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

Question

Is x a positive number?

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

priyamishra0894 · Answer

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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chetan2u · Answer

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

Archit3110 · Answer

#1 x>-4 or say -x<4 insufficient as x = - or + values #2 x^2 > 25 -55 again insufficient from 1 & 2 we get x>-4 and -55 only possible overlap range is x>5 IMO C

chetan2u · Answer

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. So, final answer is x>5

Archit3110 · Answer

chetan2u 
thanks...

sumitkrocks · Answer

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 .

Answer is C

merajul · Answer

Is x a positive number?

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

Please check whether my approach is right

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

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