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

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Manager
Joined: 31 Oct 2018
Posts: 76
Location: India
If a and b are integers and ab does not equal 0, is ab > 0?  [#permalink]

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18 Apr 2019, 09:29
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Difficulty:

55% (hard)

Question Stats:

47% (01:19) correct 53% (01:51) wrong based on 15 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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Manager
Joined: 21 Feb 2019
Posts: 118
Location: Italy
Re: If a and b are integers and ab does not equal 0, is ab > 0?  [#permalink]

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18 Apr 2019, 11:47
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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Joined: 29 Mar 2019
Posts: 2
If a and b are integers and ab does not equal 0, is ab > 0?  [#permalink]

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18 Apr 2019, 12:01
lucajava wrote:
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.

"Nevermind, got it. B = a^4 - a^ 3 gives it away
Intern
Joined: 25 Sep 2017
Posts: 3
If a and b are integers and ab does not equal 0, is ab > 0?  [#permalink]

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18 Apr 2019, 15:03
1
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
If a and b are integers and ab does not equal 0, is ab > 0?   [#permalink] 18 Apr 2019, 15:03
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