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

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

Answer: B.

Kudos please if you like my explanation!

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.
Answer B.

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

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.

Answer: B

Since the product of x and y is equal to 165, we could prime factorise 165 to find out its constituent factors.
After doing this, we can find out the ways in which 165 can be expressed as a product of two positive integers. Of all the ways, we take the way where x is as small as possible and y is as large as possible, so that we can minimize the difference, x – y.

Upon prime factorisation, 165 = 3 * 5 * 11.

Number of factors of 165 = (1+1) (1+1) (1+1) = 2 * 2 * 2 = 8

Number of ways of expressing 165 as a product of 2 of its factors =\(\frac{ 8 }{ 2}\) = 4

These 4 ways are:

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

Of these, the combination of 11 and 15 is the one where the numbers are very close to each other. Since x > y, x = 15 and y = 11.
Therefore, least possible value of x – y = 15 – 11 = 4.

The correct answer option is B.

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