Is x^2 – 10x – 20? (3) 3

Question

Is x^2 – 10x > – 20?

(1) 3 < x < 7

(2) 2 < x < 9

KSBGC · Answer

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.

amanvermagmat · Answer

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

WiziusCareers1 · Answer

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).

gvij2017 · Answer

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?

Bunuel · Answer

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.

Prasannathawait · Answer

How is the answer A?
I am also getting D

Posted from my mobile device

Mo2men · Answer

In statement 2:

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

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

Insufficient

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

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