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Is x^2 – 10x > – 20? (3) 3 < x < 7 (4) 2 < x < 9

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Bunuel
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Is x^2 – 10x > – 20? (1) 3 < x < 7 (2) 2 < x < 9 [#permalink] New post   18 Jul 2018, 02:58
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00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

62% (02:11) correct 38% (01:35) wrong based on 69 sessions
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Is x^2 – 10x > – 20?


(1) 3 < x < 7

(2) 2 < x < 9
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Official Answer
A
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D
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Is x^2 – 10x > – 20? (1) 3 < x < 7 (2) 2 < x < 9 [#permalink] New post   18 Jul 2018, 03:24
Bunuel wrote:
Is x^2 – 10x > – 20?


(1) 3 < x < 7

(2) 2 < x < 9



Statement 1 :

x ( minimum)= 4

x ( maximum) = 6

So,

\((4)^2\) - 10*4 > -20

16 -40 < -20

- 24 < -20

and

\(6^2\)- 10*6 > -20

- 24 < - 20

Sufficient


Statement 2:

x (minimum) = 3

x (maximum) =8

\((3)^2\) -10*3 > -20

-21 < -20

and

\(8^2\) - 10*8 > -20

- 16 > -20

Not Sufficient.


The best answer is A.
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amanvermagmat
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Re: Is x^2 – 10x > – 20? (1) 3 < x < 7 (2) 2 < x < 9 [#permalink] New post   18 Jul 2018, 21:23
Bunuel wrote:
Is x^2 – 10x > – 20?


(1) 3 < x < 7

(2) 2 < x < 9



We can rewrite the question stem as x^2 - 10x + 20 > 0
Or (x-5)^2 - 5 > 0. Or Is (x-5)^2 > 5.

Square root of 5 is approximately 2.24. So the thing given in question stem will be true if x-5 > 2.24 or if x-5 < -2.24
OR it will be true if x > 7.24 or if x < 2.76.

(1) x lies between 3 and 7. So x can be neither greater than 7.24 nor less than 2.76. So the question stem can never be true. Sufficient to answer with a NO.

(2) x lies between 2 and 9. But it can still be greater than 7.24 or it might not. Not sufficient.

Hence A answer
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Re: Is x^2 – 10x > – 20? (3) 3 < x < 7 (4) 2 < x < 9 [#permalink] New post   12 Jul 2019, 04:06
Considering statement (1) alone
If 3 < x < 7, then 9 < x^2 < 49 and 30 < 10x < 70
=> 9 - 49 < x^2 - 10x < 49 - 70
=> -40 < x^2 - 10x < -21
All the numbers in this range are less than -20
SUFFICIENT

Considering statement (2) alone:
If 2 < x < 9, then 4 < x^2 < 81 and 20 < 10x < 90
=> 4 - 20 < x^2 - 10x < 81 - 90
=> -16 < x^2 - 10x < -9
All the numbers in this range are more than -20
SUFFICIENT

The answer is (D).
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Is x^2 – 10x > – 20? (3) 3 < x < 7 (4) 2 < x < 9 [#permalink] New post   12 Jul 2019, 06:32
I have one query here. What if I get Yes for one statement and No for other statement. Though the answer to each statement is unique, is it correct to choose D here?
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Re: Is x^2 – 10x > – 20? (3) 3 < x < 7 (4) 2 < x < 9 [#permalink] New post   12 Jul 2019, 06:41
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gvij2017 wrote:
I have one query here. What if I get Yes for one statement and No for other statement. Though the answer to each statement is unique, is it correct to choose D here?


On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

So, for example, we can not have answer 2 from statement (1) and answer 4 from statement (2), as in this case statements would contradict each other.

Or for example in YES/NO DS questions we cannot have answer YES from statement (1) and answer NO from statement (2), as in this case statements also would contradict each other.
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Re: Is x^2 – 10x > – 20? (3) 3 < x < 7 (4) 2 < x < 9 [#permalink] New post   13 Jul 2019, 03:40
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How is the answer A?
I am also getting D

Posted from my mobile device
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Re: Is x^2 – 10x > – 20? (3) 3 < x < 7 (4) 2 < x < 9 [#permalink] New post   13 Jul 2019, 07:44
Prasannathawait wrote:
How is the answer A?
I am also getting D

Posted from my mobile device


In statement 2:

Let x=8...then -16 > -20...Answer is yes

Let x= 5..then -25 > -20...Answer is No

Insufficient
GMAT Club Bot
gmatclubot
Re: Is x^2 – 10x > – 20? (3) 3 < x < 7 (4) 2 < x < 9 [#permalink]
13 Jul 2019, 07:44
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Bunuel
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