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

Question

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

M37-14

Bunuel · Accepted Answer

Official Solution:

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

From  a^4b^3c^7 > 0  we can deduce the following:
 
 •  None of the unknowns is 0.
 
 •   b  and  c  have the same sign ( bc > 0 ). 
 
I.  \frac{b}{c} > 0 . Since  b  and  c  have the same sign, then this must be true.
 
II.  ab > 0 . We don't know anything about relationship between signs of  a  and  b . So, this option is not necessarily true.
 
III.  abc > 0 . We know that  bc > 0  but the only thing we know about  a  that it's non-zero: it can be positive as well as negative. So, this option is not necessarily true.

Answer: A

Chethan92 · Answer

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. A is the answer.

KSBGC · Answer

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.

A is the correct answer.

Archit3110 · Answer

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

KanishkM · Answer

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

Kinshook · Answer

bc > 0
b/c > 0

IMO A

Crytiocanalyst · Answer

I. \frac{b}{c} > 0 b<0, c<0 , yes definitely II. ab > 0 b can be <0 then the eqn is not satisfied and a can be >0 and <0 therefore cannot be true always III. abc > 0 b,c<0 and a>0 satisfied however if a<0 it cannot be satisfied Therefore IMO A

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions