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# If the quotient a/b positive, which of the following must be

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Math Expert
Joined: 02 Sep 2009
Posts: 52164
If the quotient a/b positive, which of the following must be  [#permalink]

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03 Sep 2012, 04:49
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5% (low)

Question Stats:

86% (00:41) correct 14% (00:59) wrong based on 1109 sessions

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If the quotient a/b positive, which of the following must be true?

(A) a > 0
(B) b > 0
(C) ab > 0
(D) a-b > 0
(E) a+b > 0

Practice Questions
Question: 32
Page: 156
Difficulty: 550

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Math Expert
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Posts: 52164
Re: If the quotient a/b positive, which of the following must be  [#permalink]

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03 Sep 2012, 04:49
1
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SOLUTION

If the quotient a/b positive, which of the following must be true?

(A) a > 0
(B) b > 0
(C) ab > 0
(D) a-b > 0
(E) a+b > 0

$$\frac{a}{b}>0$$ means $$a$$ and $$b$$ have the same sign, either both are negative or both are positive. Thus, their product will also be positive: $$ab>0$$.

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Re: If the quotient a/b positive, which of the following must be  [#permalink]

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05 Sep 2012, 18:55
4
1
a/b implies a and b have the same sign.

a<0 AND b<0

or

a>0 AND b>0

A. a>0 does not have to be true, a can be negative
B. b>0 does not have to be true, b can be negative
C. ab>0, has to be true since a AND b have the same sign
D. a-b>0 does not have to be true since a AND b can be negative and the result of a-b can be negative
E. a+b>0 does not have to be true since a AND b can be negative and the result of a+b can be negative

##### General Discussion
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Joined: 28 Aug 2012
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Re: If the quotient a/b positive, which of the following must be  [#permalink]

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03 Sep 2012, 05:10
1
a and be must have the same sign. Either both are positive or both are negative.

When multiplying a*b, the result will therefore be positive.

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Re: If the quotient a/b positive, which of the following must be  [#permalink]

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05 Sep 2012, 06:14
1
I think the best approach in such questions is to plug in numbers Since the question asks about must be true then any numbers should qualify, if a/b is positive then a and b have the same sign so a*b must be positive. (C)
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Math Expert
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Posts: 52164
Re: If the quotient a/b positive, which of the following must be  [#permalink]

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07 Sep 2012, 02:14
1
SOLUTION

If the quotient a/b positive, which of the following must be true?

(A) a > 0
(B) b > 0
(C) ab > 0
(D) a-b > 0
(E) a+b > 0

$$\frac{a}{b}>0$$ means $$a$$ and $$b$$ have the same sign, either both are negative or both are positive. Thus, their product will also be positive: $$ab>0$$.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: If the quotient a/b positive, which of the following must be  [#permalink]

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14 Jun 2013, 18:23
Hi Bunuel,
what if a=0;b=2. we have a/b as positive
as a result ab = 0. C fails.(:D is this some kind of miss in the question or Am i missing my basics here)

Tx

Bunuel wrote:
SOLUTION

If the quotient a/b positive, which of the following must be true?

(A) a > 0
(B) b > 0
(C) ab > 0
(D) a-b > 0
(E) a+b > 0

$$\frac{a}{b}>0$$ means $$a$$ and $$b$$ have the same sign, either both are negative or both are positive. Thus, their product will also be positive: $$ab>0$$.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
Math Expert
Joined: 02 Sep 2009
Posts: 52164
Re: If the quotient a/b positive, which of the following must be  [#permalink]

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14 Jun 2013, 23:56
p111 wrote:
Hi Bunuel,
what if a=0;b=2. we have a/b as positive
as a result ab = 0. C fails.(:D is this some kind of miss in the question or Am i missing my basics here)

Tx

Bunuel wrote:
SOLUTION

If the quotient a/b positive, which of the following must be true?

(A) a > 0
(B) b > 0
(C) ab > 0
(D) a-b > 0
(E) a+b > 0

$$\frac{a}{b}>0$$ means $$a$$ and $$b$$ have the same sign, either both are negative or both are positive. Thus, their product will also be positive: $$ab>0$$.

