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

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

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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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2
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.

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

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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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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.

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If abc > 0, then which of the following

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