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# If a^4b^3c^7 > 0, then which of the following must be true?

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If a^4b^3c^7 > 0, then which of the following must be true?  [#permalink]

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24 Jan 2019, 02:40
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If $$a^4b^3c^7 > 0$$, then which of the following must be true?

I. $$\frac{b}{c} > 0$$

II. $$ab > 0$$

III. $$abc > 0$$

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

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If a^4b^3c^7 > 0, then which of the following must be true?  [#permalink]

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24 Jan 2019, 02:47
$$a^4$$ will always be positive.
The question boils down to $$b^3c^7 > 0$$, means both b and c are both positive or both negative.

Statement 1:

As b and c should both be +ve or -ve at the same time.
b/c > 0.
Always true.

Statement 2:

ab > 0
Is a is +ve and b is +ve, then ab>0
Or If both a and b are -ve, then ab>0
If either one is -ve, then ab<0
May or may not be true.

Statement 3:

Same again. If bc is +ve and a is +ve, then abc > 0.
If bc is +ve and a is -ve, then abc < 0.
Not always true.

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Re: If a^4b^3c^7 > 0, then which of the following must be true?  [#permalink]

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24 Jan 2019, 02:59
Bunuel wrote:
If $$a^4b^3c^7 > 0$$, then which of the following must be true?

I. $$\frac{b}{c} > 0$$

II. $$ab > 0$$

III. $$abc > 0$$

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

Given

$$a^4b^3c^7 > 0$$

$$a^4$$ is always positive but we don't know whether a is positive or negative.

$$b^3$$could be positive or negative.

$$c^7$$ could be positive or negative.

$$a^4b^3c^7>0.$$

From this information , it's clear that either b and c will both be negative or both be positive.

I. $$\frac{b}{c} > 0$$. Always true. b and c will have the same sign. Result must be greater than 0.

II. $$ab > 0$$. could be true. we don't know the sign of a.

III. $$abc > 0$$. bc will always be positive but we don't know about a. could be . MUST not be.

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Re: If a^4b^3c^7 > 0, then which of the following must be true?  [#permalink]

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24 Jan 2019, 04:28
$$a^4b^3c^7 > 0$$

for it to hold true
a can be either +/- and b & c have to be of same sign

so
out of given options
only $$\frac{b}{c} > 0$$
would be valid
IMO A

Bunuel wrote:
If $$a^4b^3c^7 > 0$$, then which of the following must be true?

I. $$\frac{b}{c} > 0$$

II. $$ab > 0$$

III. $$abc > 0$$

A. I only
B. II only
C. III only
D. I and II only
E. I and III only
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Posts: 994
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If a^4b^3c^7 > 0, then which of the following must be true?  [#permalink]

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24 Jan 2019, 04:40
Bunuel wrote:
If $$a^4b^3c^7 > 0$$, then which of the following must be true?
I. $$\frac{b}{c} > 0$$

II. $$ab > 0$$

III. $$abc > 0$$
A. I only
B. II only
C. III only
D. I and II only
E. I and III only

IMO A

$$a^4b^3c^7 > 0$$, has to be true, then

a can be +ive or -ive
b has to be -ive, since it is having an odd power
c has to be -ive, since it is having an odd power

$$\frac{b}{c} > 0$$, This will always hold good

II. $$ab > 0$$, can be Yes when a -ive and b -ive and a No when a +ive and b -ive

III. $$abc > 0$$, can be Yes when a +ive and b -ive and a No when a -ive and b -ive
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Re: If a^4b^3c^7 > 0, then which of the following must be true?  [#permalink]

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08 Oct 2019, 02:41
Bunuel wrote:
If $$a^4b^3c^7 > 0$$, then which of the following must be true?

I. $$\frac{b}{c} > 0$$

II. $$ab > 0$$

III. $$abc > 0$$

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

bc > 0
b/c > 0

IMO A
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Re: If a^4b^3c^7 > 0, then which of the following must be true?   [#permalink] 08 Oct 2019, 02:41
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