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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