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

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Manager
Joined: 09 Dec 2009
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If x^2y^3 = 200, what is xy ?  [#permalink]

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09 Apr 2010, 19:14
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Difficulty:

75% (hard)

Question Stats:

54% (02:03) correct 46% (02:06) wrong based on 489 sessions

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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?

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Math Expert
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Posts: 51229
Re: If x^2y^3 = 200, what is xy ?  [#permalink]

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14 Apr 2010, 01:53
3
3
TheSituation wrote:
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?

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.

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CEO
Status: Nothing comes easy: neither do I want.
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Re: If x^2y^3 = 200, what is xy ?  [#permalink]

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09 Apr 2010, 22:14
1
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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Manager
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Re: If x^2y^3 = 200, what is xy ?  [#permalink]

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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: If x^2y^3 = 200, what is xy ?  [#permalink]

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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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Joined: 05 Mar 2010
Posts: 174
Re: If x^2y^3 = 200, what is xy ?  [#permalink]

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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: If x^2y^3 = 200, what is xy ?  [#permalink]

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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?
Math Expert
Joined: 02 Sep 2009
Posts: 51229
Re: If x^2y^3 = 200, what is xy ?  [#permalink]

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09 May 2012, 01:06
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 ?  [#permalink]

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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
Intern
Joined: 12 Dec 2013
Posts: 16
Re: If x^2y^3 = 200, what is xy ?  [#permalink]

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19 Oct 2014, 00:34
Hi Bunuel,

With regards to the problem above, for st 2, is it fine to approach it the following way -

(2) x/y = 2.5
x/y = 25/10 => 5/2
therefore, x = 5 & y = 2. giving xy = 10 Suff.

Math Expert
Joined: 02 Sep 2009
Posts: 51229
Re: If x^2y^3 = 200, what is xy ?  [#permalink]

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20 Oct 2014, 02:27
Rca wrote:
Hi Bunuel,

With regards to the problem above, for st 2, is it fine to approach it the following way -

(2) x/y = 2.5
x/y = 25/10 => 5/2
therefore, x = 5 & y = 2. giving xy = 10 Suff.

No, that's totally wrong. You cannot solve x/y = 2.5 for x and y. Why do you say x = 5 and y = 2? Why not x = 2.5 and y = 1? Or x = 25 and y = 10? x/y = 2.5 has infinitely many solutions for x and y - we have one equation and two unknowns!
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Re: If x^2y^3 = 200, what is xy ?  [#permalink]

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20 Oct 2014, 08:28
Thank you so much for clearing that doubt!
Intern
Joined: 20 Dec 2014
Posts: 37
Re: If x^2y^3 = 200, what is xy ?  [#permalink]

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27 Mar 2018, 05:56
TheSituation wrote:
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?

The question needs to be worded better.
X^2 * Y^3
I interpreted the question as

(X^2y)^3
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Re: If x^2y^3 = 200, what is xy ?  [#permalink]

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27 Mar 2018, 06:29
MT1988 wrote:
TheSituation wrote:
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?

The question needs to be worded better.
X^2 * Y^3
I interpreted the question as

(X^2y)^3

Edited, thank you.

Though mathematically x^2y^3 can only mean $$x^2y^3$$. If it were $$(x^2y)^3$$ it would be written as (x^2y)^3 and if it were $$(x^{2y})^3$$ it would be written as (x^(2y))^3
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If x^2y^3 = 200, what is xy ?  [#permalink]

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27 Mar 2018, 09:59
Bunuel wrote:
MT1988 wrote:
TheSituation wrote:
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?

The question needs to be worded better.
X^2 * Y^3
I interpreted the question as

(X^2y)^3

Edited, thank you.

Though mathematically x^2y^3 can only mean $$x^2y^3$$. If it were $$(x^2y)^3$$ it would be written as (x^2y)^3 and if it were $$(x^{2y})^3$$ it would be written as (x^(2y))^3

PEMDAS....

Was wondering what if my interpretation was correct?
Are there questions like that?

Took for ever to solve but if my interpretation was right would B be the answer?
Am I unnecessarily complicating the question?
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Re: If x^2y^3 = 200, what is xy ?  [#permalink]

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23 Jun 2018, 08:07
Bunuel wrote:
TheSituation wrote:
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?

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.

For Statement 2, I think we can stop at this step:
$$6.25y^5=200$$
y is raised to an odd power, so there will be one solution. we can find y... we can find x.
Re: If x^2y^3 = 200, what is xy ? &nbs [#permalink] 23 Jun 2018, 08:07
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