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# If xy = 165, where x and y are positive integers and x> y, what is the

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If xy = 165, where x and y are positive integers and x> y, what is the  [#permalink]

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06 Oct 2017, 04:40
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If xy = 165, where x and y are positive integers and x > y, what is the least possible value of x – y ?

A. 2
B. 4
C. 8
D. 15
E. 28

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Re: If xy = 165, where x and y are positive integers and x> y, what is the  [#permalink]

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06 Oct 2017, 04:49
If xy = 165, where x and y are positive integers and x > y, what is the least possible value of x – y ?

x and y are integers and xy =165
xy =165= 5*3*11 15*11 = x* y

Least possible value of x-y = 15-11 =4

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Re: If xy = 165, where x and y are positive integers and x> y, what is the  [#permalink]

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07 Oct 2017, 10:50
Bunuel wrote:
If xy = 165, where x and y are positive integers and x > y, what is the least possible value of x – y ?

A. 2
B. 4
C. 8
D. 15
E. 28

xy = 165
= 11*15
To have the least possible value of x-y, difference between x and y should be minimum
x= 15 and y= 11
x-y = 4

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If xy = 165, where x and y are positive integers and x> y, what is the  [#permalink]

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08 Oct 2017, 05:31
xy=165
Factorize xy=165
xy= 3*5*11
xy= 15*11
As x>y
Thus x=15 and y=11
Least possible value of x-y= 4

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Re: If xy = 165, where x and y are positive integers and x> y, what is the  [#permalink]

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09 Oct 2017, 10:12
xy=165
Factorising 165 gives 1x3x5x11=165
We have to find the least value of x-y and x>y
Therefore observe that, x can be (3x5)=15 and y can be 11, such that difference will be 4, which is the minimum.
Any other values of x and y will not give the minimum difference.
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Re: If xy = 165, where x and y are positive integers and x> y, what is the  [#permalink]

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09 Oct 2017, 10:29
for min value of x-y
the value of roots have to be close to mean of roots or half of the value(165)
165= 5*3*11
= 15*11
x-y =15-11=4
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Re: If xy = 165, where x and y are positive integers and x> y, what is the  [#permalink]

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12 Oct 2017, 18:01
Bunuel wrote:
If xy = 165, where x and y are positive integers and x > y, what is the least possible value of x – y ?

A. 2
B. 4
C. 8
D. 15
E. 28

Since xy = 165 and x and y are positive integers, x and y must be factors of 165. Notice that:

165 = 1 * 165 = 3 * 55 = 5 * 33 = 11 * 15

Since x > y and we want the least possible value of x – y, we want the two factors to be as close as possible. The two closest factors are 11 and 15; thus, x = 15 and y = 11, and x - y will then be 4.

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Re: If xy = 165, where x and y are positive integers and x> y, what is the &nbs [#permalink] 12 Oct 2017, 18:01
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