Math Assistance (GMAT)

Gork

The wonderfully inadequate GMAT prep software I've gotten doesn't provide explanations to questions from the practice exams, so I could use some help explaining a question I answered incorrectly.

For every positive integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is:

A. Between 2 and 10
B. Between 10 and 20
C. Between 20 and 30
D. Between 30 and 40
E. Greater than 40


Thanks in advance.

the wook

edit - nothing to see here, i totally misread the problem :P

edit the second - request for clarification: does p = the smallest prime factor of [h(100) +1] or [the smallest prime factor of h(100)] +1?

Rend

Its the smallest prime factor of h(100) +1, thus it's not necessarily even anymore, so we need to find the smallest prime factor for the odd number, not just add 1 to the smallest prime factor for the even number, right?

PeekingDuck

I'm getting E. Trying to work out a way to solve it.

Accidentally wrote D.

Gdiguy

I believe it's E (unless someone can tell me why this is totally crap):

The reason: the product of even numbers from 2 to n is the same as the product of 1 to n/2 times 2 to the n/2 power, since you can just factor a 2 out of every number...

so the product of (2*4*6*...*n) = (1*2* ... * n/2) * (2^n/2).

So h(100) is (1*2*...*50) * (2^50) + 1

But you know that (1*2*...*50) is a multiple of every prime number between 1 and 50, so that +1 absolutely cannot be divisible by any number from 1 to 50

Beedle

Gdiguy wrote: »

I believe it's E (unless someone can tell me why this is totally crap):

The reason: the product of even numbers from 2 to n is the same as the product of 1 to n/2 times 2 to the n/2 power, since you can just factor a 2 out of every number...

so the product of (2*4*6*...*n) = (1*2* ... * n/2) * (2^n/2).

So h(100) is (1*2*...*50) * (2^50) + 1

But you know that (1*2*...*50) is a multiple of every prime number between 1 and 50, so that +1 absolutely cannot be divisible by any number from 1 to 50

Looks sound to me.

PeekingDuck

Well... 2+4+6+8+...+(2n-2)+2n = n(n+1)

So here n is 50 since h(n) is evaluated at h(100)

50(50+1) = 2550

tack on the +1 and that gives you 2551

now you have to know division rules and this problem is stupid.

wait, I'm stupid.

Beedle

PeekingDuck wrote: »

Well... 2+4+6+8+...+(2n-2)+2n = n(n+1)

So here n is 50 since h(n) is evaluated at h(100)

50(50+1) = 2550

tack on the +1 and that gives you 2551

now you have to know division rules and this problem is stupid.

wait, I'm stupid.

It's the product of the even integers up to 100 though, not their sum, so Gdiguy's answer is correct.

PeekingDuck

Well I guess I need to learn how to read. Funny thing, 2551 is prime.

Gork

Thanks all, E was the correct answer.

Got another one:

Jason's salary and Karen's salary were each p percent greater in 1998 than in 1995. What is the value of p?

(1) In 1995 Karen's salary was $2000 greater than Jason's
(2) In 1998 Karen's salary was $2440 greater than Jason's

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient to answer the question
C. Both statements together are sufficient, but neither statement alone is sufficient
D. Each statement alone is sufficient
E. Statement (1) and (2) together are not sufficient

The answer is C. I would like to be able to see how to calculate p, but I keep getting caught up with too many variables because Jason's salary isn't constant.

IreneDAdler

Gork wrote: »

Thanks all, E was the correct answer.

Got another one:

Jason's salary and Karen's salary were each p percent greater in 1998 than in 1995. What is the value of p?

(1) In 1995 Karen's salary was $2000 greater than Jason's
(2) In 1998 Karen's salary was $2440 greater than Jason's

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient to answer the question
C. Both statements together are sufficient, but neither statement alone is sufficient
D. Each statement alone is sufficient
E. Statement (1) and (2) together are not sufficient

The answer is C. I would like to be able to see how to calculate p, but I keep getting caught up with too many variables because Jason's salary isn't constant.

You don't need to really calculate anything for this problem. The key concept here is that p(J+2000)=pJ+2440, so p2000=2440, which you can then use to calculate p. And you're calculating p using information from both statements, so the only answer that fits is C.

edit: J stands for Jason's salary in 1995.

Gork

Wow, I'm dumb. Thanks.

Beedle

(Edit: Hm, beaten to it and this post seems irrelevant now. Well, I'll leave it here in case anyone is interested in solving the problem in an entirely tedious amount of detail.)


Yeah, you don't need to calculate it, but if you want to do the calculation, it's indeed tricky because there are five unknowns (J0, J1, K0, K1, p; respectively Jason's and Karen's 1998 and 1995 salaries, and p). But you can do it if you keep a clear head:

The first sentence gives you J1 = (1+p)J0 (A) and K1 = (1+p)K0 (B).

Statement 1 gives you K0 = J0 + 2000 (C) and 2 gives K1 = J1 + 2440 (D).

(C) and (D) subbed into (B) gives J1 + 2440 = (1+p)(J0 + 2000) (E).

Subbing (A) into (E) gives (1+p)J0 + 2440 = (1+p)(J0 + 2000). Take (1+p)J0 from both sides leaves 2440 = 2000(1+p) gives (1+p)=2440/2000 gives p=22%.

DJ-99

This is very important. In problems like that, absolutely DO NOT waste time solving for p (or whatever it is). All you have to do is realize that you can or cannot do it, then move on.

I just took the GMAT, and believe me, you're going to want all the time you can get. The questions at the end can become extremely difficult, so you'll want to get through the easier ones as quickly as possible.

Also, I highly recommend buying the official GMAT review guide. It's the only book with actual GMAT questions, and it explains all the answers.

Good luck.

Gork

Oh, I know not to actually solve for it on the test, just for study reasons it helps to be able to understand the underlying math.

And the crappy practice test software without explanations to answers is directly from the GMAC. Go figure.

DJ-99

Gork wrote: »

Oh, I know not to actually solve for it on the test, just for study reasons it helps to be able to understand the underlying math.

And the crappy practice test software without explanations to answers is directly from the GMAC. Go figure.

I definitely don't think it's crappy. You need to realize that there aren't answer explanations for the practice tests because it's a REAL TEST. I actually had 2 questions from my practice tests appear on the real GMAT. The odds of that happening are small, but that's the reason they don't provide answer explanations. The software is in fact extremely helpful because it's exactly how the GMAT will be when you take it for real.

Definitely make sure you take both of the practice tests they offer. The scores you receive there should be a pretty decent prediction of what you get on the real thing. I got a 750 on both practice tests but then got a 780 on the real thing. I wouldn't expect much more variation than that, however (I think I got a little lucky, probably should have been around 750 again).

Good luck. If you have any questions about anything, I can probably give you some advice.