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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:37) correct
32%
(01:37)
wrong
based on 77
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If x is an integer, is y an integer?
(1) The average (arithmetic mean) of x and y is an integer.
(2) The average (arithmetic mean) of x, y, and y + 4 is x.
(1) The average (arithmetic mean) of x and y is an integer.
(2) The average (arithmetic mean) of x, y, and y + 4 is x.
15 Mar 2011, 19:16
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banksy
8. (MH) If x is an integer, is y an integer?
(1) The average (arithmetic mean) of x and y is an integer.
(2) The average (arithmetic mean) of x, y, and y + 4 is x.
(1) The average (arithmetic mean) of x and y is an integer.
(2) The average (arithmetic mean) of x, y, and y + 4 is x.
1. (x + y)/2 is an integer
i.e x + y => integer
Therefore Y is an integer since x is an integer and X+Y is also an integer
eg . x+y=5 IF x=3 then y will be 2 (both integer)
Similarly if x=2.5 y will be 2.5 (both non integer) sufficient
2. x+y+y+4=3x
x-y=4
x is an integer (x-y) is an integer .... therefore y must also be an integer sufficient
15 Mar 2011, 19:36
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I think the OA is wrong, it should be D.
From (1), (x+y)/2 = k, where k is an integer, so y = 2k - x, an integer - integer = integer, so (1) is sufficient.
From (2) (x + y + y + 4)/3 = x => x + 2y + 4 = 3x => 2x-2y = 4 => x-y = 2, so y = x + 2, an integer + integer = integer, so (2) is sufficient.
Hence the answer is D.
From (1), (x+y)/2 = k, where k is an integer, so y = 2k - x, an integer - integer = integer, so (1) is sufficient.
From (2) (x + y + y + 4)/3 = x => x + 2y + 4 = 3x => 2x-2y = 4 => x-y = 2, so y = x + 2, an integer + integer = integer, so (2) is sufficient.
Hence the answer is D.
