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If x^2y^3 = 200, what is xy ?

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If x^2y^3 = 200, what is xy ? [#permalink] New post 09 Apr 2010, 19:14
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53% (02:11) correct 47% (01:29) wrong based on 87 sessions
If x^2y^3 = 200, what is xy ?

(1) y is an integer
(2) x/y = 2.5

I get why 1 is NSF, no info on x. But with stmt 2, isnt it also NSF b/c we cant confirm if x is neg or positive or not?
[Reveal] Spoiler: OA

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Re: More Num Property Drama [#permalink] New post 09 Apr 2010, 22:14
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x^2 * y^3 = 200

since x^2 is +ve, then y must be positive to satisfy this.
now if x/y = 2.5 , if y is +_ve then x is also +ve.

I hope this helps
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Re: More Num Property Drama [#permalink] New post 10 Apr 2010, 09:09
Thanks gurpreet.

This is another good example of a question that isnt that hard, but when ive been studying for too long I'll get confused.

Thanks again.
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Re: More Num Property Drama [#permalink] New post 10 Apr 2010, 09:48
solve question only when your mind is fresh....if u feel sluggish, take a small nap.

Good luck.
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Re: More Num Property Drama [#permalink] New post 13 Apr 2010, 11:34
Stmt 1. y is an integer

to satisfy x^2 y^3 = 200 ............ y should be positive integer but x can be negative or positive
Insufficient


stmt. 2 x/y =2.5 ....... now to satify the given condition y should be positive then x has to be positive
Sufficient


IMO B
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Re: More Num Property Drama [#permalink] New post 14 Apr 2010, 01:53
Expert's post
TheSituation wrote:
If x^2y^3=200 , what is xy ?

1. y is an integer
2. x/y=2.5

[Reveal] Spoiler:
B


I get why 1 is NSF, no info on x. But with stmt 2, isnt it also NSF b/c we cant confirm if x is neg or positive or not?


If x^2y^3=200, what is xy?

(1) y is an integer --> y can be any positive integer and there will be two values of x for each y to satisfy x^2y^3=200. For example y=10 --> x^2y^3=x^2*1000=200 --> x=\frac{1}{\sqrt{5}} or x=-\frac{1}{\sqrt{5}}. So there are infinite values of xy. Not sufficient.


(2) \frac{x}{y}=2.5 --> x=2.5y. We have two equations and two variables --> x^2y^3=6.25y^5=200 --> y^5=32 --> y=2, x=5 --> xy=10. Sufficient.

Answer: B.
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Re: If x^2y^3=200 , what is xy ? 1. y is an integer 2. x/y=2.5 B [#permalink] New post 08 May 2012, 07:24
I got this problem wrong. Bunuel, can you explain if I approached it the wrong way.

I factored out 200, which = 2^3 * 5^2.

After this its obvious xy = 10

What am i missing here?
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Re: If x^2y^3=200 , what is xy ? 1. y is an integer 2. x/y=2.5 B [#permalink] New post 09 May 2012, 01:06
Expert's post
ashish8 wrote:
I got this problem wrong. Bunuel, can you explain if I approached it the wrong way.

I factored out 200, which = 2^3 * 5^2.

After this its obvious xy = 10

What am i missing here?


Check my post above: if-x-2y-3-200-what-is-xy-1-y-is-an-integer-2-x-y-2-5-b-92486.html#p713396

First of all x^2y^3=2^3*5^2 has infinitely many solutions for x and y. For ANY (nonzero) value of x there exist some y to satisfy x^2y^3=200 and vise-versa. For example x=1 and y=\sqrt[3]{200}, or x=10 and y=\sqrt[3]{2}, ... As you can see it's not necessary for x and y to be integers (3 and 2) to satisfy the given equation.

As for (1): y is an integer. y can be any positive integer and there will be two values of x for each y to satisfy x^2y^3=200. For example y=10 --> x^2y^3=x^2*1000=200 --> x=\frac{1}{\sqrt{5}} or x=-\frac{1}{\sqrt{5}}. So there are infinite values of xy. Not sufficient.

Hope it's clear.
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Re: If x^2y^3=200 , what is xy ? 1. y is an integer 2. x/y=2.5 B [#permalink] New post 23 May 2012, 03:52
ashish8 wrote:
I got this problem wrong. Bunuel, can you explain if I approached it the wrong way.

I factored out 200, which = 2^3 * 5^2.

After this its obvious xy = 10

What am i missing here?


Be careful when
1.the number type is not stated-that could be any type,integer,real etc
2.you see factorization type question-they are not always integer or prime number,unless explicitly stated.

common mistakes for me..even after months of studying
Re: If x^2y^3=200 , what is xy ? 1. y is an integer 2. x/y=2.5 B   [#permalink] 23 May 2012, 03:52
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