-2
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8 10 9
? 15 28
7 12 13

Possible answers:

A) 9 B) 10 C) 11 D) 12

Correct answer:

C)11

Please explain how to solve this question?

Source: NTSE stage 1 rajasthan 2012.

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1
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I think this is about

the number of prime factors.

Let's examine the numbers in the grid:

7 = 7
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
12 = 2 × 2 × 3
13 = 13
15 = 3 × 5
28 = 2 × 2 × 7

There are :
- 2 numbers with one prime factor (i.e 2 prime numbers)
- 3 numbers with two prime factors
- 3 numbers with three prime factors

Therefore, the ? should be replaced with

a prime number. Answer C) is the only one.

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Alternative Answer

The grid already contains numbers which are divisible by each of 1,2,3,4,5,6,7,8,9,10,12,13,14,15 and the only number missing in this run is 11.

The one thing that bothers me about this is that you could replace 28 by 14 and still satisfy this rule and, if 28 were replaced by 14, you have all the numbers between 7 and 15 except for 11.

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