Tuesday, January 26, 2010

GMAT Question of the day

How many positive integers less than 10,000 are such that the product of their digits is 210?
(A) 24
(B) 30
(C) 48
(D) 54
(E) 72

210 = 2*3*5*7.

So the numbers have to be made of above four digits.

If we take all 4 primes as separate digits, then 4*3*2*1 = 24 different numbers.

We can also make numbers from the digits 6 (2*3), 5 and 7 = 3*2*1 = 6 different numbers so total 30 numbers.

Hence the answer is B