Hello M7MBA.

Let's take a look at your question.

We have two numbers which product is 36, that is to say, $$a\cdot b=36.$$ The options for a and b are:

a=1, b=36 --------a+b=37.
a=2, b=18 --------a+b=20.
a=3, b=12 --------a+b=15.
a=4, b=9 ----------a+b=13.
a=6, b=6-----------a+b=12.
b=9, a=4-----------a+b=13.
.....

According to the list above, the minimum value of a+b is 12.

Hence, the correct answer is the option E.

I hope it helps.

Feel free to ask me again if you have a doubt.

Regards.

M7MBA wrote:Which one of the following is the minimum value of the sum of two integers whose product is 36?
(A) 37
(B) 20
(C) 15
(D) 13
(E) 12

Factor pairs of 36:
1*36
2*18
4*9
6*6

The smallest sum is yielded by the option in blue:
6+6 = 12.

The correct answer is E.

For any fixed product xy, the least possible value for x+y occurs when x=y.
If xy = 16, where x and y are positive integers, we get the following options:
x=1 and y=16, with the result that x+y = 1+16 = 17.
x=2 and y=8, with the result that x+y = 2+8 = 16.
x=y=4, with the result that x+y = 4+4 = 16.
The least possible value for x+y is yielded when x=y.

For any fixed sum x+y, the greatest possible value for xy occurs when x=y.
If x+y=10, where x and y are positive integers, we get the following options:
x=1 and y=9, with the result that xy = 1*9 = 9.
x=2 and y=8 with the result that xy = 2*8 = 16.
x=3 and y=7, with the result that xy = 3*7 = 21.
x=4 and y=6, with the result that xy = 4*6 = 24.
x=y=5, with the result that xy = 5*5 = 25.
The greatest possible value for xy is yielded when x=y.

Factors of 36 includes: (1,36), (2,18), (3,12), (4,9), and (6,6)
The pair that gives the minimum sum is
4+9=13 that is if we require distinct integers o
and
6+6 =12 if we don't require distinct integer

Therefore, we will go for the option with the overall minimum value which is 12. The correct option is e