If a 0, b 0 and c 0, is a(b - c) = 0?

Question

If  a > 0 ,  b > 0  and  c > 0 , is  a(b - c) = 0 ?

(1)  b - c = c - b

(2)  \frac{b}{c} = \frac{c}{b}

flyingbunny · Answer

Answer is D.

a>0, b>0, c>0
for 1), b-c=c-b ==>> 2b=2c ==>>b=c
therefore a(b-c)=0, suff

for 2), b/c=c/b ==>> b^2=c^2
because b>0, c>0, ==>>b=c
therefore a(b-c)=0, suff

yezz · Answer

if a>0, b>0, c>0, is a(b-c)=0?

I. b-c = c-b 
II. b/c = c/b

A(B-C) = 0 and as a>0 thus it is POSSIBLE ONLY WHEN B = C

from 1

b-c-c+b = 0 thus 2b = 2c thus b=c...suff

from 2

b/c = c/b all +ve thus b^2 = c^2 thus b=c....suff

D

fozzzy · Answer

For statement 2

we get  b^2=c^2  then  b^2 - C^2 = 0  >>  (b-c) (b+c) = 0

Why is this manipulation incorrect?

Zarrolou · Answer

That is not incorrect.

You get  (b-c) (b+c) = 0  so one (or both) terms equal zero. However we know that both b and c are positive, so (b+c) is positive as well, so b-c=0 
Hence  a(b-c)=0  => sufficient

fozzzy · Answer

So basically B+C is just redundant information once we solve till that point? Hence that case is ignored and we focus on the second case?

Zarrolou · Answer

I do not know what you mean by "redundant information", but yes: we know that  b+c  cannot be zero, so the other term ( b-c ) must be zero.

All we get from  b^2-c^2=0  in this problem is that  b-c=0

Bunuel · Answer

If a > 0, b > 0 and c > 0, is a(b - c) = 0?

Is  a(b - c) = 0 ? --> is  a=0  or  b-c=0 ? Since given that  a > 0 , then the questions basically asks whether  b-c=0 .

(1) b - c = c - b -->  2b-2c=0  -->  b-c=0 . Sufficient.
 
(2) b/c = c/b -->  b^2=c^2  -->  (b-c)(b+c)=0  -->  b+c=0  or  b-c=0  but since  b  and  c  are positive, then  b+c>0 . Therefore  b-c=0 . Sufficient.

Answer: D.

AmritaSarkar89 · Answer

Whoo!!! another super tricky question which can take you off the hooks during exam.
The simplest way to look at this question is we have 3 conditions a>0, b>0 and c>0 so thy are positive numbers but can be integers or fraction. (always proceed with this thought process - even if irrelevant here, it helps in the long run).
Question asks if a(b-c)=0 now we know a>0 thus a not equal to 0 hence b-c=0 or B=C

Statement 1
B-c=0
B=c Sufficient

Statement 2
c^2=B^2
|C|=|B|
since they are both greater than 0 hence c=b
Suffcienet
Answer is D.

+kudos I need to unlock the exams

anairamitch1804 · Answer

Nice Explanation Bunuel. Thanks for sharing your approach.

Nixondutta · Answer

This is a yes/ no question.
After simplifying the equation we get,
if b=c then b-c = 0. so the question depends on two equation.
1. Whether a is 0.
or 2. b=c.

option 1 says b = c . sufficient.
option 2 says b^2=c^c. no as b>0 and c>0, b=c. sufficient.

aakash13111989 · Answer

Bunuel  Nice approach and explanation. Its a tricky question. Thanks

Basshead · Answer

Is a = 0 or b = c?

(1)  b - c = c - b

2b = 2c 
 b = c
 
SUFFICIENT.

(2)  \frac{b}{c} = \frac{c}{b} 
 2b = 2c 
 b = c

SUFFICIENT.

Answer is D.

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 > 0, b > 0 and c > 0, is a(b - c) = 0?

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