10^d factor of?

[deagez]

If d is a positive integer and f is the product of the first 30 integers, what is the value of d?

1) 10^d is a factor of f
2) d>6

ok so obviously the answer is not D, so also not C

I chose A, because you can eventually deduct how many 10s are in 1*2*3*4...*30

however the answer here is C

I kind of see now that there 10^2 = 100 is a factor because 2*5*10 is 10^2, and 10^3 is good because 2*5*10*25*4 is 10^3,

but how would you differentiate between choice C and E? I mean it is fairly easy to come up with 10^3 and 10^2 but 10^6? I mean if I had 20 minutes I would get it, but how do you do this fast please?

[shadowsjc]

This seems like a tough one to me. On the actual GMAT, like on the practice tests, there are some problems which you'll simply have to guess and move on.

If I saw this problem on a test, this is how I would approach it:

for #1, it can't be A since d can equal 1 and be a factor of f, and it can also be 2. So A is out, which means D is also out by default. This leaves us with B, C, or E as answer choices (33% chance of getting it right)

for #2, d>6 tells you nothing at all, since it can be 7, 8, 9, or 10000. So B is out.

Thus, with very little time spent (maybe a minute tops), I have narrowed it down to C or E (50% chance of getting it right). Since I don't know any more tricks or tips for this problem, I'd guess C and move on to the next one. Of course, I could also guess E (and get it wrong) but at least I didn't spend too much time on it.

I'm sure there must be something obvious that I'm missing (maybe someone will reply with a tip later on), but the real thing to learn from questions like this is to eliminate as many wrong answers as you can, and move forward with a guess if possible. Don't waste 4-5 minutes on a problem like this (especially not by calculating out what 30! is).

[deagez]

i see how I am stupid for choosing A, because due to my own reasoning 10^1 and 10^2 are both factors of F, however there has to be a way to quickly figure out if it is C or E.

So if anyone has any idea plz post

[bharathh]

10 = 2*5

Statement 1 is asking how many 10^d are factors of 30!

30! = 1.2.3.4..30

How many of these numbers give you a 10^d?

2.5 = 10... so 10^1 is def a factor
10 itself is there ... so 10^2 is a factor

and so on.

So statement 1 is insufficient. Rule out A and D

Statement 2 by itself is insufficient as well as it doesn't help in any way. d can be any integer greater than 7. Rule out B

So we're down to C and E

If we continued the expression above we will get around 10^7 being the highest factor of 30!

Since combining the two we can state that d = 7, both statements are sufficient.

[deagez]

If we continued the expression above we will get around 10^7 being the highest factor of 30!

Since combining the two we can state that d = 7, both statements are sufficient.

I see this, but how do you quickly know that 10^7 is about 30!?

[bharathh]

10^7 is not 30!

It is a factor.

[qwe12]

If d is a positive integer and f is the product of the first 30 integers, what is the value of d?

1) 10^d is a factor of f
2) d>6

the wording of this question threw me off and i'm positive that on the gmat this will be way more clearer. where did you find this question? i'm not too happy with "first 30 integers" what does that mean? "first 30 positive or non-negative integers" is clearer.

f = 30!

(1)
d=1, 10^1 is a factor of 30!
d=2, 10^2 is a factor of 30!

NOT SUFFICIENT

(2) d>6

d=7,8,9,...

NOT SUFFICIENT

(1) and (2)

d>6, let d=7

30!/10^7

10=5*2
and 30! has seven 5's
30!=1.2.3.4.5...10....15...20....(5.5)...30

so d must be 7. if d were 8, we'd have 8 5's, which would not let 10^8 to be a factor of 30!.

(C)