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If abc > 0, then which of the following

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If abc > 0, then which of the following  [#permalink]

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New post 27 Mar 2019, 01:36
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If \(abc > 0\), then which of the following must be true?

a. \(\frac{a}{b} < 0\)

b. \(a > 0\)

c. \(\frac{ab}{c} > 0\)

d. \(bc < 0\)

e. a\(> bc\)

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Re: If abc > 0, then which of the following  [#permalink]

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New post 27 Mar 2019, 10:22
abc > 0.
Means either all 3 are positive or 2 positive and 1 negative.

Only option C satisfies this condition.
For any value of a, b and c.
Option C is always true.

C is the answer
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If abc > 0, then which of the following  [#permalink]

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New post 31 Mar 2019, 20:07
AkshdeepS Can you please explain the solution with case by case example for all 5 answer choices? I didn't understand how the answer was arrived.

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Re: If abc > 0, then which of the following  [#permalink]

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New post 31 Mar 2019, 20:24
Chethan92 wrote:
abc > 0.
Means either all 3 are positive or 2 positive and 1 negative.

Only option C satisfies this condition.
For any value of a, b and c.
Option C is always true.

C is the answer




If abc>0 then it can be all three positive or two negative and one positive. But ur answer says the other way out

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If abc > 0, then which of the following  [#permalink]

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New post 31 Mar 2019, 23:20
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AkshdeepS wrote:
If \(abc > 0\), then which of the following must be true?

a. \(\frac{a}{b} < 0\)

b. \(a > 0\)

c. \(\frac{ab}{c} > 0\)

d. \(bc < 0\)

e. \(a > bc\)



Let us first analysis all the possible cases of "\(abc > 0\)".

1) \(a > 0 , b > 0 , c > 0\), then \(abc > 0\) (always)

\(+ + +\)

2) \(a < 0 , b < 0 , c > 0\), then also \(abc > 0\)

\(- - +\)

Case 2 has two more variations as any 2 of the 3 variables can be positive and one negative

2.1) \(a < 0 , b > 0 , c < 0\)

\(- + -\)

2.2) \(a > 0 , b < 0 , c < 0\)

\(+ - -\)


All the above cases are those which are true as per given condition in the question.

Now we can check options which are 100% true according to above given information.

Remember we are not looking for could be true options. Let us try to prove the options false and eliminate one by one

a. \(\frac{a}{b} < 0\)

Not true for case (2)

As per case (2) a and b both are negative, and if we divide -a by -b, we well get positive result. Eliminate

b. \(a > 0\)

As per case (2) and (2.2) this information is not true. Eliminate

c. \(\frac{ab}{c} > 0\)

1) \((+)*(+)/(+) > 0\)

2)\((-) * (-)/ (+) > 0\)

2.1 \((-)* (+) / (-) > 0\)

2.2) \((+) *(-)/ (-) > 0\)

This information is true for every case. Correct.

d. \(bc < 0\)

As per case (1) and (2.2) this information is not true. Eliminate

e. \(a > bc\)

This information may or may not be true as no real values are known.

If a = 10 , b = 2, c = 1 (True)

If a = -5 , b = 2, c = -1

\(abc > 0\), but a is not greater than bc. (False)




Hope this helps.

As there are lot of signs there may be some typos :)
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Re: If abc > 0, then which of the following  [#permalink]

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New post 31 Mar 2019, 23:30
navingr8 wrote:
AkshdeepS Can you please explain the solution with case by case example for all 5 answer choices? I didn't understand how the answer was arrived.

Navin B



Hi,

navingr8

You can check the detailed solution.
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Re: If abc > 0, then which of the following  [#permalink]

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New post 02 Apr 2019, 19:15
AkshdeepS wrote:
If \(abc > 0\), then which of the following must be true?

a. \(\frac{a}{b} < 0\)

b. \(a > 0\)

c. \(\frac{ab}{c} > 0\)

d. \(bc < 0\)

e. a\(> bc\)


We see that either a, b, and c must be all positive,or, one positive and two negative.

Thus, we see that ab/c must be a positive number.

Answer: C
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Re: If abc > 0, then which of the following   [#permalink] 02 Apr 2019, 19:15
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