Kudos points given to everyone with correct solution. Let me know if I missed someone.

If a=0 and b=2, then a/b=0. 0 is neither positive nor negative.

For more check here: math-number-theory-88376.html#p666609

Hope it helps.
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If the quotient a/b positive, which of the following must be  [#permalink]

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10 Jul 2014, 01:35
For $$\frac{a}{b} > 0$$, I took help of numbers:

$$\frac{6}{3} = 2 & \frac{-6}{-3} = 2$$

Checking all options:

A: a>0 ............ Fail for a = -6; b = -3

B: b>0 ............... Fail for a = -6; b = -3

C: ab>0 ................ OK for both (6*3 = 18 & -6 * -3 = 18)

D: a-b > 0 ........... Fail for a = -6; b = -3

E: a+b > 0 ........... Fail for a = -6; b = -3

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If the quotient a/b positive, which of the following must be  [#permalink]

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09 May 2016, 12:35
$$\frac{a}{b}$$ is positive means $$\frac{a}{b}$$ > 0

This means that both a and b are either negative or both a and b are positive
So quotient $$\frac{a}{b}$$ will always be positive
ab > 0
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Re: If the quotient a/b positive, which of the following must be  [#permalink]

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10 May 2016, 06:26
Bunuel wrote:
If the quotient a/b positive, which of the following must be true?

(A) a > 0
(B) b > 0
(C) ab > 0
(D) a-b > 0
(E) a+b > 0

We are given that a divided by b is positive (or greater than zero). We know that in division when a quotient is positive, the two numbers being divided are either both negative or both positive.

This is also the case in multiplication; that is, to get a product that is positive, we must multiply two positive numbers or two negative numbers. Thus the only answer choice that MUST be positive is C, ab > 0.
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Posts: 80

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04 Sep 2016, 07:47

1. If the quotient a/b is positive, which of the following must be true?

(A) a>0
(B) b>0
(0 ab>0
(D) a-b>0
(E) a + b>0

Regards,
MoM
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Re: If the quotient a/b positive, which of the following must be  [#permalink]

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04 Sep 2016, 09:21
Manonamission wrote:

1. If the quotient a/b is positive, which of the following must be true?

(A) a>0
(B) b>0
(0 ab>0
(D) a-b>0
(E) a + b>0

Regards,
MoM

a/b positive means both a and b MUST of same sign. Hence, ab>0. Answer is C
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Re: If the quotient a/b positive, which of the following must be  [#permalink]

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01 Apr 2017, 06:14
Its clearly C
a/b= Positive (Thus either both are positive or both are negative)
ab>0

a b
Positive * Positive =Positive
Negative * Negative =Positive
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Re: If the quotient a/b positive, which of the following must be  [#permalink]

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17 Apr 2018, 08:42
Top Contributor
Bunuel wrote:
If the quotient a/b positive, which of the following must be true?

(A) a > 0
(B) b > 0
(C) ab > 0
(D) a-b > 0
(E) a+b > 0

Practice Questions
Question: 32
Page: 156
Difficulty: 550

The key word here is MUST

So, if we can find values of a and b that make an answer choice FALSE, then we can eliminate that answer choice.

For example, a = -3 and b = -1 satisfies the given condition that a/b is positive [since (-3)/(-1) = 3, and 3 is positive]

Now take the answer choices and plug in a = -3 and b = -1

We get:
(A) -3 > 0. FALSE. ELIMINATE A
(B) -1 > 0. FALSE. ELIMINATE B
(C) (-3)(-1) > 0 TRUE. KEEP C
(D) (-3) - (-1) > 0. FALSE. ELIMINATE D
(E) (-3) + (-1) > 0. FALSE. ELIMINATE E

By the process of elimination, the correct answer is C

Cheers,
Brent
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Re: If the quotient a/b positive, which of the following must be &nbs [#permalink] 17 Apr 2018, 08:42
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