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

Question

(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

Pritishd · Accepted Answer

Candyfloss1 ,  DQ7777777 ,  jojo95

I want to clear the confusion that a lot of the folks have around options D and E. The question is a must be true question, hence we need to read D and E accordingly.

(E) if one integer is positive, the other is negative 
Read this as - if one is positive then should the other one  MUST  be negative?

Let's say the first integer is 1 (positive). Now ask the question, should the other one MUST be negative? No, because the other integer can be 5 (positive) and the sum can still be 6
Hence, it is not mandatory for the second integer to negative if the first integer is positive.

(D) if one integer is negative, the other is positive 
Read this as - if one is negative then should the other one  MUST  be positive?

Let's say the first integer is -1 (negative). Now ask the question, should the other one MUST be positive? Yes, because the other integer has to be 7 (positive) for the sum to be 6. Similarly, if the first integer is -2 (negative) then the second integer has to be 8 (positive). Try to fit a second negative integer after picking a first negative integer and get the sum as 6. You will not be able to find such a combination

BrentGMATPrepNow · Answer

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

BrentGMATPrepNow · Answer

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

HKD1710 · Answer

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)

ScottTargetTestPrep · Answer

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

Candyfloss1 · Answer

Hello everyone,

I agree A,B,C does not have to necessarily be true. However, I am having difficulty understanding why D and E are not the probable answer.

(D) if one integer is negative, the other is positive: This could have been (-1) + 7= 6
(E) if one integer is positive, the other is negative : This could have been 7 + (-1)= 6

I will appreciate a clarification.

Thank you

DQ7777777 · Answer

((Hello everyone,

I agree A,B,C does not have to necessarily be true. However, I am having difficulty understanding why D and E are not the probable answer.

(D) if one integer is negative, the other is positive: This could have been (-1) + 7= 6
(E) if one integer is positive, the other is negative : This could have been 7 + (-1)= 6

I will appreciate a clarification.

Thank you))

^Same question! can someone please clarify?

jojo95 · Answer

Can someone please clarify why D is correct but E isn't...aren't they basically the same?

What makes them different?

Thank you in advance!

riyagoyal · Answer

In Option D it says that if one of the number is negative, eg. -1 then the other has to be positive to get the sum of positive 6
However, in case of option E, if one number is positive then the other number need not be negative, eg. a=4 then b=2 thus a+b=6. Hence option E is wrong

TheNightKing · Answer

(A) both integers are even - 3+3
(B) both integers are odd - 4+2
(C) both integers are positive 18-12
(D) if one integer is negative, the other is positive - Yes. If -12 then 18. If -24 then 30. Seems to be working.
(E) if one integer is positive, the other is negative - No. 4 then 2. If one is positive then other doesn't have to be negative.

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

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