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09 Jun 2007, 13:55
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Is ¦x - y¦>¦x - z¦?
(1) ¦y¦>¦z¦
(2) x < 0
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
6
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Please explain....
OA will be posted next day..
(1) ¦y¦>¦z¦
(2) x < 0
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
6
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Please explain....
OA will be posted next day..
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09 Jun 2007, 16:20
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The problem can be reworded as
is $$ |x-y| - |x-z| > 0 $$
$$ |x-y| $$ implies the following
$$ x - y $$ when $$ x - y > 0 $$
or $$ x - y $$ when $$ x > y $$
$$ y - x $$ when $$ x - y < 0 $$
or $$ y - x $$ when $$ x <y> z $$
$$ z - x $$ when $$ x < z $$
$$ | y | - | z | <0> 0 $$
$$ -y $$ when $$ y <0> 0 $$
$$ -z $$ when $$ z < 0 $$
This is pretty useless because its impossible to tell what is what on a number line
B says
$$ x < 0 $$
This is pretty useless by itself as well
Lets combine the two
From A and B , if x < 0 the intervals that we are worried about are y , z , 0
Doing the maths on the intervals
<------y-------z-------- 0
---y-z ---y-z ---z-y (whoops this is positive while y-z is negative)
This implies that we can't tell whether |x-y| - |x-z| > 0 by using both statements. Hence I think the answer is E
Note that I did not check for boundary condition like when x = y , x=z and x = 0 since I could deduce E from just looking at the intervals alone
I would be interested to run this by someone else who's a veteran of this method. I have just read these notes yesterday ...
is $$ |x-y| - |x-z| > 0 $$
$$ |x-y| $$ implies the following
$$ x - y $$ when $$ x - y > 0 $$
or $$ x - y $$ when $$ x > y $$
$$ y - x $$ when $$ x - y < 0 $$
or $$ y - x $$ when $$ x <y> z $$
$$ z - x $$ when $$ x < z $$
$$ | y | - | z | <0> 0 $$
$$ -y $$ when $$ y <0> 0 $$
$$ -z $$ when $$ z < 0 $$
This is pretty useless because its impossible to tell what is what on a number line
B says
$$ x < 0 $$
This is pretty useless by itself as well
Lets combine the two
From A and B , if x < 0 the intervals that we are worried about are y , z , 0
Doing the maths on the intervals
<------y-------z-------- 0
---y-z ---y-z ---z-y (whoops this is positive while y-z is negative)
This implies that we can't tell whether |x-y| - |x-z| > 0 by using both statements. Hence I think the answer is E
Note that I did not check for boundary condition like when x = y , x=z and x = 0 since I could deduce E from just looking at the intervals alone
I would be interested to run this by someone else who's a veteran of this method. I have just read these notes yesterday ...
