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# Is x < 0? (1) x^2 - x > 0 (2) |x| < 1

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Manager
Joined: 19 Nov 2017
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Is x < 0? (1) x^2 - x > 0 (2) |x| < 1  [#permalink]

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Updated on: 29 Jul 2018, 01:21
3
00:00

Difficulty:

65% (hard)

Question Stats:

47% (01:10) correct 53% (01:08) wrong based on 51 sessions

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Is $$x<0?$$ ?

(1) $$x^2 - x > 0$$

(2) $$|x| < 1$$

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Vaibhav

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Originally posted by vaibhav1221 on 28 Jul 2018, 21:18.
Last edited by Bunuel on 29 Jul 2018, 01:21, edited 2 times in total.
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Joined: 28 Jul 2018
Posts: 4
Re: Is x < 0? (1) x^2 - x > 0 (2) |x| < 1  [#permalink]

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28 Jul 2018, 21:57
1
Idk what I'm doing wrong:
We need to know if X is (-) or (+)
(1) is satisfied for all numbers outside of the range 0:1 (not including 0 and 1)
(2) is satisfied for all numbers inside range -1:1 (not including -1 and 1)

So if you take (1) and (2) together, X must be a negative number between -1:0
Manager
Joined: 19 Nov 2017
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Re: Is x < 0? (1) x^2 - x > 0 (2) |x| < 1  [#permalink]

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28 Jul 2018, 22:08
emanresu1 wrote:
Idk what I'm doing wrong:
We need to know if X is (-) or (+)
(1) is satisfied for all numbers outside of the range 0:1 (not including 0 and 1)
(2) is satisfied for all numbers inside range -1:1 (not including -1 and 1)

So if you take (1) and (2) together, X must be a negative number between -1:0

Yes you are correct in your approach. I guess i misclicked the OA as E.
Thanks. OA edited.

Posted from my mobile device
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Vaibhav

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Re: Is x < 0? (1) x^2 - x > 0 (2) |x| < 1  [#permalink]

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28 Jul 2018, 22:12
1
To find whether x < 0

Statement 1

$$x^2 - x > 0$$

=> $$x * (x - 1) > 0$$

x can be 9 satisfying x * (x - 1) = 9 * 8 = 72 > 0

x can be -9 satisfying x * (x - 1) = (-9) * (-9-1) = (-9) * (-10) = 90 > 0

Statement 1 is not sufficient

Statement 2

|x| < 1

=> x can be 0.5 or -0.5

Statement 2 is insufficient

Combining statements 1 and 2

$$x * (x - 1) > 0$$ and |x| < 1

x * (x - 1) is positive only if x and (x-1) have same sign

Case 1

x and (x-1) are positive => x-1 > 0 => x > 1 but from statement 2 |x| < 1. So this case is not possible

Case 2

x and (x-1) are both negative and range of values for statement 2 are -1 < x < 0

=> The combined interval is -1 < x < 0 => x < 0

Statements 1 and 2 together are sufficient.

Hence option C
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Joined: 22 Feb 2018
Posts: 256
Re: Is x < 0? (1) x^2 - x > 0 (2) |x| < 1  [#permalink]

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28 Jul 2018, 22:17
OA : C

Question stem : Is x<0
1.$$x^2−x>0$$
$$x(x-1)>0$$
$$x$$ and $$x-1$$ both should be either positive or negative simultaneously.
This will happen if either $$x<0$$ or $$x>1$$
$$x$$ can be either +ve or -ve.
Statement 1 alone is not sufficient to answer the question: Is x<0

2: $$|x|<1$$
This implies $$-1<x<1$$
x can be either +ve or -ve.
Statement 2 alone is not sufficient to answer the question: Is x<0

Combining 1 and 2, we get $$-1<x<0$$
$$x$$ will - ve, So combining Statement 1 and Statement 2 will be sufficient to answer : Is x<0
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Re: Is x < 0? (1) x^2 - x > 0 (2) |x| < 1  [#permalink]

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29 Jul 2018, 01:31
1
See the wavy curve approach for solving inequalities:
Attachment:

WhatsApp Image 2018-07-29 at 13.57.33.jpeg [ 80.38 KiB | Viewed 324 times ]

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Re: Is x < 0? (1) x^2 - x > 0 (2) |x| < 1 &nbs [#permalink] 29 Jul 2018, 01:31
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