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

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Math Expert
Joined: 02 Sep 2009
Posts: 47161
Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0  [#permalink]

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21 Sep 2017, 05:03
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55% (01:21) correct 45% (00:59) wrong based on 64 sessions

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Is 10x > x^10 ?

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

_________________
Senior Manager
Joined: 05 Dec 2016
Posts: 259
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0  [#permalink]

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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.

P.S. I'm not sure whether my line of reasoning is correct
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Joined: 20 Sep 2017
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Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0  [#permalink]

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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)

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.
Senior Manager
Joined: 05 Dec 2016
Posts: 259
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0  [#permalink]

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21 Sep 2017, 06:34
1
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)

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]

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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]

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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
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Re: Is 10x > x^10 ? (1) x is a positive number. (2) x^2 – 1 < 0  [#permalink]

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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.

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