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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]

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New post Updated on: 12 Jun 2013, 05:09
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If x^2y^3=200, what is xy?

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

Originally posted by heyholetsgo on 21 Aug 2011, 11:23.
Last edited by Bunuel on 12 Jun 2013, 05:09, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Xy  [#permalink]

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New post 21 Aug 2011, 11:47
Stmt1: y is an integer. y=0. xy=0
y=1 x^2*1=200
x^2=200, x=10sqrt(2)
xy= 10sqrt(2)*1=10sqrt(2).
Two different answer. Not sufficient.

Stmt2: x/y=2.5
x=2.5y
x^2*y^3=200
(2.5y)^2*y^3=200
y^5=200/6.25
y^5=32
y^5=2^5
y=2
x=2.5y=2.5*2=5
xy=5*2=10
Sufficient.

OA B
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Re: Xy  [#permalink]

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New post 21 Aug 2011, 11:50
heyholetsgo wrote:
If x^2y^3=200, what is xy?
1.) y is an integer
2.) x/y= 2.5
why is it not e? Don't we get 2 solutions for x once we get the value for y?


From the stem, we know y=+ve. thus x is +ve, because x/y=x/+ve=2.5; numerator +ve as well.

\(x=2.5y\)

\((2.5y)^2*y^3=200\)

\(6.25y^5=200\)

\(y^5=\frac{200}{6.5}\)

\(y=\sqrt[5]{\frac{200}{6.5}}\)

\(x=2.5*\sqrt[5]{\frac{200}{6.5}}\)

\(xy=2.5*{(\frac{200}{6.5})}^{\frac{2}{5}}\)

Sufficient.

Ans: "B"
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Re: Xy  [#permalink]

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New post 21 Aug 2011, 19:58
1
x^2 * y^3 = 200

1. not sufficient

as different y will yield different x. hence different xy.

2. sufficient

x/y = 2.5

(2.5y)^2 * y ^3 = 200

25/4 y ^5 = 200 = >y =2

x =5

Answer is B.
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Re: Xy  [#permalink]

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New post 21 Aug 2011, 22:13
(xy)^2*y=200

1. Insufficient

2.

(2.5y^2)^2*y=200
6.25y^5=200
y^5=200/(2.5*2.5)
y^5=80/2.5
y^5=32
y=2
xy=2.5*y^2
xy=10
B is sufficient
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Re: Xy  [#permalink]

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New post 21 Aug 2011, 22:44
1
heyholetsgo wrote:
If x^2y^3=200, what is xy?
1.) y is an integer
2.) x/y= 2.5
why is it not e? Don't we get 2 solutions for x once we get the value for y?


Even though, the solution has already been provided above, I want to point out something. The silver lining of DS questions is that you don't need to solve. If you know you will get a unique value, you are done.

Question stem: If \(x^2y^3=200\), what is xy?

Statement 1: y is an integer but x needn't be.
If y = 1, \(x = +-\sqrt{200}\)
If y = 2, x = +-5 etc
We do not know what xy is.

Statement 2:\(\frac{x}{y} = \frac{5}{2}\)
This means \(x = (\frac{5}{2})y\)
This value of x you can put above to get a unique value of y. (Since you will get y^5 = ... An odd power will give you only the positive solution here. )
Once you have the value of y, you get a unique value for x and hence you get a value for xy.
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Re: Xy  [#permalink]

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New post 05 Sep 2011, 13:18
Quote:
If x^2y^3=200, what is xy?
1.) y is an integer
2.) x/y= 2.5


This is my approach...

from question:
prime factors of 200: 2, 2, 2, 5, 5
---> x=5; y = 2

From Statement 1

Not helpful. Insufficient.

From Statement 2
x/y=5/2=2.5
Sufficient.

Answer: B
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Re: Xy  [#permalink]

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New post 20 Oct 2011, 07:25
1
gmatopoeia wrote:
Quote:
If x^2y^3=200, what is xy?
1.) y is an integer
2.) x/y= 2.5


This is my approach...

from question:
prime factors of 200: 2, 2, 2, 5, 5
---> x=5; y = 2

From Statement 1

Not helpful. Insufficient.

From Statement 2
x/y=5/2=2.5
Sufficient.

Answer: B


Good explanation
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Re: Xy  [#permalink]

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New post 25 Sep 2012, 06:42
After i get Using B the value of y=2

when I substitute in the main equation ,

x^2* y^3=200
i get
x=+/- 5

so is it not wrong?
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Re: Xy  [#permalink]

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New post 25 Sep 2012, 06:47
shankar245 wrote:
After i get Using B the value of y=2

when I substitute in the main equation ,

x^2* y^3=200
i get
x=+/- 5

so is it not wrong?


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.

Hope it helps.
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Re: If x^2y^3=200, what is xy?  [#permalink]

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