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If x and y are positive integers and x^3*y^4 = 2000 what is

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If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] New post 11 Sep 2008, 13:36
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If x and y are positive integers, and x^3*y^4 = 2,000, which of the following is the value of xy?

A. 2
B. 4
C. 8
D. 10
E. 20
[Reveal] Spoiler: OA
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Re: PS.. More Exp [#permalink] New post 11 Sep 2008, 13:51
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IgnitedMind wrote:
If x and y are positive integers and x^3*y^4 = 2000 what is the value of xy?

2

4

8

10

20


10

\((5*2)^{3}*2=2000\)


D
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Re: intergers [#permalink] New post 09 Nov 2008, 20:42
pardon me asking...is the question stem valid as-is? I am finding it hard to deduce a set of +ve integer values for x and y satisfying the below equation

x^3y^4 = 2000

even if you take x=2 and y =1, the lowest possible values, it is still <> 2000.
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Re: intergers [#permalink] New post 10 Nov 2008, 06:22
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2000 = 5^3*2^4
Hence, xy = 10
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Re: intergers [#permalink] New post 10 Nov 2008, 07:13
scthakur wrote:
2000 = 5^3*2^4
Hence, xy = 10


how long did it take you to figure out x and y? I looked at your answer before solving this so just want to estimate which method is better when taking the test.

x^3y^4 = (xy)^3 * y = 2000

a. if xy = 2 => 2^3 = 8, can't find y
b. xy = 4 (same as above)
c. xy = 8, 8^3 = 512; 2000/512 is not integer
d. xy = 10, 10^3 = 1000, y = 2000/1000 = 2
e. xy = 20, 20^3 = 8000 > 2000

so the answer is D
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Re: intergers [#permalink] New post 10 Nov 2008, 09:15
Actually, I had seen this problem before. Haaving said that, in such types of problems, it is better to break the big number into squares, cubes, etc. of smaller numbers.
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Re: intergers [#permalink] New post 10 Nov 2008, 10:49
[quote="Jcpenny"]If x and y are positive integers, and x^3y^4 = 2,000, which of the following is the value of xy?

A. 2
B. 4
C. 8
D. 10
E. 20

1000*2 = 10^3*2 = 5^3*2^4 thus xy = 10...D
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Re: intergers [#permalink] New post 11 Nov 2008, 07:28
hit n trial can help here.
we can easily guess that either x or y must be 5 here.

if y=5 we cant divide 2000 by 625 ...so x=5...and there u go...

alternatively, we can think of the possible values of (xy)3 ...where (xy)3 =1000 is most plausible option considering y to be an integer....
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Re: If x and y are positive integers, and x^3y^4 = 2,000, which [#permalink] New post 17 Mar 2014, 16:54
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] New post 17 Mar 2014, 17:01
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] New post 08 Apr 2014, 18:52
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for this problem, i factored 2000 --> 2, 2, 2, 2, 5, 5, 5... or (5*3)(2*4).

based on the factoring, x = 5 and y = 2... so xy = (5)(2) = 10

the correct answer is d.
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] New post 08 Apr 2014, 22:52
In such question it is best to see the options available.
x^3*y^4 = 2000 is essentially same as (xy)^3*y = 2000
Now, if you look at the available choices, it is 2, 4, 8, 10, 20
You can figure out looking at choices that 2, 4, 8 are too small to satisfy the equation while 20 is too large.
Hence, lets check with 10. If xy = 10, xy^3 = 1000, so y = 2000/1000 = 2 and x = 10/2 = 5.
5 & 2 being positive integers, xy=10 is the correct answer.
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] New post 11 Apr 2014, 06:57
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My Analysis with Strategy..
1 Positive Integers ( + ) , 2 Powers , 3 Prime factorization
So Prime factorization of 2000 write in Power form = 2^4 5^3
So x = 5 , y = 2 ; 5 * 2 = 10 :)
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] New post 07 May 2015, 03:17
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] New post 07 May 2015, 03:56
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In questions like this one, it's a good idea to start by Prime Factorization of the big number. Some of the students who posted their solutions above have done this already. :)

Here's a similar OG question for you to practice:

http://gmatclub.com/forum/if-y-is-the-smallest-positive-integer-such-that-65323.html

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Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] New post 31 May 2015, 02:43
X^3Y^4=(XY)^3Y=2000=10^3*2; therefore, Y=2 and XY=10--> Answer:D
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] New post 01 Jun 2015, 00:07
x^3*y^4=2000
(xy)^3=2000/y=(2/y)*10^3

(xy)=10*(2/y)^(1/3)
Since y is a positive integer taking y=2
D
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] New post 01 Jun 2015, 20:46
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Hi All,

This question involves some Number Properties; if you recognize them, think logically and choose the SIMPLEST examples possible, then you'll get to the correct answer relatively quickly.

We're told that (X^3)(Y^4) = 2,000

Since we're dealing with a product that ends in 0, at least one of the variables is a multiple of 5 and at least one of the variables is even.

So....choose two different numbers....the most obvious multiple of 5 and the most obvious even....

You'll end up with 5 and 2....Plug those in (one for X and one for Y) - it'll take no more than 2 attempts to find the one that 'fits' and you'll have the value of (X)(Y)...

Final Answer:
[Reveal] Spoiler:
D


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Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] New post 02 Jun 2015, 03:03
D
2 and 5 are in equal numbers in 1000 i.e. 2^3 and 5^3 and thus in 2 x 1000 --- number of 2 = 1+no. of 5's. Thus there product would be 20.
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is   [#permalink] 02 Jun 2015, 03:03
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