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# The product of two integers is 40. Which of the following CANNOT be

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The product of two integers is 40. Which of the following CANNOT be [#permalink]

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06 Nov 2017, 00:31
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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
[Reveal] Spoiler: OA

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Re: The product of two integers is 40. Which of the following CANNOT be [#permalink]

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06 Nov 2017, 00:37
The factors of 40 are 1,2,4,8, 5,40,10. Negative as well as postive

So 8+5 = 13 is a sum
-40-1=-41 is a sum
10+4= 14 is a sum
-10-4 = -14 is a sum

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Re: The product of two integers is 40. Which of the following CANNOT be [#permalink]

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06 Nov 2017, 04:25
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The product of the two integers is $$40(2^3*5)$$
The various combination of integers can be 1*40,2*20,4*10,5*8.
Since we have a positive integer, it can be formed as a product
of two positive or negative integers.

The sum of these two integers could be -41,-22,-14,-13,13,14,22,41
Only Option C(3) CANNOT be sum of the two numbers!
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Re: The product of two integers is 40. Which of the following CANNOT be [#permalink]

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06 Nov 2017, 18:47
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Bunuel wrote:
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

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Re: The product of two integers is 40. Which of the following CANNOT be [#permalink]

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07 Nov 2017, 00:40
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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Re: The product of two integers is 40. Which of the following CANNOT be [#permalink]

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08 Nov 2017, 17:23
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Expert's post
Bunuel wrote:
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.

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Re: The product of two integers is 40. Which of the following CANNOT be   [#permalink] 08 Nov 2017, 17:23
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