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LCM GCF

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by gmatblood » Wed Nov 02, 2011 3:40 am
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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Source: — Data Sufficiency |
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by shankar.ashwin » Wed Nov 02, 2011 3:53 am
LCM * GCF = xy
You need both. C
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by Brent@GMATPrepNow » Wed Nov 02, 2011 5:22 am
gmatblood 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.
Statement 1: The greatest common factor of x and y is 10
case a: x=10 and y=10. Here, xy=100
case b: x=10 and y=20. Here, xy=200
INSUFFICIENT

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
INSUFFICIENT

Statements 1 & 2
There'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

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) = 1800
SUFFICIENT

So, the answer is C

Cheers,
Brent
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by vaibhavgupta » Wed Nov 02, 2011 6:58 am
gmatblood 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.
Rule used for this :

HCF*LCM= Number 1* Number 2

Hence C It is!! :)
If OA is A, IMO B
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A

FML!! :/
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by gmattesttaker2 » Fri Apr 04, 2014 6:59 pm
Brent@GMATPrepNow wrote:
gmatblood 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.
Statement 1: The greatest common factor of x and y is 10
case a: x=10 and y=10. Here, xy=100
case b: x=10 and y=20. Here, xy=200
INSUFFICIENT

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
INSUFFICIENT

Statements 1 & 2
There'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

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) = 1800
SUFFICIENT

So, the answer is C

Cheers,
Brent
Hello Brent,

Can you please tell me if the following solution is correct for showing that A and B are in-sufficient? Thanks a lot for your help.

Best Regards,
Sri

1) Let x = 100 = 2^2 x 5^2
Let y = 10 = 2^1 x 5^1

GCF of 100 and 10 = 2 x 5 = 10
xy = (100)(10) = 1000


Let x = 500 = 2^2 x 5^3
Let y = 10 = 2 x 5

GCF of 500 and 10 = 2 x 5 = 10
xy = (500)(10) = 5000


Hence, in-suff.


2) Let x = 20 = 2^2 x 5
Let y = 9 = 3^2

LCM of 20 and 9 = 2^2 x 3^2 x 5 = 180
xy = (20)(9) = 180


Let x = 36 = 2^2 x 3^2
Let y = 5

LCM of 36 and 5 = 2^2 x 3^2 x 5 = 180
xy = (36)(5) = 180


Let x = 18 = 2 x 3^2
Let y = 60 = 2^2 x 3 x 5

LCM of 18 and 60 = 2^2 x 3^2 x 5 = 180
xy = (18)(60) = 1080

Hence, in-sufficient
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by Brent@GMATPrepNow » Sat Apr 05, 2014 1:39 pm
gmattesttaker2 wrote: Hello Brent,

Can you please tell me if the following solution is correct for showing that A and B are in-sufficient? Thanks a lot for your help.

Best Regards,
Sri

1) Let x = 100 = 2^2 x 5^2
Let y = 10 = 2^1 x 5^1

GCF of 100 and 10 = 2 x 5 = 10
xy = (100)(10) = 1000


Let x = 500 = 2^2 x 5^3
Let y = 10 = 2 x 5

GCF of 500 and 10 = 2 x 5 = 10
xy = (500)(10) = 5000


Hence, in-suff.


2) Let x = 20 = 2^2 x 5
Let y = 9 = 3^2

LCM of 20 and 9 = 2^2 x 3^2 x 5 = 180
xy = (20)(9) = 180


Let x = 36 = 2^2 x 3^2
Let y = 5

LCM of 36 and 5 = 2^2 x 3^2 x 5 = 180
xy = (36)(5) = 180


Let x = 18 = 2 x 3^2
Let y = 60 = 2^2 x 3 x 5

LCM of 18 and 60 = 2^2 x 3^2 x 5 = 180
xy = (18)(60) = 1080

Hence, in-sufficient
Perfect!

Cheers,
Brent
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