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# If x and y are both non-zero numbers, is x < 4 < y? (1) x < y and xy

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Joined: 21 Aug 2013
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If x and y are both non-zero numbers, is x < 4 < y? (1) x < y and xy  [#permalink]

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07 Jun 2018, 04:38
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Difficulty:

85% (hard)

Question Stats:

46% (02:05) correct 54% (02:09) wrong based on 90 sessions

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If x and y are both non-zero numbers, is x < 4 < y?

(1) x < y and xy = 4.

(2) x^2 < 16 < y^2

This question is inspired by the following OG question:
https://gmatclub.com/forum/if-x-and-y-a ... 39873.html
Senior Manager
Joined: 14 Feb 2018
Posts: 377
Re: If x and y are both non-zero numbers, is x < 4 < y? (1) x < y and xy  [#permalink]

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07 Jun 2018, 04:54
According to statement 1, x<y, xy = 4.

Thus, possible values of x, y are -
x and y positive, x = 1, y = 4....Does not satisfy the inequality, so NO.

x = -4, y = -1, so YES.
Also, for fractions, the condition is satisfied.

Thus, insufficient.

Statement 2, says x^2<16<y^2.

For positive values condition is satisfied but for negative values, it won't. Thus, insufficient.

On combining, we see that x has to be less than y, and y has to be greater than 4, to satisfy the equation in statement 2.

Thus, C.

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Re: If x and y are both non-zero numbers, is x < 4 < y? (1) x < y and xy  [#permalink]

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08 Jun 2018, 18:56
amanvermagmat wrote:
If x and y are both non-zero numbers, is x < 4 < y?

(1) x < y and xy = 4.

(2) x^2 < 16 < y^2

This question is inspired by the following OG question:
https://gmatclub.com/forum/if-x-and-y-a ... 39873.html

Given, x and y are non-zero numbers.

Question stem:- x < 4 < y? (Y/N)

Statement 1, x < y and xy = 4.

when x=1, y=4; Is x < 4 < y? Ans:- No (Since x=1<4 but y=4 which not greater than 4)
When x=$$\frac{1}{2}$$, y=8; Is x < 4 < y? Ans:- Yes (Since x=$$\frac{1}{2}$$<4 & y=8>4)

Hence, St1 is not sufficient.

Statement 2, $$x^2$$ < 16 < $$y^2$$
Or, |x| < 4 < |y|-------------------(2)

Hence, St2 is not sufficient.

(1)+(2) combining,

we have from st1, x<y.................(1)
from (2), -4<x<4 (except zero), y>4 and y< -4----(3)
from (1) and (3), we have x<4<y.

Hence sufficient.

Ans. C
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Re: If x and y are both non-zero numbers, is x < 4 < y? (1) x < y and xy  [#permalink]

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05 Jun 2020, 12:00
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Re: If x and y are both non-zero numbers, is x < 4 < y? (1) x < y and xy   [#permalink] 05 Jun 2020, 12:00