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15 Jul 2019, 01:04
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vinayakvaish
Joined: 29 May 2018
Last visit: 19 Oct 2020
Posts: 93
Given Kudos: 52
Location: India
Schools: Marshall '22 (A$) IIMA PGPX "21 (D) Duke '22 (D) IIMB EPGP "21 (A) McCombs '22 (A) IIMC MBAEx "21 (WD) Georgia Tech '22 (A$) Johnson '22 (WD)
GMAT 1: 700 Q48 V38
GMAT 2: 720 Q49 V39
GPA: 4
Schools: Marshall '22 (A$) IIMA PGPX "21 (D) Duke '22 (D) IIMB EPGP "21 (A) McCombs '22 (A) IIMC MBAEx "21 (WD) Georgia Tech '22 (A$) Johnson '22 (WD)
GMAT 2: 720 Q49 V39
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15 Jul 2019, 01:16
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Statement 1: x + y is odd will give us 2 cases:
1) x and y as integers: one has to be even, other has to be odd for sum to be odd
2) x and y as decimals: 2.5 + 0.5= 3
Insufficient
Statement 2: x-y is even
1) x and y as integers: both x and y are even or both are odd
2) x and y as decimals: 2.5-0.5= 2
insuffcient
Combined: for both to be integers if both are odd- x+y= odd is violated
if both are even- x+y=odd is violated
if one is odd, one is even- x-y=even is violated
Hence x and y have to be decimals
Answer C
Hit Kudos!!
1) x and y as integers: one has to be even, other has to be odd for sum to be odd
2) x and y as decimals: 2.5 + 0.5= 3
Insufficient
Statement 2: x-y is even
1) x and y as integers: both x and y are even or both are odd
2) x and y as decimals: 2.5-0.5= 2
insuffcient
Combined: for both to be integers if both are odd- x+y= odd is violated
if both are even- x+y=odd is violated
if one is odd, one is even- x-y=even is violated
Hence x and y have to be decimals
Answer C
Hit Kudos!!
15 Jul 2019, 07:16
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Neither Statement is sufficient alone, because x and y could be integers, or could be decimal numbers.
Using both Statements, we know x+y is an odd integer, and x-y is an even integer, so if we add x+y and x-y we must get an odd integer as our answer. So x+y+x-y = 2x is an odd integer, and x is half of an odd integer, so x is not an integer. That's what we wanted to know, so the two Statements together are sufficient and the answer is C.
Using both Statements, we know x+y is an odd integer, and x-y is an even integer, so if we add x+y and x-y we must get an odd integer as our answer. So x+y+x-y = 2x is an odd integer, and x is half of an odd integer, so x is not an integer. That's what we wanted to know, so the two Statements together are sufficient and the answer is C.
