If A, B, C are three integers and AB+C is even; which of the following must be true?
A)A+C is even
B)B+C is even
C)ABC is even
1) Only C
2) Both A and B
3) Both B and C
4) All of them
5) None of them
The OA is the option E.
I don't know how to solve this PS question. Experts I need your help. I'd be thankful.
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If A,B,C are three integers and AB+C is even . . . .
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elias.latour.apex
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To make things easy, let us assume that our odd numbers are 1 and that our even numbers are 2.
AB+C is even.
So what if C is 1? Then AB must also be odd. In other words, all three numbers must be 1 (odd).
What if C is 2? Then AB must also be even. So AB must equal 2 or 4.
So these are our options:
1) 1,1,1
2) 2,1,2
3) 1,2,2
4) 2,2,2
The first answer suggests that A+C must be even. But this is proved false by scenario 3.
The second answer suggests that B+C must be even. But this is proved false by scenario 2.
The third answer suggests that ABC must be even. But this is proved false by scenario 1.
Thus, (E) must be the best answer.
AB+C is even.
So what if C is 1? Then AB must also be odd. In other words, all three numbers must be 1 (odd).
What if C is 2? Then AB must also be even. So AB must equal 2 or 4.
So these are our options:
1) 1,1,1
2) 2,1,2
3) 1,2,2
4) 2,2,2
The first answer suggests that A+C must be even. But this is proved false by scenario 3.
The second answer suggests that B+C must be even. But this is proved false by scenario 2.
The third answer suggests that ABC must be even. But this is proved false by scenario 1.
Thus, (E) must be the best answer.
Elias Latour
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Hi VJesus12,
We're told that A, B, C are all integers and (A)(B)+C is EVEN. We're asked which of the following MUST be true (meaning "which of these things is ALWAYS TRUE no matter how many different examples we come up with?"). This question can be answered by TESTing VALUES or using Number Property Rules.
To start, since (A)(B) + C = an EVEN, there are a limited number of possible 'combinations' of Odds and Evens that will 'fit' here:
(Even)(Even) + (Even) = Even
(Even)(Odd) + (Even) = Even
(Odd)(Even) + (Even) = Even
(Odd)(Odd) + (Odd) = Even
A)A+C is even
In the 3rd example, this is NOT true. Eliminate Answer B and Answer D.
B)B+C is even
In the 2nd example, this is NOT true. Eliminate Answer C.
C)ABC is even
In the 4th example, this is NOT true. Eliminate Answer A.
There's only one answer remaining...
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
We're told that A, B, C are all integers and (A)(B)+C is EVEN. We're asked which of the following MUST be true (meaning "which of these things is ALWAYS TRUE no matter how many different examples we come up with?"). This question can be answered by TESTing VALUES or using Number Property Rules.
To start, since (A)(B) + C = an EVEN, there are a limited number of possible 'combinations' of Odds and Evens that will 'fit' here:
(Even)(Even) + (Even) = Even
(Even)(Odd) + (Even) = Even
(Odd)(Even) + (Even) = Even
(Odd)(Odd) + (Odd) = Even
A)A+C is even
In the 3rd example, this is NOT true. Eliminate Answer B and Answer D.
B)B+C is even
In the 2nd example, this is NOT true. Eliminate Answer C.
C)ABC is even
In the 4th example, this is NOT true. Eliminate Answer A.
There's only one answer remaining...
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
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Scott@TargetTestPrep
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Since AB + C is even, we can have:VJesus12 wrote:If A, B, C are three integers and AB+C is even; which of the following must be true?
A)A+C is even
B)B+C is even
C)ABC is even
1) Only C
2) Both A and B
3) Both B and C
4) All of them
5) None of them
Case 1: A, B, and C are all odd,
or
Case 2: A, B, and C are all even,
or
Case 3: A is odd and B and C are even,
or
Case 4: B is odd and A and C are even.
Now let's analyze the three given statements.
If it's case 3, A + C is odd and thus it's not even.
If it's case 4, B + C is odd and thus it's not even.
If it's case 1, ABC is odd and thus it's not even.
Thus, none of the scenarios have to be true.
Answer: E
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