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If ab^2 > 0 and ac < 0, then which of the following must be true?

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If ab^2 > 0 and ac < 0, then which of the following must be true?  [#permalink]

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New post 23 Jan 2019, 01:52
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If \(ab^2 > 0\) and \(ac < 0\), then which of the following must be true?


I. \(ab >0\)

II. \(b^2c < 0\)

III. \(a*c^2 > 0\)

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

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Re: If ab^2 > 0 and ac < 0, then which of the following must be true?  [#permalink]

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New post 23 Jan 2019, 03:02
Bunuel wrote:
If \(ab^2 > 0\) and \(ac < 0\), then which of the following must be true?
I. \(ab >0\)

II. \(b^2c < 0\)

III. \(a*c^2 > 0\)

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


IMO D

If \(ab^2 > 0\) and \(ac < 0\)

From above you can imply the following
a is +ive, b can be +ive or -ive and c is -ive

I. \(ab >0\), True or False , by using the above

II. \(b^2c < 0\), Always true

III. \(a*c^2 > 0\), Always true
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Re: If ab^2 > 0 and ac < 0, then which of the following must be true?  [#permalink]

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New post 23 Jan 2019, 03:27
Bunuel wrote:
If \(ab^2 > 0\) and \(ac < 0\), then which of the following must be true?


I. \(ab >0\)

II. \(b^2c < 0\)

III. \(a*c^2 > 0\)

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


Given:
\(ab^2 > 0\) - Since b^2 must be positive only, a would be positive too (to get positive product)

and \(ac < 0\) - Since a is positive (obtained above), c must be negative to get negative product

So we have 'a' positive, 'c' negative and no idea about 'b'.

I. \(ab >0\)
Since we have no idea about b, we don't know whether ab will be positive or not.

II. \(b^2c < 0\)
b^2 will be positive (note that none of these is 0) and c is negative so product will be negative. This is true.

III. \(a*c^2 > 0\)
a is positive and c^2 will be positive too. So product is positive. This is true too.

Answer (D)
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Re: If ab^2 > 0 and ac < 0, then which of the following must be true?  [#permalink]

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New post 23 Jan 2019, 04:41
Bunuel wrote:
If \(ab^2 > 0\) and \(ac < 0\), then which of the following must be true?


I. \(ab >0\)

II. \(b^2c < 0\)

III. \(a*c^2 > 0\)

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



Given,

\(ab^2>0.\)

a must be positive. a>0. It is not possible to tell whether b is positive or negative as \(b^2>0\). don't know anything about b.

ac<0. we know that a>0. So, c<0.

I. \(ab >0\)

a>0. don't know anything about b. could be true. MUST not one.

II. \(b^2c < 0\)

b>0 and c<0. Must be true.

III. \(a*c^2 > 0\)

a>0 and \(c^2>0\). Must be true.

D is the correct answer.
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Re: If ab^2 > 0 and ac < 0, then which of the following must be true?  [#permalink]

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New post 23 Jan 2019, 05:40
Bunuel wrote:
If \(ab^2 > 0\) and \(ac < 0\), then which of the following must be true?


I. \(ab >0\)

II. \(b^2c < 0\)

III. \(a*c^2 > 0\)

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



for expression ab^2>0 & ac<0 to be valid
a +ve , b -ve or +ve and c -ve

in that case only
case
II. \(b^2c < 0\)

III. \(a*c^2 > 0\)
would be valid
IMO D
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Re: If ab^2 > 0 and ac < 0, then which of the following must be true?   [#permalink] 23 Jan 2019, 05:40
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If ab^2 > 0 and ac < 0, then which of the following must be true?

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