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19 Aug 2016, 03:07
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
77% (01:17) correct
23%
(01:44)
wrong
based on 320
sessions
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Not Attempted Yet
x and y are positive integers. If xy + x is odd, then which of the following must be even?
A. x
B. y
C. x + y
D. xy − x
E. x^2 − y
A. x
B. y
C. x + y
D. xy − x
E. x^2 − y
Updated on: 02 May 2020, 10:20
Originally posted by BrentGMATPrepNow on 19 Aug 2016, 06:05.
Last edited by BrentGMATPrepNow on 02 May 2020, 10:20, edited 1 time in total.
Last edited by BrentGMATPrepNow on 02 May 2020, 10:20, edited 1 time in total.
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Bunuel
x and y are positive integers. If xy + x is odd, then which of the following must be even?
A. x
B. y
C. x + y
D. xy − x
E. x^2 − y
A. x
B. y
C. x + y
D. xy − x
E. x^2 − y
Some important rules regarding the products of evens and odds:
1. (ODD)(ODD) = ODD
2. (ODD)(EVEN) = EVEN
3. (EVEN)(EVEN) = EVEN
4. ODD +/- ODD = EVEN
5. ODD +/- EVEN = ODD
6. EVEN +/- EVEN = EVEN
As we can see from #1, IF the product of two integers is ODD, then the two integers must both be odd.
Given: xy + x is ODD
If we FACTOR xy + x, we get x(y + 1)
So, we're told that x(y + 1) is ODD
From rule #1 above, we can conclude that x is ODD and (y + 1) is ODD
If (y + 1) is odd, then we can be certain that y is EVEN
Now check the answer choices:
A. x = ODD
B. y = EVEN (done!!)
C. x + y = ODD + EVEN = ODD
D. xy − x = (ODD)(EVEN) - ODD = EVEN - ODD = ODD
E. x^2 − y = (ODD)(ODD) - EVEN = ODD - EVEN = ODD
Answer:
General Discussion
19 Aug 2016, 04:15
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Bunuel
x and y are positive integers. If xy + x is odd, then which of the following must be even?
A. x
B. y
C. x + y
D. xy − x
E. x^2 − y
A. x
B. y
C. x + y
D. xy − x
E. x^2 − y
x y xy + x
1 2 3 odd
2 1 4 Even case
2 3 5 Even
5 2 15 odd
3 3 12 even
IMO option B is correct.
OA please..let me know if I am missing anything...
