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 · Accepted 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

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

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