Chapter 6 · Class 7 CBSE · MCQ Test
Number Patterns & Puzzles MCQ Test — Class 7 CBSE
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Number Patterns & Puzzles — MCQ Questions
1What is the next number in the pattern: 3, 7, 11, 15, ___?
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Answer: 19
Hint: Look for the constant difference between consecutive numbers.
Solution:
First, find the difference between consecutive terms: 7 - 3 = 4, 11 - 7 = 4, 15 - 11 = 4.
The pattern is to add 4 to the previous term to get the next term.
Therefore, the next number in the sequence is 15 + 4 = 19.
2Observe the pattern: 1, 4, 7, 10, ... Which of the following statements correctly describes the rule for this pattern?
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Answer: Start with 1 and add 3 to the previous number.
Hint: Check the difference between successive terms to find the operation.
Solution:
Compare the first two terms: 4 - 1 = 3.
Compare the second and third terms: 7 - 4 = 3.
Compare the third and fourth terms: 10 - 7 = 3.
The pattern shows a constant addition of 3 to the previous term, starting with 1.
3A 3×3 magic square has numbers arranged such that the sum of the numbers in each row, each column, and both main diagonals is the same. This constant sum is called the magic constant. If a 3×3 square has a magic constant of 15, which of the following statements must be true?
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Answer: The number in the center cell must be 5.
Hint: For a 3x3 magic square, the middle number has a special relationship with the magic constant.
Solution:
In any 3×3 magic square, the number in the center cell is always equal to the magic constant divided by 3.
Given the magic constant is 15.
Therefore, the number in the center cell = 15 / 3 = 5.
Other options are not necessarily true. For example, the sum of all numbers in a 3x3 magic square with magic constant M is 3M, so it would be 3 × 15 = 45, not 15.
4Consider a 3×3 magic square where the magic constant is 24. If one row has the numbers 7, ___, 13, what is the missing number?
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Answer: 4
Hint: The sum of numbers in any row of a magic square must equal the magic constant.
Solution:
The magic constant for this square is 24.
In a magic square, the sum of numbers in any row must equal the magic constant.
Let the missing number be 'x'. So, for the given row: 7 + x + 13 = 24.
Combine the known numbers: 20 + x = 24. Solving for x, we get x = 24 - 20 = 4.
5A sequence starts with 1, 1. Each subsequent number is the sum of the two preceding numbers. What is the 6th term in this sequence?
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Answer: 8
Hint: Write down the terms step-by-step, adding the two previous numbers each time.
Solution:
The sequence starts with the 1st term = 1 and the 2nd term = 1.
3rd term = 1st term + 2nd term = 1 + 1 = 2.
4th term = 2nd term + 3rd term = 1 + 2 = 3.
5th term = 3rd term + 4th term = 2 + 3 = 5.
6th term = 4th term + 5th term = 3 + 5 = 8.
6Find the next number in the sequence: 2, 5, 11, 23, ___.
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Answer: 47
Hint: This pattern might involve both multiplication and addition/subtraction. Look for a consistent operation.
Solution:
Let's analyze the differences between consecutive terms: 5 - 2 = 3, 11 - 5 = 6, 23 - 11 = 12.
The differences (3, 6, 12) are doubling each time, suggesting a multiplicative part in the rule.
Let's test the rule (previous number × 2) + K:
(2 × 2) + 1 = 5, (5 × 2) + 1 = 11, (11 × 2) + 1 = 23. The rule is (previous number × 2) + 1.
Applying this rule to the last term: (23 × 2) + 1 = 46 + 1 = 47.
7Which of the following statements about triangular numbers is TRUE?
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Answer: The sum of two consecutive triangular numbers is always a square number.
Hint: Recall the definition of triangular numbers and their relation to square numbers. List out the first few triangular numbers.
Solution:
Triangular numbers are 1, 3, 6, 10, 15, 21, ...
Option A is false because some triangular numbers (like 1, 3, 15, 21) are odd.
Option B is false; triangular numbers are n(n+1)/2, not n(n+1).
Option D is false; adding consecutive odd numbers starting from 1 results in square numbers (1, 1+3=4, 1+3+5=9).
Option C is TRUE: 1+3=4 (2²), 3+6=9 (3²), 6+10=16 (4²). The sum of the nth and (n+1)th triangular numbers is (n+1)².
8What is the next number in the sequence of square numbers: 1, 4, 9, 16, 25, ___?
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Answer: 36
Hint: Each number in the sequence is the result of multiplying an integer by itself.
Solution:
Identify the pattern: 1 = 1 × 1 = 1², 4 = 2 × 2 = 2², 9 = 3 × 3 = 3², 16 = 4 × 4 = 4², 25 = 5 × 5 = 5².
The sequence consists of consecutive square numbers.
The next number will be the square of the next integer, which is 6.
So, the next number is 6 × 6 = 6² = 36.
9Rahul was asked to find the rule for the pattern: 2, 6, 12, 20, 30, ... He said, 'The rule is to add 4, then add 6, then add 8, then add 10, and so on. So, the next number will be 30 + 12 = 42.' Is Rahul's reasoning correct?
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Answer: Yes, his reasoning is correct, and the next number is 42.
Hint: Look at the differences between consecutive terms and see if they form a pattern themselves.
Solution:
Calculate the differences between consecutive terms: 6 - 2 = 4, 12 - 6 = 6, 20 - 12 = 8, 30 - 20 = 10.
The differences are 4, 6, 8, 10. This sequence of differences shows an increase of 2 each time (4+2=6, 6+2=8, 8+2=10).
Following this pattern, the next difference after 10 would be 10 + 2 = 12.
Therefore, the next number in the original sequence would be 30 + 12 = 42. Rahul's reasoning is correct.
10A gardener plants flowers in a triangular arrangement. Figure 1: 1 flower (a single dot) Figure 2: 3 flowers (a triangle with 2 flowers on each side) Figure 3: 6 flowers (a triangle with 3 flowers on each side) Figure 4: 10 flowers (a triangle with 4 flowers on each side) How many flowers will be in Figure 5?
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Answer: 15
Hint: The number of flowers in each figure forms a sequence. Find the rule for generating the next term.
Solution:
The number of flowers in each figure forms the sequence: 1, 3, 6, 10.
Find the differences between consecutive terms: 3 - 1 = 2, 6 - 3 = 3, 10 - 6 = 4.
The differences are increasing by 1 each time (2, 3, 4). This means the next difference for Figure 5 will be 5.
Add this difference to the last term in the sequence: 10 + 5 = 15.
Alternatively, this sequence represents triangular numbers, where the nth triangular number is given by the formula n(n+1)/2. For n=5, the 5th triangular number is 5(5+1)/2 = 5 × 6 / 2 = 15.
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Tips for Number Patterns & Puzzles MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Number Patterns & Puzzles MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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