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# Is |x|^2 - 5|x| + 6 > 0? (1) |x| > 2 (2) |x| < 3

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Is |x|^2 - 5|x| + 6 > 0? (1) |x| > 2 (2) |x| < 3  [#permalink]

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Updated on: 20 Mar 2019, 10:39
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85% (hard)

Question Stats:

33% (02:13) correct 67% (02:12) wrong based on 36 sessions

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Is $$|x|^2-5|x|+6>0?$$

(1) $$|x|>2$$

(2) $$|x|<3$$

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Originally posted by Asad on 20 Mar 2019, 08:55.
Last edited by Bunuel on 20 Mar 2019, 10:39, edited 1 time in total.
Renamed the topic and edited the question.
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Is |x|^2 - 5|x| + 6 > 0? (1) |x| > 2 (2) |x| < 3  [#permalink]

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Updated on: 24 Mar 2019, 03:13
Is $$|x|^2-5|x|+6>0?$$
1) $$|x|>2$$
2) $$|x|<3$$

Let, |x| = a

$$|x|^2-5|x|+6>0$$ becomes $$a^2-5a+6>0$$

i.e. Question is Is$$(a-2)(a-3) > 0?$$

Which is possible when both (a-2) and (a-3) are greater than 0

i.e. Question : Is a > 3 OR a<2? cause a=IxI can NOT be negative

Statement 1: a > 2

NOT SUFFICIENT

Statement 2: a < 3

NOT SUFFICIENT

Combining the two statements
2 < a < 3
SUFFICIENT

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Originally posted by GMATinsight on 20 Mar 2019, 09:24.
Last edited by GMATinsight on 24 Mar 2019, 03:13, edited 1 time in total.
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Is |x|^2 - 5|x| + 6 > 0? (1) |x| > 2 (2) |x| < 3  [#permalink]

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Updated on: 24 Mar 2019, 08:23
Is $$|x|^2-5|x|+6>0?$$
1) $$|x|>2$$
2) $$|x|<3$$

#1
at x= 3 , we get $$|x|^2-5|x|+6>0?$$ = 0
and x=4 $$|x|^2-5|x|+6>0?$$= 2 ;insufficient
#2
x=2,1 $$|x|^2-5|x|+6>0?$$=0
insufficient

from 1&2
2>x<3
sufficient
IMO C

Originally posted by Archit3110 on 20 Mar 2019, 09:34.
Last edited by Archit3110 on 24 Mar 2019, 08:23, edited 1 time in total.
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Re: Is |x|^2 - 5|x| + 6 > 0? (1) |x| > 2 (2) |x| < 3  [#permalink]

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23 Mar 2019, 11:45
Is $$|x|^2-5|x|+6>0?$$

(1) $$|x|>2$$

(2) $$|x|<3$$

In inequality it is better to verify the answer by plugging in the original equation.

1) if x=3 then $$|x|^2-5|x|+6 =0$$ ans is NO.
if x=4 then $$|x|^2-5|x|+6 =2$$ ans is Yes
Hence Insufficient

2) If x=2 $$|x|^2-5|x|+6$$ =0 ans is NO.
if x=0 then $$|x|^2-5|x|+6$$ =6 ans is Yes
Hence B is also Insufficient

1+2

-3< x <-2 or 2<x<3
take a value x=$$\frac{5}{2}$$ $$\rightarrow$$ 2.5 putting in eqn.
$$\frac{25}{4}-\frac{25}{2}+6<0$$
So a definite NO.
IMO C
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Re: Is |x|^2 - 5|x| + 6 > 0? (1) |x| > 2 (2) |x| < 3  [#permalink]

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24 Mar 2019, 01:35
stne wrote:
Is $$|x|^2-5|x|+6>0?$$

(1) $$|x|>2$$

(2) $$|x|<3$$

2) If x=2 $$|x|^2-5|x|+6$$ =0 ans is NO.
if x=0 then $$|x|^2-5|x|+6$$ =6 ans is Yes
Hence B is also Insufficient

GMATinsight
Here the explanation of statement 2 says: B is Insufficient.
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Posts: 1352
Re: Is |x|^2 - 5|x| + 6 > 0? (1) |x| > 2 (2) |x| < 3  [#permalink]

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24 Mar 2019, 04:11
stne wrote:
Is $$|x|^2-5|x|+6>0?$$

(1) $$|x|>2$$

(2) $$|x|<3$$

2) If x=2 $$|x|^2-5|x|+6$$ =0 ans is NO.
if x=0 then $$|x|^2-5|x|+6$$ =6 ans is Yes
Hence B is also Insufficient

GMATinsight
Here the explanation of statement 2 says: B is Insufficient.

Archit3110
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Re: Is |x|^2 - 5|x| + 6 > 0? (1) |x| > 2 (2) |x| < 3   [#permalink] 24 Mar 2019, 04:11
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