If n and y are positive integers and 450Y = n^3, which of

[GMAT 5/18]

Absolutely no idea how to derive this answer, so any help would be great! :)

If n and y are positive integers and 450Y = n^3, which of the following must be an integer?

I. y/(3 x 2^2 x 5)

II. y/(3^2 x 2 x 5)

III. y/(3 x 2 x 5^2)

a. None
b. I only
c. II only
d. III only
e. I, II, and III

[Guest]

450y=n^3
=> 2*3^2*5^2(y)=n^3
Therefore y has to be 2^2*3*5 to satisfy the condition

1. y/(3 x 2^2 x 5) Definitely YES
2) Not always YES
3) Not always YES

Therefore A.

What is the OA?

[Guest]

I mean B

[GMAT 5/18]

Thanks for your explanation. Yes, B is the correct answer.

I think I am following your reasoning, but if you or someone else could explain why "Therefore y has to be 2^2*3*5 to satisfy the condition", that would be great.

It looks like the answer produces 2, 3, and 5 all to have ^3, but I am still not sure I understand.

[dbernst]

For a number to equal any integer to the third power, it must contain prime factors raised to the power of three. For example, a prime number raised to the third power, such as 27, will only contain 3^3 in its prime box.

As for non-prime integers raised to the third power, they can always be reduced to their prime factors, each raised to the third power. For example, 6^3 can be factored to (2x3)^3, or (2^3)(3^3).

In the problem at hand, we already have 3^2 * 5^2 * 2. That means y must add one power of 3, one power of 5, and 2 powers of 2 for n^3 to be an integer.

Answer choice B is the only choice that explicitly offers this particular set of powers.

Hope that helps!
-dan

[Saurabh Malpani]

Hey Gmat 5/18 are you taking GMAT on 18th of May? Even I am taking GMAT on 18th of May. So where are you based out of?

Thanks
Saurabh Malpani

[GMAT 5/18]

Yep, I am taking it on the 18th of May. I will be taking it in Kansas City. What about you?

I'm hoping to score 800, but realistically would be pretty happy with 700+.

[Saurabh Malpani]

Well ya I won't mind at all scoring 700+ well I will be taking it at Princeton!!!

Let me knwo if I can help you in anyway!

[GMAT 5/18]

Thanks Saurabh, same goes for me.

[tony.su.tuo]

Hi all, new to the forum and have a quick question even after the explanations.

Can I use satisfying numbers to try to prove validity of the question? I took y=6 and n=30 which satisfy the first part and clearly fails all of I II and III. Thought the statement is an universal one so plugging in numbers can work, and apparently not. Can anyone help me with my logic flaw?

Thanks!

Tarantula

[jnelson0612]

Hi all, new to the forum and have a quick question even after the explanations.

Can I use satisfying numbers to try to prove validity of the question? I took y=6 and n=30 which satisfy the first part and clearly fails all of I II and III. Thought the statement is an universal one so plugging in numbers can work, and apparently not. Can anyone help me with my logic flaw?

Thanks!

Tarantula

Hi,
It would be fine to plug in numbers but let's check the numbers that you chose. The equation given is:
450Y = n^3

If I substitute in to this equation your numbers of y=6 and n=30, we get:
450(6) = (30)^3

Here's where we run into trouble. 450 * 6 = 2700, whereas 30^3 is 27,000. Because these numbers do not fit the equation, we cannot use them to test the answers.

Please let us know if you have further questions. :-)