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Bunuel
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Bunuel
The product of two integers is 40. Which of the following CANNOT be the sum of these two integers?

(A) -41

(B) -14

(C) 3

(D) 13

(E) 14
Prime factorization of 40 = 2^3 * 5
(A) -41 = -40 - 1

(B) -14 = -10 - 4

(C) 3 - Correct

(D) 13 = 8+5

(E) 14 = 10+4

Answer C
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IMO C

xy=40 = 1*40 = 2*20 = 4*10 = 5*8

only C can't be the sum to any of the above
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Bunuel
The product of two integers is 40. Which of the following CANNOT be the sum of these two integers?

(A) -41

(B) -14

(C) 3

(D) 13

(E) 14

Let’s list the possible number combinations that can multiply to 40.

1, 40 or -1, -40

2, 20 or -2, -20

4, 10 or -4, -10

5, 8 or -5, -8

We see that the possible sums from the above pairs are:

41, -41, 22, -22, 14, -14, 13 and -13

From the given answer choices, the only sum that is not possible is 3.

Answer: C
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Bunuel
The product of two integers is 40. Which of the following CANNOT be the sum of these two integers?

(A) -41

(B) -14

(C) 3

(D) 13

(E) 14

Let's examine PAIRS of values with a product of 40

-1 and -40 add to -41 ELIMINATE A
-2 and -20 add to -22 no options to eliminate
-4 and -10 add to -14 ELIMINATE B
4 and 10 add to 14 ELIMINATE E
5 and 8 add to 13 ELIMINATE D

By the process of elimination, the correct answer is C

Cheers,
Brent
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