If a and b are nonzero numbers, Is a-b0?

Question

If a and b are nonzero numbers, Is a-b>0?

(1) |a|-b>0
(2) a-|b|>0

jwang516 · Answer

Re-arrange the equation in the question stem by adding b to both sides and we notice that the question is really asking: 
Is a > b?

Also note that both a and b cannot be 0:

S1:
Re-arrange the equation by adding b to both sides and we get:
|a| > b
Note that the abs value hides the sign of a. We can test a few numbers that both meets the criteria |a| > b :
If a = -3 and b = 2 a < b
If a = 3 and b = 2 then a > b
Therefore, it is not sufficient.

S2:
Re-arrage the equation by adding |b| to both sides and we get:
a > |b|
Note that |b| hides the sign of b, but since a > |b| that means a must be positive since absolute value of a number is always positive and b cannot be 0
if b is negative: a > b since a is positive and a positive is always > a negative
if b is positive, a > b since we are given that a > |b|

Therefore, the answer is B

Bunuel · Answer

Please name topics properly. Read rule 3 in our  RULES OF POSTING . Thank you.

CEdward · Answer

If a and b are nonzero numbers, Is a-b>0?

a-b > 0 ---> a > b?

(1) |a|-b>0 --> |a| > b 
Insufficient b/c a can be positive or negative

(2) a-|b|>0 --> a > |b|
Sufficient b/c irrespective of whether b is positive or negative, a is greater than b.

Answer is B.

If a and b are nonzero numbers, Is a-b>0?

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If a and b are nonzero numbers, Is a-b>0?

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