MAT - SQUARE SERIES - MCQs - 7

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NMMS CLASS 8 – SQUARE BASED SERIES

Mental Ability Test (MAT) | Number Series | 20 MCQs

Instructions:
1. Choose the correct answer for each question.
2. Click Submit to check your answers.
3. Correct questions will turn GREEN.
4. Wrong questions will turn RED.
5. Click Answer to see the correct answer.
6. Click View Explanation to understand the pattern.
7. Use Retry to attempt the test again.

Question 1 – Normal

Find the missing number in the following series:

1, 4, 9, 16, 25, ?

A) 30 B) 35 C) 36 D) 49

Correct Answer: C) 36

The terms are consecutive square numbers:
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
Therefore, the next term is:
6² = 36.

Question 2 – Twisted

The numbers are formed using square numbers. Find the next term:

3, 8, 15, 24, 35, ?

A) 42 B) 46 C) 48 D) 50

Correct Answer: C) 48

Observe:
3 = 2² − 1
8 = 3² − 1
15 = 4² − 1
24 = 5² − 1
35 = 6² − 1

Therefore:
7² − 1 = 49 − 1 = 48.

Question 3 – Normal

Find the missing number:

4, 16, 36, 64, 100, ?

A) 120 B) 121 C) 144 D) 169

Correct Answer: C) 144

These are squares of even numbers:
2² = 4
4² = 16
6² = 36
8² = 64
10² = 100
Next even number = 12.
12² = 144.

Question 4 – Twisted

Find the next number:

2, 6, 12, 20, 30, ?

A) 36 B) 40 C) 42 D) 44

Correct Answer: C) 42

The pattern is:
1 × 2 = 2
2 × 3 = 6
3 × 4 = 12
4 × 5 = 20
5 × 6 = 30
Therefore:
6 × 7 = 42.

This is also related to consecutive-number products.

Question 5 – Normal

Find the next term in the series:

1, 9, 25, 49, 81, ?

A) 100 B) 110 C) 121 D) 144

Correct Answer: C) 121

These are squares of odd numbers:
1² = 1
3² = 9
5² = 25
7² = 49
9² = 81
Next odd number = 11.
11² = 121.

Question 6 – Twisted

The sequence is formed using decreasing square numbers. Find the missing term:

100, 81, 64, 49, 36, ?

A) 25 B) 24 C) 20 D) 16

Correct Answer: A) 25

100 = 10²
81 = 9²
64 = 8²
49 = 7²
36 = 6²
Therefore the next term is 5² = 25.

Question 7 – Normal

Find the next number:

2, 5, 10, 17, 26, ?

A) 35 B) 36 C) 37 D) 38

Correct Answer: C) 37

Each term is one more than a square:
1² + 1 = 2
2² + 1 = 5
3² + 1 = 10
4² + 1 = 17
5² + 1 = 26
Therefore:
6² + 1 = 36 + 1 = 37.

Question 8 – Twisted

The sequence contains two interwoven square patterns. Find the next number:

2, 4, 10, 16, 26, 36, ?

A) 42 B) 48 C) 50 D) 52

Correct Answer: C) 50

Separate odd and even positions.

Odd positions: 2, 10, 26, ?
These are 1²+1, 3²+1, 5²+1, 7²+1.
So next odd-position term = 49 + 1 = 50.

Even positions: 4, 16, 36 = 2², 4², 6².

Question 9 – Normal

Find the missing term:

16, 25, 36, 49, 64, ?

A) 72 B) 75 C) 81 D) 100

Correct Answer: C) 81

The terms are consecutive squares from 4² onwards:
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81.

Question 10 – Twisted

Find the next number:

6, 13, 22, 33, 46, ?

A) 58 B) 59 C) 61 D) 63

Correct Answer: C) 61

Look at the differences:
13 − 6 = 7
22 − 13 = 9
33 − 22 = 11
46 − 33 = 13
The differences are consecutive odd numbers.
Next difference = 15.
46 + 15 = 61.

