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

Question

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

Bunuel · Accepted Answer

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.

Spunkerspawn · Answer

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.

Zinsch123 · Answer

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.

ziko · Answer

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)

Bunuel · Answer

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.

p111 · Answer

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 · Answer

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.

PareshGmat · Answer

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

rhine29388 · Answer

\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

JeffTargetTestPrep · Answer

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.

Manonamission · Answer

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

abhimahna · Answer

a/b positive means both a and b MUST of same sign. Hence, ab>0. Answer is C

Shiv2016 · Answer

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

BrentGMATPrepNow · Answer

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

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

mimajit · Answer

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

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

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