If abc ≠ 0, is abc 0 ?

Question

If  abc ≠ 0 , is  abc > 0  ?

(1)  |a –b | = |a| - |b| 
 
(2)  |b + c| = |b| + |c|

mikemcgarry · Answer

A brilliant question! Thanks, Mike :-)

avigadl · Answer

from 2 you get that b,c should have the same sign therefore the question collapses to a>?0 NS.
from 1 you get that a,b should have same sign (try different signs and get contradiction) the question collapses to c>?0 NS.
Combine together, NS as if all tree positive then its true if all negative you get false.
WDYT?

Sent from my iPhone using GMAT Club Forum

chetan2u · Answer

Hi..

Clearly each sentence talks of two variables, hence insufficient individually..

Combined..
(1)  |a –b | = |a| - |b| 
I tells us that a>b or a=b and also both a and B are of same sign.
You can square also to find it..
 a^2+b^2-2ab=a^2+b^2-2|a||b|........ 2|a||b|-2ab=0... 
So a*b is POSITIVE and both are of same SIGN.
 
(2)  |b + c| = |b| + |c|
Here B and C are of same sign.

So combined all three are of same SIGN..
But if all three are positive, and is YES 
If all three are NEGATIVE, and is NO
Insuff

C

septwibowo · Answer

#STATEMENT 1
- Plugin value, we can get a&b both positive or a&b both negative.
- Hence, insufficient.

#STATEMENT 2
- Plugin value, we can get b&c both positive or b&c both negative.
- Hence, insufficient.

Anyway statement #1 and #2 only talk about 2 out of 3 variable - INSUFFICIENT from the begining.

#BOTH STATEMENT TOGETHER
We have two combinations :
1. a,b and c all POSITIVE = YES for the question.
2. a,b and c all NEGATIVE = NO for the question.
INSUFFICIENT

Therefore, the answer is E.

Is this correct? :oops:

septwibowo · Answer

chetan2u

Why you choose C although both statement insufficient?

Mo2men · Answer

Let's take 2 & -2 and plug them across the statements (or choose any 2 values). I choose a number and its apposite to make calculations easy.

(1)  |a –b | = |a| - |b|

(a,b) = (2, 2)
 |2 –2 | = |2| - |2| = 0

(a,b) = (-2, -2)
 |-2 +2 | = |2| - |2| = 0

(a,b) = (-2, 2) and (2,- 2) are invalid as RHS does not equal LHS

Conclusion is a & b must have same sign but c can be any number with any sign

Insufficient

(2)  |b + c| = |b| + |c|

(b,c) = (2, 2)
 |2 + 2| = |2| + |2| = 4

(b,c) = (-2,-2)
 |-2 -2| = |-2| + |-2| = 4

(b,c) = (-2, 2) and (2,- 2) are invalid as RHS does not equal LHS

Conclusion is b & c must have same sign but a can be any number with any sign

Insufficient

Combining 1 & 2

Case I : 2, 2 , 2.................Answer is Yes

Case II : -2, -2,-2..............Answer is NO

Insufficient

Answer: E

If abc ≠ 0, is abc > 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

My Rewards