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14 Jul 2017, 00:17
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A
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Difficulty:
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26%
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If x is an odd integer, is y an odd integer?
(1) The average of x and y is an integer.
(2) The average of x, y, and (y + 1) is an integer.
(1) The average of x and y is an integer.
(2) The average of x, y, and (y + 1) is an integer.
14 Jul 2017, 01:02
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Bunuel
If x is an odd integer, is y an odd integer?
(1) The average of x and y is an integer.
(2) The average of x, y, and (y + 1) is an integer.
(1) The average of x and y is an integer.
(2) The average of x, y, and (y + 1) is an integer.
Given : x is an odd integer
DS: y is an odd integer ?
Let x = 2n+1
y = 2m or 2m+1
Statement 1 : (2n+1)
Average of x and y (y even) = ((2n+1) + 2m) /2 = Not an integer
Average of x and y (y odd) = ((2n+1)+(2m+1))/2 = An integer
SUFFICIENT
Statement 2: average of x, y and y+1 ( y even) = (2n+1+2m + 2m +1)/3 = (2n +4m+2)/3 THis may be an integer or many be not.
average of x, y and y+1 ( y odd) = (2n+1+2m+1 + 2m +2)/3 = (2n +4m+4)/3 This may be an integer or many be not.
NOT SUFFICIENT
Answer A
14 Jul 2017, 01:03
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Bunuel
If x is an odd integer, is y an odd integer?
(1) The average of x and y is an integer.
(2) The average of x, y, and (y + 1) is an integer.
(1) The average of x and y is an integer.
(2) The average of x, y, and (y + 1) is an integer.
Average = Sum/No. of terms
1) (x+y)/2 = integer
If x = odd
y = has to be odd, otherwise the average will not be an integer.
x = 1
y = 1
Avg. = 1
x = 3
y = 3
Avg. 3
x = 3
y = 2
avg. = 2.5 (Not allowed)
Sufficient.
2) (x + y + y+1)/3 is an integer
x = 5
y = 3
y + 1 = 4
Avg. = 12/3 = 4
y = odd
x = 1
y = 2
y+1 = 3
Avg. = 6/3 = 2
Y = even
Insufficient.
A is the answer.
