Note:
|x-y| = |y-x| = the distance between y and x
|x| = |x-0| = the distance between x and 0
RashedVai wrote:
Is |a-c| + |a| = |c|?
(1) ab > bc
(2) ab < 0
Question stem, rephrased:
Is |c-a| + |a-0| = |c-0| ?
In words:
If the distance between c and a is added to the distance between a and 0, is the result equal to the distance between c and 0?
The answer will YES if a is between c and 0, as in the following cases:
c.....a.....0 --> (distance between c and a) + (distance between a and 0) = distance between c and 0
0.....a.....c --> (distance between c and a) + (distance between a and 0) = distance between c and 0
The answer will NO if a is NOT between c and 0, as in the following cases:
a.....c.....0 --> (distance between c and a) + (distance between a and 0) > distance between c and 0
0.....c.....a --> (distance between c and a) + (distance between a and 0) > distance between c and 0
Statement 1: ab>bcIf b=1, a=2 and c=1, then a is NOT between c and 0, so the answer to the question stem is NO.
If b=1, a=-1 and c=-2, then a IS between c and 0, so the answer to the question stem is YES.
INSUFFICIENT.
Statement 2: ab<0No information about c.
INSUFFICIENT.
Statements combined: ab>bc and ab<0Case 1: b>0, implying in Statement 1 that a>c and in Statement 2 that a<0
Linking together c<a and a<0, we get:
c<a<0
Since a is between c and 0, the answer to the question stem is YES.
Case 2: b<0, implying in Statement 1 that a<c and in Statement 2 that a>0
Linking together 0<a and a<c, we get:
0<a<c
Since a is between c and 0, the answer to the question stem is YES.
In both cases, the answer to the question stem is YES.
SUFFICIENT.
_________________
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As your tutor, I won't simply teach you how I would approach problems.
I'll unlock the best way for YOU to solve problems.
Available all over the world for virtual sessions and in NYC for live sessions.
For more information, please email me at GMATGuruNY@gmail.com.