Data Sufficiency

Is 2a < a x a - b ?

(1) 0 < a < 2

(2) -2 < b < 0

I go for E

2a<a^2 -b

1) Insufficient as we do n't have values for b
2) Insufficient as we do n't have values for a

combining 1) and 2)

if a=1 and b= -1

2< 1-(-1) ---> 2<2 ( cannot happen) so--> NO

if a=1 and b= -1.5

2< 1-(-1.5) --> 2< 2.5 ---> Yes

As we can prove both Yes and No , so answer should be E

Anurag@Gurome wrote:

koby_gen wrote:Is 2a < a x a - b ?

(1) 0 < a < 2
(2) -2 < b < 0

Is it (a² - b) or a(a - b)?

(a² - b)

Thanks

I'm getting E.

Statement asks if 2a < a^2 - b. You could rephrase as 2a < (a + b)(a - b) if you want.

Statement 1: Tells nothing about the value of B. Insufficient.

Statement 2: Tells nothing about the value of A. Insufficient.

Combined, we could plug in a = 1 and b = -1. 2(1) < 1^2 - (-1). In this case, 2 = 2, and the answer to the initial question is NO. However, we could also plug in a = 1/2 and b = -1, in which case 2(1/2) < 1^2 -(-1) = 1 < 2, in which case the answer to the question is YES.

Thus, INSUFFICIENT.

Consider f(a) = a²-2a-b

the minimum value is for a=1, f(1)=-1-b, knowing the sign of -1-b will give the answer

1) 0<a<2 ----> not help to know the sign of -1-b
2) -2<b<0 ----> -1<-1-b<1, -1-b could be both sign, Hence NOT SUFF

1&2-----> NOT SUFF

Answer is E

Anurag@Gurome wrote:

koby_gen wrote:Is 2a < a x a - b ?

(1) 0 < a < 2
(2) -2 < b < 0

Is it (a² - b) or a(a - b)?

Hi Anurag,

is there any other approach apart from "putting values" for inequality questions?

1. 0< a< 2 ; this mean that " a" is +ve so a can be 0.5, 1, 1.5 or 1.9, however no "b" info. therefore INSUFF.

2. -2 < b<0 ; b is -ve, "'b" can be -1.5,-1,-0.5 , no "a" info, so INSUFF.

Combining (1) &(2)

2a < a x a - b ?

a = 0.5, b = -0.5

1<0.25 + 0.5 ;

a = 0.5, b = -1

1 < 0.25 +1 ..... different result from above.

So E is the answer.