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Is x^2 – 10x > – 20? (1) 3 < x < 7 (2) 2 < x < 9

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Math Expert
Joined: 02 Sep 2009
Posts: 51072
Is x^2 – 10x > – 20? (1) 3 < x < 7 (2) 2 < x < 9  [#permalink]

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18 Jul 2018, 01:58
00:00

Difficulty:

35% (medium)

Question Stats:

71% (02:04) correct 29% (02:20) wrong based on 28 sessions

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Is x^2 – 10x > – 20?

(1) 3 < x < 7

(2) 2 < x < 9

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Director
Joined: 31 Oct 2013
Posts: 844
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Is x^2 – 10x > – 20? (1) 3 < x < 7 (2) 2 < x < 9  [#permalink]

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18 Jul 2018, 02:24
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.

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Joined: 21 Aug 2013
Posts: 1412
Location: India
Re: Is x^2 – 10x > – 20? (1) 3 < x < 7 (2) 2 < x < 9  [#permalink]

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18 Jul 2018, 20:23
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.

Re: Is x^2 – 10x > – 20? (1) 3 < x < 7 (2) 2 < x < 9 &nbs [#permalink] 18 Jul 2018, 20:23
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