Are x and y consecutive integers? (1) x + y = 15 (2) x – y = 3

Question

Are x and y consecutive integers?

(1) x + y = 15
(2) x – y = 3

CrackverbalGMAT · Answer

Statement 1:   x + y = 15

x = 7, y = 8; x + y = 15. YES, x and y are consecutive integers.

x = 6, y = 9; x + y = 15. NO, x and y are not consecutive integers

Therefore Statement 1 Alone is Insufficient  . Answer options could be B, C or E

Statement 2:   x - y = 3

The difference of 2 consecutive integers has to be 1. Therefore they are not consecutive integers.

Therefore Statement 2 Alone is Sufficient  .

Option B

Arun Kumar

Gknight5603 · Answer

but i think that it is not mentioned that both x and y are integers.
even 3.5 and 0.5 will satisfy the second statement.

Posted from my mobile device

CrackverbalGMAT · Answer

Hello aish5063

The questions asks if x and y are consecutive integers.

From statement B, whatever value we input, to get a difference of 3 means they are not  consecutive integers . 3.5 and 0.5 may satisfy the condition x - y = 3, but they are not consecutive integers.

chetan2u · Answer

so what do we have to prove => 
First |x-y|=1, and if answer is yes for |x-y|=1, then whether x and y are integers.

(1) x + y = 15
7+8 = 15...Yes
5+10=15...No

(2) x – y = 3
x and y may or may not be integers, but  |x-y|
eq{1} .
So answer is always NO, irrespective of values of x and y.
Suff

B

bond001 · Answer

statement 1 not sufficient 
x and y could be nonintegers we do not know whether they are integer or not

statement 2 sufficient 
difference between a consecutive integer is 1 
since the difference is 3 we can say they are not a consecutive integer
over here if the difference was 1 between x and y we do not know whether they are integer or not 
but our question asked over here is  'Are x and y consecutive integers'  
again for x and y to be consecutive the minimum condition it needs to satisfy is that the difference is 1 this is the trick in this sum.

Hit kudos if you like the explanation

Are x and y consecutive integers? (1) x + y = 15 (2) x – y = 3

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