GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 07:21

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58432
If ab^2 > 0 and ac < 0, then which of the following must be true?  [#permalink]

### Show Tags

23 Jan 2019, 02:52
00:00

Difficulty:

5% (low)

Question Stats:

80% (00:57) correct 20% (01:08) wrong based on 87 sessions

### HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58432
Re: If ab^2 > 0 and ac < 0, then which of the following must be true?  [#permalink]

### Show Tags

04 Jul 2019, 08:23
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

Official Solution:

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 the product of two numbers to be positive they must have the same sign and since the square of a number is always more than or equal to 0, then $$ab^2 > 0$$ implies that $$a>0$$ and $$b \neq 0$$

Since $$a>0$$, from above, then $$ac < 0$$ implies that $$c < 0$$

So, we have that: $$a > 0$$, $$c < 0$$ and $$b \neq 0$$

Let's check the options:

I. $$ab >0$$. Not true if $$b < 0$$

II. $$b^2c < 0$$. Always true since $$b^2 > 0$$ and $$c < 0$$

III. $$a*c^2 > 0$$. Always true since $$a > 0$$ and $$c^2 > 0$$

_________________
##### General Discussion
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: If ab^2 > 0 and ac < 0, then which of the following must be true?  [#permalink]

### Show Tags

23 Jan 2019, 04:02
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
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: If ab^2 > 0 and ac < 0, then which of the following must be true?  [#permalink]

### Show Tags

23 Jan 2019, 04:27
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.

_________________
Karishma
Veritas Prep GMAT Instructor

VP
Joined: 31 Oct 2013
Posts: 1465
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If ab^2 > 0 and ac < 0, then which of the following must be true?  [#permalink]

### Show Tags

23 Jan 2019, 05:41
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.

GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5031
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If ab^2 > 0 and ac < 0, then which of the following must be true?  [#permalink]

### Show Tags

23 Jan 2019, 06:40
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
Re: If ab^2 > 0 and ac < 0, then which of the following must be true?   [#permalink] 23 Jan 2019, 06:40
Display posts from previous: Sort by