How to do this one

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8. 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

[spoiler]
ans [/spoiler]D

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Hi shibsriz,

To answer this question, you have to be very careful to be thorough (2 of the answers are "partial work" answers, meaning that could very easily get to one of those answers and think that you're correct, but you're not):

We're dealing with numbers less than 10,000 and we need the product of the digits to equal 210, so let's deal with THAT first:

210 = (2)(3)(5)(7)

With THOSE 4 digits (2,3,5,7), we could end up with 4x3x2x1 = 24 different numbers

But the question DID NOT state that the digit had to be prime, so that's NOT the only way to get to 210 using 4 digits:

We could use (1,5,6,7), and end up with 4x3x2x1 = 24 additional numbers

AND we have to consider numbers that are NOT 4-digits; we could use (5,6,7), which gives us 3x2x1 = 6 additional numbers

24 + 24 + 6 = 54

Final Answer: D

GMAT assassins aren't born, they're made,
Rich