If x, y and x/y are integers, is x

Question

If x, y and  \frac{x}{y}  are integers, is x < 0 ?

(1) x < |y|
(2) |x| = |y|

chetan2u · Accepted Answer

\frac{x}{y}  will be an integer only when x=0 or x is a multiple of y, irrespective of the signs. 
We can write these mathematically as
1) x is 0 and y could be anything. 
2) x > 0 and  |y|\leq x  or for that matter  |y|\leq |x| 
3) x < 0 and  |y|\leq |x|

(1) x < |y|
Case (2) is out. 
x could be 0 or less than 0.
However, case 1 and case 3 possible. 
Insufficient

(2) |x| = |y|
Case 1 is out. 
However, case 2 and case 3 possible. 
Insufficient

Combined 
Only case 3 left. 
x<0.
Sufficient

C

Crytiocanalyst · Answer

(1) x<|y|
x if positive has to be greater than y for x/y to be integer which cannot be satisfied by the given statement

only way the inequality is satisfied for x -ve and y positive and same values forx/y to be integer

(2) |x|=|y|
for x=10 and y=10 x>0 answer no 
for x=-10 and y=10 x<0 answer yes 
Clearly insufficient

Therefore IMO A

stne · Answer

(1)  x < |y|

x  can be  0  and  y =1  , ans NO.

x can be  -1  and  y =1  , ans yes

(2)  |x| = |y|

x =y =1  , ans is NO
  x=-1 , y=1  , ans is yes

1+2

X can only be  -ve

IMO ans should be c

Ozzy11100 · Answer

chetan2u

Are you certain that  OA: A is correct?

Correct me if I'm wrong, but there are scenarios which satisfy ALL conditions in which  x = 0, AND in which x = neg int .

Surely we need STATEMENT 2 and STATEMENT 2 TOGETHER in order to rule out x = 0, right?

Please clarify my misunderstanding.

If x, y and x/y are integers, is x < 0? (1) x < |y| (2) |x| = |y|

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