value of D

[gmatmachoman]

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?

[Stuart@KaplanGMAT]

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.

[gmatmachoman]

Now it makes sense!
d >6 is very much required to get a single value of d.

thx Stuart

[jerryragland]

@Stuart

Thanks for your reply...

Is there a generalized way to find how many x in y? If x is a factor of y. Like in the above 10s in 30!

[scoowhoop]

St 1 says 10 ^ d is a factor of f:
from this we can find d=5

Remember with data sufficiency that both statements should be treated as factual information and will NEVER contradict each other. You determined from the first statement that d=5 but this directly contradicts the second statement d>6 . This should raise a huge flag that something you did is wrong.

Also, don't forget that 25 can be factored to 5*5 so you get --> 5, 10, 15, 20, 5*5, 30 --> 10^7, therefore all (1) tells you is that d<=7

[dxgamez]

If the st 1 was 100^d is a factor of f, how would it change then? i'd think st 2 would have to change but i have no idea what.


I am trying to figure out Stuart's explanation. 100^d = (2x2x5x5)^d and the same thing is that we have 7 5's in 30!. Does that mean that d = 5?

trying to grasp the idea with another problem. Stuart, if you could help. Thanks!

[Stuart@KaplanGMAT]

If the st 1 was 100^d is a factor of f, how would it change then? i'd think st 2 would have to change but i have no idea what.


I am trying to figure out Stuart's explanation. 100^d = (2x2x5x5)^d and the same thing is that we have 7 5's in 30!. Does that mean that d = 5?

trying to grasp the idea with another problem. Stuart, if you could help. Thanks!

Since, as you pointed out, 100 is made up of two 2s and two 5s, we need a pair of each of those to make 1 "d".

30! has 7 5s as factors, which we can group as (5*5)*(5*5)*(5*5)*5, giving us 3 pairs of 5s (and 1 loner 5 that does nobody any good).

So, for 100^d to be a factor of 30!, the maximum possible value of d is 3.

[dxgamez]

Thanks a lot Stuart. Much better now, I understand where I went wrong.

[gmatmachoman]

If the st 1 was 100^d is a factor of f, how would it change then? i'd think st 2 would have to change but i have no idea what.


I am trying to figure out Stuart's explanation. 100^d = (2x2x5x5)^d and the same thing is that we have 7 5's in 30!. Does that mean that d = 5?

trying to grasp the idea with another problem. Stuart, if you could help. Thanks!

.

SO if it is 1000^d is a factor of f....then d will be equal to 1...

[gmatmachoman]

If the st 1 was 100^d is a factor of f, how would it change then? i'd think st 2 would have to change but i have no idea what.


I am trying to figure out Stuart's explanation. 100^d = (2x2x5x5)^d and the same thing is that we have 7 5's in 30!. Does that mean that d = 5?

trying to grasp the idea with another problem. Stuart, if you could help. Thanks!

.

SO if it is 1000^d is a factor of f....then d will be equal to 1...

@stuart

If the st 2 would have mentioned something like d>2,

So we can't definitely say the value of D. so Can we pick E???

[Stuart@KaplanGMAT]

If the st 1 was 100^d is a factor of f, how would it change then? i'd think st 2 would have to change but i have no idea what.


I am trying to figure out Stuart's explanation. 100^d = (2x2x5x5)^d and the same thing is that we have 7 5's in 30!. Does that mean that d = 5?

trying to grasp the idea with another problem. Stuart, if you could help. Thanks!

.

SO if it is 1000^d is a factor of f....then d will be equal to 1...

@stuart

If the st 2 would have mentioned something like d>2,

So we can't definitely say the value of D. so Can we pick E???

Now I'm confused!

Which question are we working with? The original one or one of the "what if"s?

[Testluv]

SO if it is 1000^d is a factor of f....then d will be equal to 1...

As Stuart pointed out, there are a maximum of 7 10s in 30! [So, for 10^n, n =< 7]

1000^d = (10^3)^d = 10^(3d)

Because d is a positive integer, it could be 1 or 2. [3d =< 7 where d is a positive integer]

If it was 10 000^d, then d must be 1. [4d =< 7 where d is a positive integer]

If the st 2 would have mentioned something like d>2,

So we can't definitely say the value of D. so Can we pick E???

If (2) of the original question had been d>2, then, yes, the answer to the original question would be E. "d" could then be any positive integer from 3 to 7.

[gmatmachoman]

SO if it is 1000^d is a factor of f....then d will be equal to 1...

As Stuart pointed out, there are a maximum of 7 10s in 30! [So, for 10^n, n =< 7]

1000^d = (10^3)^d = 10^(3d)

Because d is a positive integer, it could be 1 or 2. [3d =< 7 where d is a positive integer]

If it was 10 000^d, then d must be 1. [4d =< 7 where d is a positive integer]

If the st 2 would have mentioned something like d>2,

So we can't definitely say the value of D. so Can we pick E???

If (2) of the original question had been d>2, then, yes, the answer to the original question would be E. "d" could then be any positive integer from 3 to 7.

TestLuv,

Again awesome....I am of the opinion, U r chanceless!!! Incredible...

Becox stuart also got confused with my question ..( I too got confused)as we digressed from the topic with so many "if's...(aApologies Stuart for not asking the right query)

But u rightly picked the thread & entangled the knot...OMG....that's superb Deepak!!

thx a lot Deepak & stuart for clearing my doubts