If a and b are integers and ab does not equal 0, is ab 0?

Question

If a and b are integers and ab does not equal 0, is ab > 0?

(1) b =  a^4 - a^3 
(2) a is to the right of 0 on the number line.

lucajava · Answer

Given:  ab ≠ 0 .

Statement 1 :  b = a^4 - a^3 , hence the question can be rewritten as: is  a^5 - a^4 > 0 ? We cannot know it, since  a^5  could be either positive or negative. Insufficient.

Statement 2 : it tells us that  a  is positive, but we don't know anything about  b . Insufficient.

Statements 1 + 2 :  a^5 - a^4 >0 ?  Yes , because  a  is positive and  a  to the fifth power is greater than  a  to the fourth power.

Pick  C .

Road2700 · Answer

A being positive still does not tell us anything about b? so i don't think C would be the answer. please help clarify

"Nevermind, got it. B = a^4 - a^ 3 gives it away

jaysonbeatty · Answer

This question is all about the positive/negative rules of multiplication and addition/subtraction. The rules are
+ * + = +
+ * - = -
- * - = +

So, to know ab >0 we have to know the signs of a and b OR if a and b have the same sign OR if a and b have different signs.

Statement 1.

Regardless of sign, a^4 is positive. a^3 is either positive or negative based on the sign of a. So, b must be positive and a^4 must be bigger than a^3 based on the conditions of the question. These conditions are a and b are integers and neither a or b equal 0. FYI, if a could be 0 < a < 1 then a^4 would be smaller than a^3, but I digress.

Statement one tells us the sign of b but tells us nothing about a, so is insufficient by itself. Eliminate A and D

Statement 2.

This tells us a is positive. As we need to know the signs of both, insufficient by itself.

But them together - you know the signs of a and b, so sufficient. C is correct.

Jayson Beatty
Indigo Prep

stne · Answer

Statement 1 :  a^3(a-1)=b

a cannot be 1 as then b=0 , for a>1, i.e. 2,3,4 etc b is positive hence ab >0
for a<0 i.e. a=-1, -2 etc b >0 hence ab= -ve 
Hence insuff.

Statement 2 = nothing about b hence insuff.
1+2

if a>0 and an integer and a 
eq 1 then b>0 hence ab>0 
Suff.

aliakberza · Answer

Sorry I might have missed something but how did you go from a^4 - a^3 > b to a^5 - a^4 >0. How did you increase a's power by one?

lucajava · Answer

ab = a(a^4 - a^3) = a^5 - a^4 . The question asks whether  ab  is greater than zero or not, so we can say that we are looking for  a^5 - a^4 > 0 .

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If a and b are integers and ab does not equal 0, is ab > 0?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards