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If x and y are positive integers such that x > y and the least common

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If x and y are positive integers such that x > y and the least common  [#permalink]

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New post 09 Oct 2018, 04:00
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Question Stats:

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If x and y are positive integers such that x > y and the least common multiple and greatest common divisor of the two integers are 36 and 6 respectively, what is the value of x – y?

(1) x = 18
(2) x + y = 30
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Re: If x and y are positive integers such that x > y and the least common  [#permalink]

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New post 09 Oct 2018, 05:10
rencsee wrote:
If x and y are positive integers such that x > y and the least common multiple and greatest common divisor of the two integers are 36 and 6 respectively, what is the value of x – y?

(1) x = 18
(2) x + y = 30


Let's start by making a list of all the possible numbers:
numbers whose have 36 as a multiple: 1,2,3,4,6,9,12,18, 36
numbers whose have 6 as a divisor: 6, 12, 18, 24, 30, 36

Therefore, we have only two options for x and y: x=36,y=6 and x=18, y=12
both (1) and (2) separately tell us that of these two options, it must be x=18, y=12, therefore x=y = 6. Each statement on its own is sufficient! answer D.
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Re: If x and y are positive integers such that x > y and the least common  [#permalink]

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New post 15 Oct 2018, 20:18
Not sure why statement A is correct

Posted from my mobile device
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Re: If x and y are positive integers such that x > y and the least common  [#permalink]

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New post 15 Oct 2018, 21:16
MJ1993 wrote:
Not sure why statement A is correct

Posted from my mobile device


Hi MJ1993,

If you know that \(x=18=2*3^2\), you can figure y from LCM and GCD.

\(LCM=36= 2^2*3^2\)
GCD= 6 = 2*3
\(x= 2*3^2\)
\(y= 2^2*3\) <-- this is what left

Also, there is a little rule worth to memorize in the LCM/GCD topic.

LCM of x and y * GCD of x and y= x*y
so in this case: 36*6=xy, if you know the value of x, you get y very fast
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Re: If x and y are positive integers such that x > y and the least common  [#permalink]

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New post 15 Oct 2018, 21:29
1
MJ1993,

Let me explain.

Theory:
The product of LCM and GCD(HCF) of two numbers is equal to the product of two numbers. i.e.

\(LCM(x,y) \times HCF(x,y) = x \times y.\)

Now, consider the given question. we have the following information from the question stem:

LCM(x,y) = 36, GCD(x,y) = 6, and x > y.

Statement(1): x = 18. Using the above-mentioned formula, we can easily compute the value of y. Hence, sufficient to answer the question.

Statement(2): x+y = 30. We know \(xy = LCM(x,y) \times HCF(x,y) = 36 \times 6 = 216.\)

\((x-y)^2 = (x+y)^2 - 4xy\) . Hence, we can find the value of x-y. Sufficient.

Hope this helps.
Thanks.
GMAT Club Bot
Re: If x and y are positive integers such that x > y and the least common   [#permalink] 15 Oct 2018, 21:29
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If x and y are positive integers such that x > y and the least common

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