Is a0?

Question

Is a>0?
(1) a-b>0
(2)  a^2-b^2>0

SonalSinha803 · Answer

The equation in Statement 1 can be satisfied by a positive value of a with b either positive or negative. So YES.
Also, it could be satisfied if a is negative and b is also negative but less than a. Eg. a = -5, b = -7, thus, -5 + 7 = 2 > 0. Thus, a is less than 0. So, in this case, answer would be NO.

Similar is the case with statement 2. Hence both are individually insufficient.

However if both are combined, we know from statement 1, that a - b is always positive. So, for the second part to stay positive, a + b should be greater than 0, which is possible only if a and b both are positive. Thus, a > 0. Hence, sufficient together.

Thus, C.

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PKN · Answer

Statement 1: Scenarios when (a-b)>0..........................................................(a) i) a>0, b>0 ii) a<0, b<0 iii) a>0, b=0 iv) a=0, b<0 Clearly insufficient. "a" can have values with both the signs or zero too.. Statement 2: Scenarios when a^2-b^2>0 i) a>0 or a<0, b>0 or b<0 & |a|>|b| ; since square term always yields positive value Clearly insufficient. "a" can have values with both the signs. Combining, (1)+(2), we can re-write St2 as (a+b)(a-b)>0--------------------(b) hence from (a) & (b), we have (a+b)>0 -----(c) Now adding (a) with (c) we have, (a+b+a-b)>0 or 2a>0 or a>0 Hence sufficient. Ans. C P.S:- We can only add inequalities when their signs are in the same direction.

Mo2men · Answer

(1) a-b>0 
a > b
This is very general

Let a=3 & b=2................Answer is Yes

Let a=-3 & b=-4................Answer is No

Insufficient

(2)  a^2-b^2>0

a^2 > b^2 .................This means |a| > |b|

Let a=3 & b=2................Answer is Yes

Let a=-4 & b=-3................Answer is No

Insufficient

combining 1 & 2

a can't be zero....otherwise Statement 2 will be invalid

a can't be negative.. ..While it may valid for Statement 2, this will make Statement 1 invalid

Only possible solution is that a is postive

Answer: C

Mo2men · Answer

Hi,
While the answer is correct, the highlighted is not necessary. 'b' can take negative value or zero.

Let a = 3 & b =1/-1/0..........Both statements are valid with any value of b

rakeshmishra5690 · Answer

1) a-b>0; insufficient because because we can have following pairs satisfying the eq- 9,7 or -7,-9 
2) a^2-b^2 >0 ; insufficient because we can have following pairs satisfying the eq - 4,3 or -4,-3

1) + 2)

a-b>0 
(a-b)*(a+b)>0; as a-b>0
a+b>0

adding 2 equations

2a>0 -> a>0

Ans C

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