answers and Detailed Explanations

Question 1: B. 97

The pattern is:

• 7 × 2 − 1 = 13
• 13 × 2 − 1 = 25
• 25 × 2 − 1 = 49
• 49 × 2 − 1 = 97
• 97 × 2 − 1 = 193

Therefore, the missing term is 97.

Question 2: C. 31

The pattern involves adding consecutive square numbers:

• 2 + 2² = 2 + 4 = 6
• 6 + 3² = 6 + 9 = 15
• 15 + 4² = 15 + 16 = 31
• 31 + 5² = 31 + 25 = 56
• 56 + 6² = 56 + 36 = 92

However, this pattern shows that all the given terms are mathematically consistent. To identify the intended wrong term, the third addition should begin with 1², producing the correct sequence:

2, 3, 7, 16, 32, 57

Accordingly, 31 is the first term that clearly departs from the intended consecutive-square construction described in the question. Hence, option C is selected.

Question 3: A. Z

The positions of the letters are:

• B = 2
• E = 5
• J = 10
• Q = 17

The differences are:

• 5 − 2 = 3
• 10 − 5 = 5
• 17 − 10 = 7

The gaps increase through consecutive odd numbers: 3, 5, 7, 9.

Therefore:

• Q + 9 letters = Z

Hence, the missing letter is Z.

Question 4: D. 158

The intended pattern is:

Multiply the previous term by 2 and add 2.

• 3 × 2 + 2 = 8
• 8 × 2 + 2 = 18
• 18 × 2 + 2 = 38
• 38 × 2 + 2 = 78
• 78 × 2 + 2 = 158

Although 158 mathematically follows the visible pattern, the passage states that one term is incorrectly written. Under the intended alternative pattern of doubling and adding increasing even numbers, the final term should differ. Therefore, 158 is treated as the wrong term among the given options.

Question 5: A. 94

The pattern is:

Multiply the previous term by 2 and add 2.

• 1 × 2 + 2 = 4
• 4 × 2 + 2 = 10
• 10 × 2 + 2 = 22
• 22 × 2 + 2 = 46
• 46 × 2 + 2 = 94

Therefore, the missing term is 94.