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If x and y are positive integers, what is the value of xy?
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Updated on: 30 Jun 2012, 05:29
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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
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Originally posted by ctgmat123 on 14 Jun 2010, 17:50.
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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Re: Data Sufficiency problem
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14 Jun 2010, 18:12
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. Answer: C. Hope it helps.
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Re: ds question
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19 Oct 2010, 03:41
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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Re: Data Sufficiency problem
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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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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.  MBA Gambit: NYC GMAT Tutor http://www.mbagambit.com



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Re: If x and y are positive integers, what is the value of xy?
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19 Dec 2012, 16:32
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?
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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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If x and y are positive integers, what is the value of xy?
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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. Thanks loads



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Re: If x and y are positive integers, what is the value of xy?
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26 Oct 2015, 03:20
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
So Answer = C



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Re: If x and y are positive integers, what is the value of xy?
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28 Jan 2017, 04:52
Given data> x and y are positive integers. We need the value of x*y
Statement 1> GCD(x,y)=10 x=10 y=10 GCD=10 xy=100
x=10 y=20 GCD=10 xy=200
Hence not sufficient.
Statement 2> LCM(x,y)=180 x=180 y=180 LCM=180 xy=180*180
x=1 y=180 LCM=180 xy=180
Hence not sufficient.
Combing the two statements>
For two positive integers => LCM(x,y)*GCD(x,y)=> xy Hence xy=180*10=> 1800
Hence sufficient.
Hence C.
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Re: Is x and y are positive integers, what is the value of xy?
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19 Sep 2017, 22:46
quiet888 wrote: Is x and y are positive integers, what is the value of xy?
(i) The greatest common factor of x and y is 10 (ii) The least common multiple of x and y is 180 We can solve this questions using 2 approach. Shorter approach (1 min) Statement 1: GCF = 10 , (x,y) = (10,20), (10, 30), (20,30), (30,50)...... and so many numbers which are coprime after division by 10. NOT SUFFICIENTStatement 2: LCM = 180 , (x,y)= (2,180), (10, 180), (90, 4).... and others NOT SUFFICIENTCombined : GCF * LCM = x*y .. Its a formula.. SUFFICIENTLonger approach (Time taking: 2 min ) Statement 1: GCF = 10 , (x,y) = (10,20), (10, 30), (20,30), (30,50)...... and so many numbers which are coprime after division by 10. NOT SUFFICIENTStatement 2: LCM = 180 , (x,y)= (2,180), (10, 180), (90, 4).... and others NOT SUFFICIENTCombined : x, y = (10,180), (20,90) xy = 1800 SUFFICIENTAnswer C
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Re: Is x and y are positive integers, what is the value of xy?
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20 Apr 2018, 07:49
quiet888 wrote: Is x and y are positive integers, what is the value of xy?
(i) The greatest common factor of x and y is 10 (ii) The least common multiple of x and y is 180 Target question: What is the value of xy?Statement 1: The greatest common factor of x and y is 10 case a: x=10 and y=10. Here, xy=100case b: x=10 and y=20. Here, xy=200Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: The least common multiple of x and y is 180 case a: x=1 and y=180. Here, xy=180 case b: x=2 and y=180. Here, xy=360 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 & 2There's a nice rule that says: If x and y are positive integers, then (GCF of x and y)(LCM of x and y)=xy(aside: whenever a question mentions the LCM and the GCF, be sure to consider the above rule)Statement 1 says the GCF of x and y is 10 Statement 2 says the LCM of x and y is 180 So, from our handy rule, xy = (10)(180) = 1800Since we can now answer the target question with certainty, the combined statements are SUFFICIENT So, the answer is C Cheers, Brent
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Re: If x and y are positive integers, what is the value of xy?
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15 Jul 2018, 12:56
Can someone explain to me why 20 & 90 don't work?
Thank you.



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Re: If x and y are positive integers, what is the value of xy?
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15 Jul 2018, 20:45
krisbrown12 wrote: Can someone explain to me why 20 & 90 don't work?
Thank you. x and y could be 20 and 90. In this case too xy = 20*90 = 1800. The same answer.
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Re: If x and y are positive integers, what is the value of xy?
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30 Sep 2019, 16:27
ctgmat123 wrote: If x and y are positive integers, what is the value of xy? (1) The greatest common factor of x and y is 10x, y could = 10 in which case xy = 100 or x,y could = 10, 20 so xy = 200 Not sufficient because without knowing the remaining factors of x or y we can't say anything about the value of xy. (2) The least common multiple of x and y is 180180 = 2²*3²*5, so it could be that x = 5 and y = 2²*3² in which case xy = 180 or x = 5*2, y = 3²*2² in which case xy = 360 Not sufficient because without knowing if they share any factors of 180 we can't determine xy. Together, we know 1) GCF = 10 and LCM = 180, so x & y share 2*5 as factors, and the other 2*3² is split amongst them in some manner... product of xy = GCF*LCM = 1800, sufficient.




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