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If a and b are integers and ab does not equal 0, is ab > 0? 18 Apr 2019, 09:29
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

59% (01:40) correct 41% (01:35) wrong based on 88 sessions

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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.
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C
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If a and b are integers and ab does not equal 0, is ab > 0? 18 Apr 2019, 11:47
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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.
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If a and b are integers and ab does not equal 0, is ab > 0? 18 Apr 2019, 12:01
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lucajava
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.
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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
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If a and b are integers and ab does not equal 0, is ab > 0? 18 Apr 2019, 15:03
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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
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If a and b are integers and ab does not equal 0, is ab > 0? 07 Jun 2019, 01:32
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jaysonbeatty
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
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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\(\neq\)1 then b>0 hence ab>0
Suff.
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If a and b are integers and ab does not equal 0, is ab > 0? 08 Jun 2019, 15:31
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lucajava
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.
Show more

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?
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If a and b are integers and ab does not equal 0, is ab > 0? 10 Jun 2019, 03:15
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aliakberza
lucajava
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.

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?
Show more

\(ab = a(a^4 - a^3) = a^5 - a^4\). The question asks whether \(ab\) is greater than zero or not, so we can say that we are looking for \(a^5 - a^4 > 0\).
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If a and b are integers and ab does not equal 0, is ab > 0? 06 Sep 2023, 10:43
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