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Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0

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Bunuel
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Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0 [#permalink] New post   21 Sep 2017, 05:03
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A
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E

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65% (hard)

Question Stats:

52% (01:49) correct 48% (01:38) wrong based on 98 sessions
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Is 10x > x^10 ?

(1) x is a positive number.
(2) x^2 – 1 < 0
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C
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Alexey1989x
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Re: Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0 [#permalink] New post   21 Sep 2017, 05:39
We need to locate one of the following scenarios:
x<0 or x>10^1/9
(1) x>0
If x lies between 0 and 10^1/9 then NO
If x > 10^1/9 then YES
(2) x lies in interval (-1;1)
Insufficient as long as different cases are possible, see example from (1)

combining (1)+(2) we have that x lies between (0;1), again example from (1) shows that it's not sufficient.

Answer E.
P.S. I'm not sure whether my line of reasoning is correct
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Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0 [#permalink] New post   Updated on: 22 Sep 2017, 02:36
(1) х > 0
if х = 10^(1/9) (approx.1.29) than 10х = х^10 and NO
if 0 < х < 10^(1/9) than YES
If х > 10^(1/9) and x <0 than NO
Unsufficient

(2) -1 < х < 1
Unsufficient, see (1)

(1) + (2) sufficient, see (1)

Answer D

Sorry, if (1) + (2) sufficient than Answer C, not D (thx Alexey1989x)

Originally posted by scabr on 21 Sep 2017, 06:26.
Last edited by scabr on 22 Sep 2017, 02:36, edited 1 time in total.
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Re: Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0 [#permalink] New post   21 Sep 2017, 06:34
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scabr wrote:
(1) х > 0
if х = 10^(1/9) (approx.1.29) than 10х = х^10 and NO
if 0 < х < 10^(1/9) than YES
If х > 10^(1/9) and x <0 than NO
Unsufficient

(2) -1 < х < 1
Unsufficient, see (1)

(1) + (2) sufficient, see (1)

Answer D


scabr Answer D means that both statements are sufficient to answer the question
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Re: Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0 [#permalink] New post   21 Sep 2017, 06:53
lets examine two stm seperately-
stm 1 x is a +ve number . it measn if x=1 then yes x#1 then its false so stm1 is not suufic.

stm2- it says that x2 is less then 1 it means that x is rational no .

Combine both stm we deduce that x is a positive but rational no hence sufficent ...Its C
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Re: Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0 [#permalink] New post   21 Sep 2017, 10:39
The answer has to be C
The above equality will hold for x=1 but not for higher value of X say 2,3 4 etc so statement 1 insufficient
Statement is also not sufficient as for 0 the the inequality will not hold
So both of them taken together gives x=1
Thus C is the answer
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Re: Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0 [#permalink] New post   22 Sep 2017, 05:18
Bunuel wrote:
Is 10x > x^10 ?

(1) x is a positive number.
(2) x^2 – 1 < 0


(1) x is a positive number.

Let x = 1/2.........5 > (1/2)^10.............Answer is Yes

Let x = 2...........20 > (2)^10..............Answer is No

Insufficient

(2) x^2 – 1 < 0

x^2 < 1

-1 < x < 1

Let x = 1/2.........5 > (1/2)^10.............Answer is Yes

Let x =-1/2.........-5 > (-1/2)^10.............Answer is No

Insufficient

Combine 1 & 2

From Statement 1, x > 0

From Statement 2, -1 < x < 1

We can conclude that 0 < x < 1 ...............our example of 1/2 gives clear answer.

Answer: C
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Re: Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0 [#permalink]
22 Sep 2017, 05:18
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Bunuel
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