Question 11 – Normal

Find the next term:

121, 144, 169, 196, 225, ?

A) 240 B) 250 C) 256 D) 289

Correct Answer: C) 256

121 = 11²
144 = 12²
169 = 13²
196 = 14²
225 = 15²
Therefore the next term is:
16² = 256.

Question 12 – Twisted

Identify the pattern and find the missing number:

1, 5, 11, 19, 29, ?

A) 39 B) 40 C) 41 D) 43

Correct Answer: C) 41

The pattern is n² + n − 1:
1² + 1 − 1 = 1
2² + 2 − 1 = 5
3² + 3 − 1 = 11
4² + 4 − 1 = 19
5² + 5 − 1 = 29
Therefore:
6² + 6 − 1 = 36 + 6 − 1 = 41.

Question 13 – Normal

Find the next number:

1, 16, 81, 256, 625, ?

A) 900 B) 1024 C) 1296 D) 1444

Correct Answer: C) 1296

These are fourth powers:
1⁴ = 1
2⁴ = 16
3⁴ = 81
4⁴ = 256
5⁴ = 625
Therefore:
6⁴ = 1296.
So the answer is 1296.

Question 14 – Twisted

Find the next term:

4, 10, 18, 28, 40, ?

A) 50 B) 52 C) 54 D) 56

Correct Answer: C) 54

Find the differences:
10 − 4 = 6
18 − 10 = 8
28 − 18 = 10
40 − 28 = 12
The differences increase by 2.
Next difference = 14.
40 + 14 = 54.

Question 15 – Normal

The terms are obtained by adding consecutive square numbers. Find the next term:

1, 5, 14, 30, 55, ?

A) 81 B) 90 C) 91 D) 95

Correct Answer: C) 91

Look at the differences:
5 − 1 = 4 = 2²
14 − 5 = 9 = 3²
30 − 14 = 16 = 4²
55 − 30 = 25 = 5²
Next difference = 6² = 36.
Therefore:
55 + 36 = 91.

Question 16 – Twisted

Find the missing number:

7, 12, 19, 28, 39, ?

A) 50 B) 51 C) 52 D) 54

Correct Answer: C) 52

Differences are:
12 − 7 = 5
19 − 12 = 7
28 − 19 = 9
39 − 28 = 11
Next difference = 13.
Therefore:
39 + 13 = 52.

Question 17 – Normal

Find the missing number:

9, 36, 81, 144, 225, ?

A) 256 B) 289 C) 324 D) 361

Correct Answer: C) 324

These are squares of multiples of 3:
3² = 9
6² = 36
9² = 81
12² = 144
15² = 225
Next = 18².
18² = 324.

Question 18 – Twisted

Find the next number:

2, 11, 26, 47, 74, ?

A) 96 B) 101 C) 107 D) 109

Correct Answer: C) 107

The pattern is:
3(1²) − 1 = 2
3(2²) − 1 = 11
3(3²) − 1 = 26
3(4²) − 1 = 47
3(5²) − 1 = 74
Therefore:
3(6²) − 1 = 108 − 1 = 107.

Question 19 – Normal

The numbers are squares of consecutive prime numbers. Find the next term:

4, 9, 25, 49, 121, ?

A) 144 B) 169 C) 196 D) 225

Correct Answer: B) 169

The square roots are:
√4 = 2
√9 = 3
√25 = 5
√49 = 7
√121 = 11
These are consecutive prime numbers.
The next prime number is 13.
13² = 169.

Question 20 – Twisted

Find the next term:

2, 7, 14, 23, 34, ?

A) 45 B) 46 C) 47 D) 48

Correct Answer: C) 47

The pattern can be written as:
1² + 1 = 2
2² + 3 = 7
3² + 5 = 14
4² + 7 = 23
5² + 9 = 34

The added numbers are consecutive odd numbers: 1, 3, 5, 7, 9, 11.
Therefore:
6² + 11 = 36 + 11 = 47.