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# Is |x|<6? 1) (x+6)(x-6)≤0 2) (x-6)(x-9)≤0

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VP
Joined: 23 Feb 2015
Posts: 1353
Is |x|<6? 1) (x+6)(x-6)≤0 2) (x-6)(x-9)≤0  [#permalink]

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23 Mar 2019, 08:50
1
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Difficulty:

95% (hard)

Question Stats:

15% (01:36) correct 85% (01:43) wrong based on 27 sessions

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Is $$|x|<6?$$
1) $$(x+6)(x-6)≤0$$
2) $$(x-6)(x-9)≤0$$

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“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

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Director
Joined: 27 May 2012
Posts: 947
Is |x|<6? 1) (x+6)(x-6)≤0 2) (x-6)(x-9)≤0  [#permalink]

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Updated on: 24 Mar 2019, 11:55
1
Is $$|x|<6?$$
1) $$(x+6)(x-6)≤0$$
2) $$(x-6)(x-9)≤0$$

The answer seems to be D
Unless I am missing something both the statements do seem to contradict each other.
Statement 1 . -6<x<6 , so Yes |x| < 6
Statement 2: 6<x<9 So a definite NO |x| $$\nless$$ 6

Edit:
Missed the equal to in the question above.
If x=6 or -6 then |x|=6 So it's a NO
IF -6<x<6 then |x| < 6 so it's a Yes
Hence Statement 1 is Insufficient.

Ans= B
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- Stne

Originally posted by stne on 23 Mar 2019, 11:19.
Last edited by stne on 24 Mar 2019, 11:55, edited 2 times in total.
Manager
Joined: 19 Jan 2019
Posts: 110
Re: Is |x|<6? 1) (x+6)(x-6)≤0 2) (x-6)(x-9)≤0  [#permalink]

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23 Mar 2019, 20:01
1
stne wrote:
Is $$|x|<6?$$
1) $$(x+6)(x-6)≤0$$
2) $$(x-6)(x-9)≤0$$

The answer seems to be D
Unless I am missing something both the statements do seem to contradict each other.
Statement 1 . -6<x<6 , so Yes |x| < 6
Statement 2: 6<x<9 So a definite NO |x| $$\nless$$ 6

Here's what you are missing. (X+6)(x-6) <=0
X can be equal to -6 or can be equal to +6.. in these cases your answer would be definite no because |X| = 6

Now take this case of (x-6)(X+6) < 0
X-6<0 and X+6>0
-6<X<6

X can range from any values between 6 and -6.
Take X equals to 3...

Statement 1 is not sufficient on its own

Statement 2 :

If X = 9 and even if X= 6..
|X| < 6 , a definite no { (x-6)(x-9) = 0}

And 6>X>9 {(x-6)(x-9)<0

Take X as 7 |X| < 6, a definite no...

Statement 2 is sufficient on its own..

Posted from my mobile device
Director
Joined: 27 May 2012
Posts: 947
Re: Is |x|<6? 1) (x+6)(x-6)≤0 2) (x-6)(x-9)≤0  [#permalink]

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24 Mar 2019, 11:56
thyagi wrote:
stne wrote:
Is $$|x|<6?$$
1) $$(x+6)(x-6)≤0$$
2) $$(x-6)(x-9)≤0$$

The answer seems to be D
Unless I am missing something both the statements do seem to contradict each other.
Statement 1 . -6<x<6 , so Yes |x| < 6
Statement 2: 6<x<9 So a definite NO |x| $$\nless$$ 6

Here's what you are missing. (X+6)(x-6) <=0
X can be equal to -6 or can be equal to +6.. in these cases your answer would be definite no because |X| = 6

Now take this case of (x-6)(X+6) < 0
X-6<0 and X+6>0
-6<X<6

X can range from any values between 6 and -6.
Take X equals to 3...

Statement 1 is not sufficient on its own

Statement 2 :

If X = 9 and even if X= 6..
|X| < 6 , a definite no { (x-6)(x-9) = 0}

And 6>X>9 {(x-6)(x-9)<0

Take X as 7 |X| < 6, a definite no...

Statement 2 is sufficient on its own..

Posted from my mobile device

Correct , Thank you, Missed that equal to criteria. Added the edit to my Post above.
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- Stne
Re: Is |x|<6? 1) (x+6)(x-6)≤0 2) (x-6)(x-9)≤0   [#permalink] 24 Mar 2019, 11:56
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