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

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chetan2u
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If x, y and x/y are integers, is x < 0? (1) x < |y| (2) |x| = |y| [#permalink] New post   04 Sep 2021, 21:22
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If x, y and \(\frac{x}{y}\) are integers, is x < 0 ?

(1) x < |y|
(2) |x| = |y|
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chetan2u
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If x, y and x/y are integers, is x < 0? (1) x < |y| (2) |x| = |y| [#permalink] New post   09 Sep 2021, 05:18
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chetan2u wrote:
If x, y and \(\frac{x}{y}\) are integers, is x < 0 ?

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


\(\frac{x}{y}\) 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
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Crytiocanalyst
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Re: If x, y and x/y are integers, is x < 0? (1) x < |y| (2) |x| = |y| [#permalink] New post   04 Sep 2021, 23:00
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chetan2u wrote:
If x, y and \(\frac{x}{y}\) are integers, is x<0?

(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
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Re: If x, y and x/y are integers, is x < 0? (1) x < |y| (2) |x| = |y| [#permalink] New post   08 Sep 2021, 21:47
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chetan2u wrote:
If x, y and \(\frac{x}{y}\) are integers, is x < 0 ?

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



(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
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Re: If x, y and x/y are integers, is x < 0? (1) x < |y| (2) |x| = |y| [#permalink] New post   08 Sep 2021, 22:14
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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.
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Re: If x, y and x/y are integers, is x < 0? (1) x < |y| (2) |x| = |y| [#permalink]
08 Sep 2021, 22:14
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