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

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Carcass
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If the sum of two integers is 6, then it must be true that [#permalink] New post   05 Jan 2021, 07:36
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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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GreenlightTestPrep
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Re: If the sum of two integers is 6, then it must be true that [#permalink] New post   05 Jan 2021, 09:37
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Carcass 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


Kudos for the right answer and explanation


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] New post   05 Jan 2021, 09:38
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Carcass 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


Kudos for the right answer and explanation

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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mrk9414
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Re: If the sum of two integers is 6, then it must be true that [#permalink] New post   19 Aug 2021, 07:52
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GreenlightTestPrep wrote:
Carcass 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


Kudos for the right answer and explanation

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



what is the difference between option D and E ?
I don't see any difference between them .
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If the sum of two integers is 6, then it must be true that [#permalink] New post   19 Aug 2021, 08:57
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mrk9414 wrote:
what is the difference between option D and E ?
I don't see any difference between them .


Many people will view D and E as identical, but they're aren't.
The (incorrect) idea is that the conditional statement "If A is true then B must also be true" implies a second conditional statement that says "If B is true then A must also be true"
Here's a counter-example to show why this is not true:

"If an animal is a cow, then that animal must have 2 eyes"
I think we all agree on the truth of this conditional.
However, does this also mean the following conditional must also be true: "If an animal has 2 eyes, then that animal must be a cow"?
No.
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Re: If the sum of two integers is 6, then it must be true that [#permalink] New post   10 Feb 2023, 03:17
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