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# If x and y are positive integers, what is the value of xy?

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If x and y are positive integers, what is the value of xy? [#permalink]

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14 Jun 2010, 17:50
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If x and y are positive integers, what is the value of xy?

(1) The greatest common factor of x and y is 10
(2) The least common multiple of x and y is 180
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jun 2012, 05:29, edited 2 times in total.
Edited the question and added the OA
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14 Jun 2010, 18:12
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ctgmat123 wrote:
Can someone walk me through this one?

If x and y are positive integers, what is the value of xy?

1) The greatest common factor of x and y is 10
2) the least common multiple of x and y is 180

THanks

Welcome to the Gmat Club. Below is a solution for your problem:

If x and y are positive integers, what is the value of xy?

(1) The greatest common factor of x and y is 10. Clearly insufficient as multiple values are possible for $$xy$$: for instance if $$x=y=10$$, $$GCF(x,y)=10$$ and $$xy=100$$ BUT if $$x=10$$ and $$y=20$$, $$GCF(x,y)=10$$ and $$xy=200$$.

(2) the least common multiple of x and y is 180. Also insufficient as again multiple values are possible for $$xy$$: for instance if $$x=10$$ and $$y=180$$, $$LCM(x,y)=180$$ and $$xy=1800$$ BUT if $$x=1$$ and $$y=180$$, $$LCM(x,y)=180$$ and $$xy=180$$.

(1)+(2) The most important property of LCM and GCF is: for any positive integers $$x$$ and $$y$$, $$xy=GCF(x,y)*LCM(x,y)$$, hence $$xy=GCF(x,y)*LCM(x,y)=10*180=1800$$. Sufficient.

Hope it helps.
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19 Oct 2010, 03:41
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satishreddy wrote:
if X and Y are positive integers, what is the value of xy

1) the greatest common factor of X and Y is 10
2) the least common multiple of X and Y is 180

This is just a formula based.

( GCFof x and y )* (LCM of x and y)= x * y

This is valid for all the numbers.Hope this will do.

Consider KUDOS if u find it helpful.Thanks.
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20 Oct 2010, 12:27
Nice, I didn't know GCF(X&Y)*LCM(X&Y)=X*Y

Kudos!!
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24 Feb 2012, 14:14
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Some solutions above rely on the "property" that GCFxLCM is xy, which is nice when you know the property. Unfortunately, it is nearly impossible to learn all such properties for the GMAT. Here's a away to (try) to derive the property for this and similar problems:

GCF = 10 = 2x5
LCM = 180 = 3x3x2x2x5

The solution centers on the definition of LCM. Remember how we find LCM for two numbers? We take all the prime factors the two numbers share and multiply them by prime factors that the numbers don't share.

ie, LCM of (2x2x5x7) and (2x7x11) would be: (2x2x5x7x11)

Since we are looking for the actual product of x and y, the result will be the LCM times the factors they share (since we didn't double count them in the original LCM calculation), namely the GCF, since that's what the GCF encapsulates.

Hence, xy = LCM x GCF.

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Re: If x and y are positive integers, what is the value of xy? [#permalink]

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19 Dec 2012, 16:32
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This is tough.

whenever you see such question break down into factors the numbers.

So we want information to exactly calculate $$X*Y$$

1) we have 10 and the factor are 2 and 5 a bunch of numbers could have 2 and 5 in the shaded region to calculate the GCF (remembre that to obtain the GCF you take between two numbers those have the least power). Insuff

2) the same as above 180 equal $$2^2$$ $$3^2$$ and $$5$$ but nothing more . insuff

1) and 2) for any two positive integers X and Y, $$X*Y$$ $$=$$ $$(LCM of X and Y) x (GCF of X and Y)$$. So you have: $$2*5$$ from $$GCF$$ and $$2^2$$ $$3^2$$ and $$5$$ from$$LCM$$. So you can calculate exactly the value of $$X*Y$$

I 'll wait from Bunuel if my explanation is correct
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Re: If x and y are positive integers, what is the value of xy? [#permalink]

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19 Dec 2012, 17:07
I think answer should be C as the property is GCF (x,y) * LCM(x,y) = Product of the two numbers
Hence value of xyv= 10*180= 1800

To prove A as insufficient you can plug numberssay X = 10 , Y = 30 GCF =10 product = 300 Another case X = 10 Y = 10 Hence product = 100

To prove B as insufficient you can plug in numbers X= 90 Y = 180 , Another case X=1 Y = 180
Hence Insufficient

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Re: If x and y are positive integers, what is the value of xy? [#permalink]

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13 Jul 2014, 22:36
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If x and y are positive integers, what is the value of xy? [#permalink]

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09 Nov 2014, 00:22
hello
I've been trying to wrap my head around all that gcd and lcm would tell me about the numbers. When actual numbers are given it is a little easier. But when not, it gets hard, for me (like this : If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b? (1) a = 2b + 6 (2) a = 3b ------sorry about this.. i cant paste urls yet)

So I need some generalizations (so i can summarize finally )

-What do GCD and LCM tell us about the numbers?
-Is it ever possible to know the numbers themselves when the LCM or GCD are given?
-We found the product of numbers here. Can we find the numbers themselves in any case?
Please help me, even if you know the answer to one of these questions. Also let me know if any of them don't make sense, and why.
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Re: If x and y are positive integers, what is the value of xy? [#permalink]

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26 Oct 2015, 03:20
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X and Y are integers

$$XY= ?$$

Statement 1

GCF( greatest Common factor) of x and y = $$10$$

x = 10 and y = 10
GCF = 10
hence xy = 100

x = 10 and y = 30
GCF = 10
hence xy = 300

Clearly Not Sufficient

Statement 2

LCM( least common multiple) of x and y = $$180$$

x= 180 and y = 1
LCM = 180
hence xy= 180

x=180 and y = 2
LCM = 180
Hence xy = 360

Clearly not sufficient

Now Combining Statement 1 and 2

we Know that
HCF of x and y * Lcm of x and y = x* y

Therefore $$10 * 180 = 1800$$

Sufficient

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Re: If x and y are positive integers, what is the value of xy? [#permalink]

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16 Mar 2016, 10:20
Use the rule => GCD * LCM = product of two integers
hence C is sufficient
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Re: If x and y are positive integers, what is the value of xy?   [#permalink] 16 Mar 2016, 10:20
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