If x is an odd integer, is y an odd integer?

Question

(1) The average of x and y is an integer.
(2) The average of x, y, and (y + 1) is an integer.

shashankism · Answer

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

akshayk · Answer

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.

Luckisnoexcuse · Answer

given x is odd

(1) x+y is 2k (even integer)

x+y can only be even when either both x & y are odd or both are even .. in this case x is odd and hence y is also odd ..Sufficient (y can only take integer values for the average to be integer)

(2) x, y, y+1 is 3k (even or odd integer)

if k is odd then 3k is odd

y is an integer then y+y+1 has to be even which is not possible since both are consecutive and their sum would be odd
y is even then y+y+1 will be odd
y is odd then y+y+1 will be odd 
but we need y+y+1 to be even

if k is even then 3k is even
y is an integer then y+y+1 has to be odd which can be irrespective of value of y to be even or odd........Not sufficient

Hence A

If x is an odd integer, is y an odd integer?

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GMAT Data Sufficiency (DS) Questions

If x is an odd integer, is y an odd integer?

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