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# Is |x| > 10?

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Math Expert
Joined: 02 Aug 2009
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08 Oct 2017, 21:06
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Is |x| > 10?

(1) $$x^2-12x+20=0$$

(2) x < 10
[Reveal] Spoiler: OA

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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Intern
Joined: 04 Nov 2015
Posts: 35
Re: Is |x| > 10? [#permalink]

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08 Oct 2017, 21:26
chetan2u wrote:
Is |x|>10?

(1) $$x^2-12x+20=0$$
(2) x < 10

I suppose the ans should be E.
The question asks us -10<x<10 .
from 1: we get x =2 ,10 (Not sufficient)
from 2: x<10 (Not sufficient).

Combining also yields no new info.

Regards,
Sandeep
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Joined: 21 Jun 2014
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Re: Is |x| > 10? [#permalink]

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08 Oct 2017, 22:21
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sandeep211986 wrote:
chetan2u wrote:
Is |x|>10?

(1) $$x^2-12x+20=0$$
(2) x < 10

I suppose the ans should be E.
The question asks us -10<x<10 .
from 1: we get x =2 ,10 (Not sufficient)
from 2: x<10 (Not sufficient).

Combining also yields no new info.

Regards,
Sandeep

It should be A. Because we have only 2 values for x, either 2 or 10, and hence we can clearly say that mod x is not greater than 10.

Also -10<x<10 is not correct. The question says mod x > 10. So either X < -10 or X>10.

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Intern
Joined: 08 Oct 2017
Posts: 1
Re: Is |x| > 10? [#permalink]

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09 Oct 2017, 00:26

Explanation:

We are supposed to find a definite yes or no answer for whether x is between -10 and 10 excluding -10 and 10.

1) $$x^2-12x+20=0$$
This equation gives us 2 and 10. If it is 2, answer is yes. If it is 10, answer is no. So, the information is not sufficient.

2) x<10
x is less than not equal to 10. If we take 3 answer is yes. If we take -20, answer is no. So, we don't have a definite yes or no. Hence, information not sufficient.

Combining both 1) and 2)
The only answer is 2. This gives a definite yes to our original question (whether x is between -10 and 10 excluding -10 and 10).
So, the option C is our answer.
Manager
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Re: Is |x| > 10? [#permalink]

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09 Oct 2017, 01:51
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surabhichaudhary20 wrote:

Explanation:

We are supposed to find a definite yes or no answer for whether x is between -10 and 10 excluding -10 and 10.

1) $$x^2-12x+20=0$$
This equation gives us 2 and 10. If it is 2, answer is yes. If it is 10, answer is no. So, the information is not sufficient.

2) x<10
x is less than not equal to 10. If we take 3 answer is yes. If we take -20, answer is no. So, we don't have a definite yes or no. Hence, information not sufficient.

Combining both 1) and 2)
The only answer is 2. This gives a definite yes to our original question (whether x is between -10 and 10 excluding -10 and 10).
So, the option C is our answer.

In the first statement, for X= 10, the answer is No and for X= 2, the answer is still No . So it is sufficient.

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Re: Is |x| > 10? [#permalink]

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09 Oct 2017, 03:33
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(1) Solving, we get x=2;10. Hence |x|<10 anyway, so YES sufficient.
(2) x= 5 |5|<10
x= -100 |100|>10 NOT sufficient

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Re: Is |x| > 10? [#permalink]

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09 Oct 2017, 06:19
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chetan2u wrote:
Is |x| > 10?

(1) $$x^2-12x+20=0$$
(2) x < 10

The questions asks is x >10 or x < -10

1) We get two solutions for x 2 and 10. These two solutions sujests that x is neither greater than 10 nor less - 10. Sufficient
2) This tells that x is less than 10 but doesnt tell that x is less than - 10 or not. Insufficient

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Re: Is |x| > 10? [#permalink]

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09 Oct 2017, 22:15
Bunuel lot of different answers here, could you kindly clarify?
Math Expert
Joined: 02 Sep 2009
Posts: 44412
Re: Is |x| > 10? [#permalink]

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09 Oct 2017, 23:22
Amerendra wrote:
Bunuel lot of different answers here, could you kindly clarify?

saicharan1191 solution is correct. The answer is A.

Is |x| > 10?

(1) $$x^2-12x+20=0$$:

x = 2 or x = 10. In either case the answer to the question whether |x| > 10 is NO. Sufficient.

(2) x < 10:

If x = 0, then the answer is YES but if x = -100, then the answer is NO. Not sufficient.

Hope it's clear.
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Re: Is |x| > 10? [#permalink]

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10 Oct 2017, 01:52
Ans should be A. X =2,10. Hence in both cases value of x is lesser than 10. Hence A is sufficient.

If x is less than 10. X can be -1 or 11. Here value of x is less than 10 in one case and more than 10 in one case. So not sufficient.

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Re: Is |x| > 10?   [#permalink] 10 Oct 2017, 01:52
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