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Math Expert V
Joined: 02 Sep 2009
Posts: 58422
If ab > 0, which of the following must be negative?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 88% (00:51) correct 12% (00:56) wrong based on 195 sessions

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If ab > 0, which of the following must be negative?

(A) a + b
(B) |a| + b
(C) b - a
(D) a/b
(E) -a/b

Kudos for a correct solution.

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If ab > 0, which of the following must be negative?  [#permalink]

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1
Bunuel wrote:
If ab > 0, which of the following must be negative?

(A) a + b
(B) |a| + b
(C) b - a
(D) a/b
(E) -a/b

Kudos for a correct solution.

If ab > 0 the we Infer that a and b both have same sign i.e. either both a and b are Positive or Both a and b are Negative

Now Checking Options:

(A) a + b will be positive for both a and b to be positive hence INCORRECT OPTION

(B) |a| + b will be positive for both a and b to be positive hence INCORRECT OPTION

(C) b - a May be positive for both a and b to be positive (e.g. b=3 and a=2) henceINCORRECT OPTION

(D) a/b will be positive for both a and b to be positive or Negative hence INCORRECT OPTION

(E) -a/b will always be Negative because an and b have same sign so a/b will be positive therefore -a/b will be Negative hence CORRECT

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Re: If ab > 0, which of the following must be negative?  [#permalink]

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Bunuel wrote:
If ab > 0, which of the following must be negative?

(A) a + b
(B) |a| + b
(C) b - a
(D) a/b
(E) -a/b

Kudos for a correct solution.

ab > 0 implies that ab have the same sign. Either both are positive or negative.

Pick 4 Numbers for a and b respectively. Two positives a = 10 and b = 5 and two negatives a = -10 b = -5. Plug in and POE as soon you find any non negative result. E will always be negative.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If ab > 0, which of the following must be negative?  [#permalink]

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Hi All,

These types of questions are perfect for TESTing VALUES. Since the question asks which of the following MUST be NEGATIVE, if an answer can EVER be positive then you can eliminate it immediately.

We're told that AB > 0. We're asked which of the 5 answers MUST be NEGATIVE...

IF....
A = 2
B = 3

Answer A: 2+3 = 5 NOT a match
Answer B: |2| + 3 = 5 NOT a match
Answer C: 3-2 = 1 NOT a match
Answer D: 2/3 = NOT a match

There's only one answer left....

Answer E: -2/3 = This IS a match

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Math Expert V
Joined: 02 Aug 2009
Posts: 8006
Re: If ab > 0, which of the following must be negative?  [#permalink]

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reto wrote:
Bunuel wrote:
If ab > 0, which of the following must be negative?

(A) a + b
(B) |a| + b
(C) b - a
(D) a/b
(E) -a/b

Kudos for a correct solution.

ab > 0 implies that ab have the same sign. Either both are positive or negative.

Pick 4 Numbers for a and b respectively. Two positives a = 10 and b = 5 and two negatives a = -10 b = -5. Plug in and POE as soon you find any non negative result. E will always be negative.

Hi,
if there would have been an answer choice b-lal.., your chosen numbers will give you negative results...
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Math Expert V
Joined: 02 Aug 2009
Posts: 8006
Re: If ab > 0, which of the following must be negative?  [#permalink]

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1
Bunuel wrote:
If ab > 0, which of the following must be negative?

(A) a + b
(B) |a| + b
(C) b - a
(D) a/b
(E) -a/b

Kudos for a correct solution.

Hi,
many of us have solved this with picking values..
But it is very important to look at the answer and pick up number ....
There may be many instances where the number picked up may give us a wrong answer and we may have two or three answer left .. we may have to again start with POE in remaining choices, although eventually we will come to correct answer after some more steps...
I feel if we know properties of number , we can easily get to the answer...

in this particular Q, we have both the numbers of same sign..
Therefore any addition, subtraction can give you any answer depending on the values we take...
However multiplication , division and sum of modulus of the numbers(i donot think GMAT will test us in more complicated issues) will always be the ones closer to the answer..
Here the division will always be positive if the fraction is positive ..., But will be -ive if there is a -ive sign in front
Or in other words it will take sign that is in front of fraction...
hence E will be correct..
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Math Expert V
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Posts: 58422
Re: If ab > 0, which of the following must be negative?  [#permalink]

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Bunuel wrote:
If ab > 0, which of the following must be negative?

(A) a + b
(B) |a| + b
(C) b - a
(D) a/b
(E) -a/b

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

You might solve this problem a different way, but let’s see how a chart would work. First, you need to figure out the possible signs of a and b that match the constraint ab> 0:
Attachment: 2015-06-29_1659.png [ 9.14 KiB | Viewed 4186 times ]

There are two scenarios that match: either a and b are both positive or they are both negative. That is, a and b have the same sign. Now test the answer choices.

(A) a + b: If a and b are both positive, then a + b will be positive. Eliminate (A).

(B) |a| + b: |a| will always be positive. If b is positive, |a | + b will be positive. Eliminate (B).

(C) b - a: If a and b are both positive, b - a could be either positive or negative. If b is 6 and a is 3, 6 - 3 = 3, which is positive. Eliminate (C).

(D) a/b: If a and b are both positive, a/b will be positive. Eliminate (D)

(E) -a/b. If a and b are both positive, -a/b will be negative. If a and b are both negative, -a/b will still be negative. (E) is the correct answer.
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Re: If ab > 0, which of the following must be negative?  [#permalink]

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If ab > 0, which of the following must be negative?
If the product of a and b is positive, a and b must have the same sign (either both positive or both negative). Therefore we're looking for the answer choice for which a and b will (with certainty) have opposite signs. E is the only option.
(A) a + b
(B) |a| + b
(C) b - a
(D) a/b
(E) -a/b
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Re: If ab > 0, which of the following must be negative?  [#permalink]

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If ab > 0, which of the following must be negative?

This means a & b have same signs.

(A) a + b =====> Positive
(B) |a| + b =====> Positive
(C) b - a =====> Positive
(D) a/b =====> Positive
(E) -a/b =====> Negative

Except for option E, where the value will always be negative, all other options can have positive values.

Hence, Answer is E
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Re: If ab > 0, which of the following must be negative?  [#permalink]

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whenever we see which of the following ,then always start with option E , most of times the answer is hidden at the last option which is commonly used by GMAT to waste the time of aspirant . we see that ab>0 then a or b must be -ve or +ve so only E states that it will be -ve in all cases . hence E
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Re: If ab > 0, which of the following must be negative?  [#permalink]

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Bunuel wrote:
If ab > 0, which of the following must be negative?

(A) a + b
(B) |a| + b
(C) b - a
(D) a/b
(E) -a/b

Since ab is greater than zero, a and b are either both positive or both negative. Scanning our answer choices, we see that -a/b must be negative. For example, if a and b are both positive, then -a/b is a negative divided by a positive, which results in a negative quotient. If a and b are both negative, then -a/b is a positive divided by a negative, which also results in a negative quotient.

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Re: If ab > 0, which of the following must be negative?  [#permalink]

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Bunuel wrote:
If ab > 0, which of the following must be negative?

(A) a + b
(B) |a| + b
(C) b - a
(D) a/b
(E) -a/b

Kudos for a correct solution.

ab>0

Thus , both a and b are positive or both are negative.

Option E) - a/b

a/b >0 , As both a and b have the same sign. When we multiply positive result of a/b by a negative sign. Ultimate result will be negative.

E is the correct answer. Re: If ab > 0, which of the following must be negative?   [#permalink] 21 Feb 2019, 16:06
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