SOLUTION: Which of the following CANNOT be the sum of two integers that have a product of 30? a) 31 b) 17 c) -11 d) –21

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Question 275104: Which of the following CANNOT be the sum of two integers that have a product of 30?
a) 31 b) 17 c) -11 d) –21

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
answer is selection c (-21)

here's why:

your product is 30.

this means that a*b must = 30

the possible factors are:

30*1
15*2
10*3
6*5

the sum of these are:

31
17
13
11

they can be either both plus or both minus and the product will be positive.

so the sum of these can be:
+/- 31
+/- 17
+/- 13
+/- 11

31, 17, and 11 are part of your selections so they're good.

the only one that is not good is 21.

if you look at all the numbers that can add up to 21, you will see:

1 + 20
2 + 19
3 + 18
4 + 17
5 + 16
6 + 15
7 + 14
8 + 13
9 + 12
10 + 11

none of the products of these numbers equals 30.

your answer is selection d (-21).