factors

[vipulgoyal]

. How many prime factors does N have?
1). N is factor of 7200
2). 180 is factor of N

[Anju@Gurome]

. How many prime factors does N have?
1). N is factor of 7200
2). 180 is factor of N

There are some basic standards that proper GMAT problem follows.
For example, GMAT problem never asks for 'number of prime factors', they ask for 'number of different prime factors' as the phrase 'number of prime factors' is ambiguous and someone might count three 2s as three prime factors which doesn't make any sense.

So, I'll answer this problem assuming it is asking for number of different prime factors of N.

Statement 1: Consider the following two cases,

• N = 2 ---> 1 prime factor
  N = 6 = 2*3 ---> 2 different prime factors

Not sufficient

Statement 2: Consider the following two cases,

• N = 180 = (2²)*(3²)*5 ---> 3 different prime factors
  N = 7*180 = (2²)*(3²)*5*7 ---> 4 different prime factors

Not sufficient

1 & 2 Together: Now, N is of the form 180k for some positive integer k and 7200/N is an integer.
--> 7200/(180k) = 40/k is an integer

Now, 40 = (2³)*5, k is a multiple of 2 and 5 only.
As 2 and 5 are already factors of 180, number of different prime factors of N = 180k is same as the number of different prime factors of 180.

Sufficient

The correct answer is C.

Note : If the problem is designed to mean three 2s as three prime factors, then the correct answer will be E. But don't expect anything like that in GMAT.

[vipulgoyal]

Anju I have rechecked the Qustion says how many prime factors not differant prime factors

here is how I done

1. (2^5 x 3^2 x 5^2)/N = I
2. N/ 2^2 x 3^2 x 5 = I

5<= Total no of prime factors <= 9

Hence E