Solution:
Consider first statement (1) alone.
ab = 2ab.
Or ab = 0.
This means either a = 0 or b = 0 or both a and b are 0.
But the main question says that a is positive.
Or a is not 0.
So b = 0.
Or (1) alone is sufficient to answer the question.
Next consider (2) alone.
It means la+bl = la-bl.
Square both sides.
We get (la+bl)^2 = (la-bl)^2.
Or a^2 + b^2 + 2ab = a^2 + b^2 - 2ab.
Or 4ab = 0.
Or ab = 0.
Using the same reasoning as for statement (1), since a is not 0, b= 0.
So (2) alone is also sufficient to answer the question.
The correct answer is (D).
Kaplan Problem
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Statement 1: ab=2ab
The above statement will be true when either a or b is zero. Both can also be zero, however we are given a is positive.
Thus b has to be zero. - SUFFICIENT.
Statement 2: |a+b| = |a-b|
We have four possible cases here.
1) a+b = a-b. so 2b=0. so b=0
2) a+b = b-a. so 2a=0. so a=0. this is invalid possibility because we are give that a is positive.
3) -a-b = a-b. so 2a=0. so a=0. this is invalid possibility because we are give that a is positive.
4) -a-b = b-a. so 2b=0. so b=0
SUFFICIENT.
Answer is D.
The above statement will be true when either a or b is zero. Both can also be zero, however we are given a is positive.
Thus b has to be zero. - SUFFICIENT.
Statement 2: |a+b| = |a-b|
We have four possible cases here.
1) a+b = a-b. so 2b=0. so b=0
2) a+b = b-a. so 2a=0. so a=0. this is invalid possibility because we are give that a is positive.
3) -a-b = a-b. so 2a=0. so a=0. this is invalid possibility because we are give that a is positive.
4) -a-b = b-a. so 2b=0. so b=0
SUFFICIENT.
Answer is D.
reply2spg wrote:if a is positive, what is the value of b?
1. ab = 2ab
2. |a+b| = |a-b|
Force and mind are opposites; morality ends where a gun begins.
