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

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Manager
Joined: 28 Aug 2008
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If x and y are positive integers and x^3*y^4 = 2000 what is  [#permalink]

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11 Sep 2008, 14:36
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86% (01:27) correct 14% (01:36) wrong based on 675 sessions

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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
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is  [#permalink]

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08 Apr 2014, 19:52
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1
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

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11 Sep 2008, 14:51
4
2
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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09 Nov 2008, 21:42
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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10 Nov 2008, 07:22
2
2000 = 5^3*2^4
Hence, xy = 10
Manager
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10 Nov 2008, 08:13
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

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10 Nov 2008, 10:15
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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10 Nov 2008, 11:49
1
[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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11 Nov 2008, 08:28
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....
Intern
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is  [#permalink]

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08 Apr 2014, 23:52
1
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]

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11 Apr 2014, 07:57
2
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]

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07 May 2015, 04:56
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

Best Regards

Japinder
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is  [#permalink]

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31 May 2015, 03:43
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]

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01 Jun 2015, 01:07
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]

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01 Jun 2015, 21:46
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)...

GMAT assassins aren't born, they're made,
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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Manager Joined: 21 May 2015 Posts: 240 Concentration: Operations, Strategy GMAT 1: 750 Q50 V41 Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] ### Show Tags 02 Jun 2015, 04:03 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. _________________ Apoorv I realize that i cannot change the world....But i can play a part Manager Joined: 26 Mar 2017 Posts: 134 Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] ### Show Tags 10 Jun 2017, 07:09 jmyer028 wrote: 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. I've done exactly the same Ive got it right in front of me on my test simulation booklet But didn't know what to do with the prime factors (just to nervous) I think if you don't stay calm on test day you'll get nowhere !! _________________ I hate long and complicated explanations! EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12669 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x and y are positive integers and x^3*y^4 = 2000 what is [#permalink] ### Show Tags 10 Jun 2017, 11:28 1 Hi daviddaviddavid, Most of the questions that you'll face on Test Day will become easier to deal with IF you get in the habit of taking notes (including writing down what the question asks you to solve for). After reading through this prompt - and taking all of the necessary notes - the last thing you should have written down is.... "(X)(Y) = ?" In that way, you will know your 'goal' and when you have the necessary information to answer the question that is asked. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If x and y are positive integers and x^3*y^4 = 2000 what is  [#permalink]

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10 Jun 2017, 11:49
Imo D
2^4*5^3=2000 hence xy=10

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If x and y are positive integers and x^3*y^4 = 2000 what is  [#permalink]

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Updated on: 10 Jun 2017, 12:11
1
EMPOWERgmatRichC wrote:
Hi daviddaviddavid,

Most of the questions that you'll face on Test Day will become easier to deal with IF you get in the habit of taking notes (including writing down what the question asks you to solve for).

After reading through this prompt - and taking all of the necessary notes - the last thing you should have written down is.... "(X)(Y) = ?"

In that way, you will know your 'goal' and when you have the necessary information to answer the question that is asked.

GMAT assassins aren't born, they're made,
Rich

thank you =)

Ill try my best

at the moment I'm just so disappointed. My test is on Tuesday and I just got 570 today

When I went through the quant questions again, I could solve at least 10 of them (wrong ones) at ease and within seconds but it appears that I'm just freezing under pressure

One questions was x+y = negative ?

(1) x negative
(2) y positive

And I quickly picked C. I guess the algorithm must have thought I'm mentally disabled.

I guess self-confidence and calmness are crucial in order to get a good score.

Sorry for off-topic
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Originally posted by daviddaviddavid on 10 Jun 2017, 11:59.
Last edited by daviddaviddavid on 10 Jun 2017, 12:11, edited 1 time in total.
If x and y are positive integers and x^3*y^4 = 2000 what is &nbs [#permalink] 10 Jun 2017, 11:59

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

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