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

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Bunuel
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If the quotient a/b positive, which of the following must be true? [#permalink] New post   03 Sep 2012, 05:49
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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
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C
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Bunuel
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Re: If the quotient a/b positive, which of the following must be true? [#permalink] New post   03 Sep 2012, 05:49
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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: \(ab>0\).

Answer: C.
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Re: If the quotient a/b positive, which of the following must be true? [#permalink] New post   05 Sep 2012, 19:55
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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

Answer: C.
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Re: If the quotient a/b positive, which of the following must be true? [#permalink] New post   03 Sep 2012, 06:10
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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.

Answer C.
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Re: If the quotient a/b positive, which of the following must be true? [#permalink] New post   05 Sep 2012, 07:14
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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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Re: If the quotient a/b positive, which of the following must be true? [#permalink] New post   07 Sep 2012, 03:14
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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: \(ab>0\).

Answer: C.

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 true? [#permalink] New post   14 Jun 2013, 19:23
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: \(ab>0\).

Answer: C.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Bunuel
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Re: If the quotient a/b positive, which of the following must be true? [#permalink] New post   15 Jun 2013, 00:56
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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: \(ab>0\).

Answer: C.

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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Re: If the quotient a/b positive, which of the following must be true? [#permalink] New post   10 Jul 2014, 02:35
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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

Answer = C
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Re: If the quotient a/b positive, which of the following must be true? [#permalink] New post   09 May 2016, 13:35
\(\frac{a}{b}\) 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
correct answer - C
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Re: If the quotient a/b positive, which of the following must be true? [#permalink] New post   10 May 2016, 07:26
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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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Re: If the quotient a/b positive, which of the following must be true? [#permalink] New post   04 Sep 2016, 08:47


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 true? [#permalink] New post   04 Sep 2016, 10:21
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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 true? [#permalink] New post   01 Apr 2017, 07:14
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 true? [#permalink] New post   17 Apr 2018, 09:42
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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 true? [#permalink] New post   15 Jul 2019, 01:31
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


First recognise that for a/b to be positve both a and b can either be positive or ether be neagative . Once that is established

1) a> 0 ya but a can also be negative and if even b is neagative we will have a positive value.
2) B> 0 same analogy as above.
C) AB >0 this must be true in both scenarios when both a and b are positive and both are negative . hence it must be true that ab>0
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Re: If the quotient a/b positive, which of the following must be true? [#permalink] New post   14 Mar 2024, 23:31
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