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05 Jul 2016, 12:21
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A and B are integers. The expression (A+1)(B+1) is even. What can be said about A and B?
A. They are both even numbers.
B. At least one of them is even.
C. At least one of them is odd.
D. They are both odd.
E. Nothing can be said surly on A and B
A. They are both even numbers.
B. At least one of them is even.
C. At least one of them is odd.
D. They are both odd.
E. Nothing can be said surly on A and B
Updated on: 02 May 2020, 10:26
Originally posted by BrentGMATPrepNow on 16 Aug 2016, 16:28.
Last edited by BrentGMATPrepNow on 02 May 2020, 10:26, edited 1 time in total.
Last edited by BrentGMATPrepNow on 02 May 2020, 10:26, edited 1 time in total.
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Bunuel
A and B are integers. The expression (A+1)(B+1) is even. What can be said about A and B?
A. They are both even numbers.
B. At least one of them is even.
C. At least one of them is odd.
D. They are both odd.
E. Nothing can be said surly on A and B
A. They are both even numbers.
B. At least one of them is even.
C. At least one of them is odd.
D. They are both odd.
E. Nothing can be said surly on A and B
Another approach is to systematically test all 4 possible cases:
case a: A is EVEN and B is EVEN
The expression (A+1)(B+1) becomes (EVEN+1)(EVEN+1) = (ODD)(ODD) = ODD
case b: A is EVEN and B is ODD
The expression (A+1)(B+1) becomes (EVEN+1)(ODD+1) = (ODD)(EVEN) = EVEN
case c: A is ODD and B is EVEN
The expression (A+1)(B+1) becomes (ODD +1)(EVEN+1) = (EVEN)(ODD) = EVEN
case d: A is ODD and B is ODD
The expression (A+1)(B+1) becomes (ODD +1)(ODD+1) = (EVEN)(EVEN) = EVEN
Since we're told that (A+1)(B+1) is even, we can rule out case a.
So, cases b, c and d are all possible.
Now check the answer choices:
A. They are both even numbers. Case d says otherwise. ELIMINATE A
B. At least one of them is even. Case d says otherwise. ELIMINATE B
C. At least one of them is odd. Yes. All all 3 possible cases, at least one value is ODD
Answer: C
General Discussion
05 Jul 2016, 13:20
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Odd x Odd = Odd
Odd x Even = Even
Even x Even = Even
To fulfill condition Either (A+1) or (B+1) needs to be Even
So either A or B needs to be odd
Or Atleast one of them is odd.
Ans C. At least one of them is odd.
Good luck
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Odd x Even = Even
Even x Even = Even
To fulfill condition Either (A+1) or (B+1) needs to be Even
So either A or B needs to be odd
Or Atleast one of them is odd.
Ans C. At least one of them is odd.
Good luck
=========================================================================================
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"If this post helps you on your GMAT journey, drop a +1 Kudo "
