gmatmachoman wrote:If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?
(1) 10^d is a factor of f
(2) d>6
From the stem I could understand, f is nothing but 30!
St 1 says 10 ^ d is a factor of f:
from this we can find d=5
So IMO A
St 2 doesnt help
Am i correct?
Not quite!
You're correct, f = 30!. All that we know about d from the stem is that it's a positive integer. We think: we want some juicy info about the relationship between d and f.
(1) 10^d is a factor of f.
Well, even ignoring the other numbers f is a multiple of 10, 20 and 30, each of which is a multiple of 10; so, we know that 10^1, 10^2 and 10^3 are all factors of f. Therefore, d could be 1, 2 or 3 (and possibly other numbers as well - as soon as we find more than 1 possible answer, we're done): insufficient.
(2) d > 6
who cares! Based on (2) alone d could be any integer greater than 6: insufficient.
Together: now we need to see how many 10s we can get out of 30!.
Well, 10 = 2*5.
30! has a
lot of 2s as factors, but nowhere near as many 5s. So, let's not worry about the 2s, the 5s will be what limit the number of 10s.
Among the factors of 30! we have:
5, 10, 15, 20, 25, 30
giving us a total of 7 5s (remember, 25=5*5 - that's our bonus 5) as factors.
Since we have a total of 7 5s, the maximum number of 10s that go into 30! is also 7.
Therefore, since 10^d goes into 30! and d > 6, d MUST be 7. Together sufficient, apart insufficient: choose C.
