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# Is x a positive number? (1) x + 6 > 2 (2) x^2 > 25

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Math Expert
Joined: 02 Sep 2009
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Is x a positive number? (1) x + 6 > 2 (2) x^2 > 25  [#permalink]

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06 May 2019, 03:03
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Difficulty:

35% (medium)

Question Stats:

65% (00:55) correct 35% (01:06) wrong based on 63 sessions

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Is x a positive number?

(1) x + 6 > 2
(2) x^2 > 25

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Joined: 19 Oct 2018
Posts: 7
Re: Is x a positive number? (1) x + 6 > 2 (2) x^2 > 25  [#permalink]

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06 May 2019, 05:37
1. X+6 > 2 , therefore x can be positive or negative since x can be equal to 100 or x can be equal to -3 as well
Therefore statement 1 is not sufficient

2. X^2 >25
Therefore x^2 - 25 >0
(X+5)(x-5)> 0
Therefore either x>-5 and x<5 OR x<-5 and x>5
Therefore statement 2 is also not sufficient

Therefore Option E

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Posts: 8310
Re: Is x a positive number? (1) x + 6 > 2 (2) x^2 > 25  [#permalink]

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06 May 2019, 05:39
1
Is x a positive number?

(1) x + 6 > 2
So, x>-4... x can be 10, 20 or -3, -1/2
Insuff

(2) x^2 > 25
so $$x^2>5^2.....x<-5..or..x>5$$
Insuff

combined..
Statement I says x>-4, and statement II says that x<-5 or x>5.
The range of x that is common to both statements is x>5, so x will be positive.

C
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Is x a positive number? (1) x + 6 > 2 (2) x^2 > 25  [#permalink]

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Updated on: 06 May 2019, 06:27
Bunuel wrote:
Is x a positive number?

(1) x + 6 > 2
(2) x^2 > 25

#1
x>-4
or say -x<4
insufficient as x = - or + values
#2
x^2 > 25
-5<x>5
again insufficient
from 1 & 2
we get x>-4 and -5<x>5
only possible overlap range is x>5
IMO C

Originally posted by Archit3110 on 06 May 2019, 06:12.
Last edited by Archit3110 on 06 May 2019, 06:27, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 8310
Re: Is x a positive number? (1) x + 6 > 2 (2) x^2 > 25  [#permalink]

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06 May 2019, 06:18
Archit3110 wrote:
Bunuel wrote:
Is x a positive number?

(1) x + 6 > 2
(2) x^2 > 25

#1
x>-4
or say x<4

insufficient as x = - or + values
#2
x^2 > 25
-5<x>5
again insufficient
from 1 & 2
we get x<4 and -5<x>5
value of x will be + or -ve not sure
IMO E
chetan2u ; range given is x<4 or x>-4 / why have you considered range of x to be always +ve?
should nt the answer be 'e' in this case.

Hi,
x>-4 does not mean x<4, but -x<4...
So statement I says that x>-4. x could be anything GREATER than -4 so both negative and positive value possible.
Now, statement II says that x<-5 or x>5..
Combined..
when you take x<-5, the statement I does not have any values in this range, so discard x<-5, as statement I says it is NOT possible.
Now x>5 and x>-4 have a common range only when x>5.
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Re: Is x a positive number? (1) x + 6 > 2 (2) x^2 > 25  [#permalink]

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06 May 2019, 06:26
chetan2u
thanks...

chetan2u wrote:
Archit3110 wrote:
Bunuel wrote:
Is x a positive number?

(1) x + 6 > 2
(2) x^2 > 25

#1
x>-4
or say x<4

insufficient as x = - or + values
#2
x^2 > 25
-5<x>5
again insufficient
from 1 & 2
we get x<4 and -5<x>5
value of x will be + or -ve not sure
IMO E
chetan2u ; range given is x<4 or x>-4 / why have you considered range of x to be always +ve?
should nt the answer be 'e' in this case.

Hi,
x>-4 does not mean x<4, but -x<4...
So statement I says that x>-4. x could be anything GREATER than -4 so both negative and positive value possible.
Now, statement II says that x<-5 or x>5..
Combined..
when you take x<-5, the statement I does not have any values in this range, so discard x<-5, as statement I says it is NOT possible.
Now x>5 and x>-4 have a common range only when x>5.
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Re: Is x a positive number? (1) x + 6 > 2 (2) x^2 > 25  [#permalink]

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06 May 2019, 09:30
From Statement 1 : X>-4 ....X can be +ve or -ve hence Statement 1 is not sufficient.

From statement 2 : (x-5)(x+5)>0 hence Either X<-5 or X>5 again we can not conclude whether x is positive or not , hence again statement 2 again is not sufficient.

However , if we combine statement 1 and 2 we can conclude that X >5 , hence together statement 1 and 2 are sufficient .

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Re: Is x a positive number? (1) x + 6 > 2 (2) x^2 > 25  [#permalink]

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22 Nov 2019, 10:13
Is x a positive number?

(1) x + 6 > 2
(2) x^2 > 25

Please check whether my approach is right
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Re: Is x a positive number? (1) x + 6 > 2 (2) x^2 > 25   [#permalink] 22 Nov 2019, 10:13
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