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If the sum of two integers is 6, then it must be true that

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If the sum of two integers is 6, then it must be true that [#permalink]

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New post 23 Nov 2015, 12:28
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If the sum of two integers is 6, then it must be true that

(A) both integers are even
(B) both integers are odd
(C) both integers are positive
(D) if one integer is negative, the other is positive
(E) if one integer is positive, the other is negative

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Re: If the sum of two integers is 6, then it must be true that [#permalink]

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New post 23 Nov 2015, 12:31
Bunuel wrote:
If the sum of two integers is 6, then it must be true that

(A) both integers are even
(B) both integers are odd
(C) both integers are positive
(D) if one integer is negative, the other is positive
(E) if one integer is positive, the other is negative


If one number is negative, then the ONLY way to get a sum of 6 is for the other number to be positive.
So, D must be true.

Cheers,
Brent
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Re: If the sum of two integers is 6, then it must be true that [#permalink]

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New post 23 Nov 2015, 12:35
Bunuel wrote:
If the sum of two integers is 6, then it must be true that

(A) both integers are even
(B) both integers are odd
(C) both integers are positive
(D) if one integer is negative, the other is positive
(E) if one integer is positive, the other is negative


Another approach.

We're asked to find a statement that MUST be true. So, if we can find a case where a statement is false, we can ELIMINATE that answer choice.

(A) both integers are even : it could be the case that the numbers are 1 and 5. ELIMINATE A
(B) both integers are odd : it could be the case that the numbers are 2 and 4. ELIMINATE B
(C) both integers are positive : it could be the case that the numbers are -1 and 7. ELIMINATE C
(D) if one integer is negative, the other is positive : Can't think of a counterexample so KEEP D for now
(E) if one integer is positive, the other is negative : it could be the case that the numbers are 1 and 5. ELIMINATE E

By the process of elimination, the correct answer is D

Cheers,
Brent
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Re: If the sum of two integers is 6, then it must be true that [#permalink]

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New post 24 Nov 2015, 12:23
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In a must be true question my approach to find the right answer is to negate each choice. The correct choice would not be negated.

Suppose x & y are two integers such that x + y = 6

(A) both integers are even - Wrong
Can we have x + y = 6 when both are not even? Yes. (1+5=6)

(B) both integers are odd - Wrong
Can we have x + y = 6 when both are not odd? Yes. (2+4=6)

(C) both integers are positive - Wrong
Can we have x + y = 6 when only one is positive? Yes (7 + (-1) = 6)

(D) if one integer is negative, the other is positive - Correct
Can we have x + y = 6 when x is negative and y is also negative? No. ((-1) + 7 = 6), here 7 can not be -ve.

(E) if one integer is positive, the other is negative - wrong
Can we have x + y = 6 when x is positive and y is NOT negative? Yes. (7 + (-1) = 6)
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Re: If the sum of two integers is 6, then it must be true that [#permalink]

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New post 27 Jan 2017, 10:35
Bunuel wrote:
If the sum of two integers is 6, then it must be true that

(A) both integers are even
(B) both integers are odd
(C) both integers are positive
(D) if one integer is negative, the other is positive
(E) if one integer is positive, the other is negative


Since the sum of two integers is 6, the two integers can be either both even (e.g., 4 and 2) or both odd (e.g., 1 and 5). So, answer choices A and B DO NOT HAVE to be true. Let’s test the remaining answer choices:

C) both integers are positive

Both integers DO NOT HAVE to be positive. For instance, one integer could be 8 and the other -2.

D) if one integer is negative, the other is positive

Answer choice D is correct. Since two negative integers cannot sum to 6, if one of the integers is negative, the other MUST BE POSITIVE.

Answer: D
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Re: If the sum of two integers is 6, then it must be true that [#permalink]

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Re: If the sum of two integers is 6, then it must be true that   [#permalink] 30 Jun 2018, 17:30
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