Celestial09 wrote:

Hi,

Couldn't understood the question yet...

waiting for the explanation and OA.

thanks

celetial

30! = 1*2*3*4*5*...*28*29*30

So all the numbers from 1 to 30 are factors of 30!. Also, all numbers which you can make by combining these factors are factors of 30!

So 2*29 = 58 is a factor of 30!, 2*4*8 = 64 is a factor of 30! and so on...

You want a number which is not a factor of 30!

The smallest number that is not a factor of 30! is 31. But it is a prime number. You want the smallest number that is not a factor of 30! and is not prime. So the next smallest such number would be 31*2 = 62.

Now think why no other number between 31 and 62 can be number which is not a factor of 30! and not prime.

32 = 4*8 (both factors of 30! so 32 is a factor of 30!)

33 = 3*11 (both factors of 30! so 33 is a factor of 30!)

34 = 2*17 (both factors of 30! so 34 is a factor of 30!)

and so on...

37 = 37 (prime)

and so on...

Basically, you want the number to be composed of two numbers such that at least one of them is not a factor of 30!. The first such number is 31. You multiply it by the smallest number 2 to get a non prime number which is not divisible by 30!.

Answer (D)

Do focus a bit on this logic. To solve the question, you can use the options of course!

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Karishma

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