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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 09 Apr 2010, 20:14
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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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Re: If x^2y^3 = 200, what is xy ? [#permalink]

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New post 09 Apr 2010, 23:14
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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Re: If x^2y^3 = 200, what is xy ? [#permalink]

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New post 10 Apr 2010, 10:09
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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New post 10 Apr 2010, 10:48
solve question only when your mind is fresh....if u feel sluggish, take a small nap.

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

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New post 13 Apr 2010, 12:34
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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New post 14 Apr 2010, 02:53
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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.

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

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New post 08 May 2012, 08:24
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 ? [#permalink]

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New post 09 May 2012, 02:06
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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New post 23 May 2012, 04:52
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
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Re: If x^2y^3 = 200, what is xy ? [#permalink]

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New post 19 Oct 2014, 01:34
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.

please do let me know! Thanks in advance!
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Re: If x^2y^3 = 200, what is xy ? [#permalink]

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New post 20 Oct 2014, 03:27
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.

please do let me know! Thanks in advance!


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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New post 20 Oct 2014, 09:28
Thank you so much for clearing that doubt!
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Re: If x^2y^3 = 200, what is xy ? [#permalink]

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New post 27 Mar 2018, 06:56
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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New post 27 Mar 2018, 07:29
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 27 Mar 2018, 10:59
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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New post 23 Jun 2018, 09:07
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.

Answer: B.


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 ?   [#permalink] 23 Jun 2018, 09:07
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