Data Sufficiency

Is a + b > 0?

1. 7a - b > 0

2. b - 6a > 0

[spoiler]How C is the answer ?[/spoiler]

heshamelaziry wrote:Is a + b > 0?

1. 7a - b > 0

2. b - 6a > 0

[spoiler]How C is the answer ?[/spoiler]

Statement 1:

7a - b > 0
7a > b

So, 7 a's are bigger than 1 b, but we don't know their positive/negative status. Insufficient.

Statement 2: Similar reasoning. Insufficient.

Combo:

When the inequality arrows are pointing in the same direction, you can stack the inequalities, and add them:

7a - b > 0
b - 6a > 0;

...rearranging

7a - b > 0
-6a +b > 0
_____________
a > 0 (adding the two inequalities)

So, a is positive. The second statement tells us:
b > 6a

If a is pos, and b is bigger than "a" (bigger than six of them), then of course, b is also positive.

Because both a and b are positive, their sum is positive.

The statements, although independently insufficient, are sufficient in combination.

Choose C.

Look at statement 1 first

7a-b>0

First do two easy plugs

senario 1. a=2 and b=3 7(2)-3>0 and 2+3>0
snenario 2. a=-2 and b=-20 (7(-2))- (-20)>0 and -2 + (-20) = -22 <0
so does not answer the question

2. b-6a>0

use same plugs

Senario 1. b=10 and a=1 10-6(1)>0 10+1>0
Senario 2. b=-2 and a=2 -2-(6(-2))>0 2+ (-2) =0
So does not answer the question

Now if we use both together we can answer the question