Answer: B.
Discussed at:
42. Coordinate Geometry
If y is a negative number greater than -8, is x greater than the average
(arithmetic mean) of y and -8 ?
(1) On the number line, x is closer to -8 than it is to y.
(2) x = 4y
Given:
.
Q: is x greater than the average of -8 and x? Or: is
? -->
?
-----
{-8}
-----
{average}
-----
{y} (average of y and -8 is halfway between y and -8).
(1) On the number line, x is closer to -8 than it is to y.
Now, as
is closer to
than it (
) is to
, then
is either in the green area, so less
than average OR in the red area, so also less than average. Answer to the question is NO.
Sufficient.
(2)
--> is
? --> is
? --> is
? We don't now that. Not
sufficient. (we've gotten that if
(for instance if
), then the answer to the
question is YES, but if
(for instance if
), then the answer to the question is
NO.)
Answer: A.
Discussed at:
43. Rate Problem

Car X leaves Town A at 2 p.m. and drives toward Town B at a constant rate of m miles per hour. Fifteen minutes later, Car Y begins driving from Town B to Town A at a constant rate of n miles an hour. If both Car X and Car Y drive along the sameroute, will Car X be closer to Town A or Town B when it passes Car Y ?
(1) Car X arrives in Town B 90 minutes after leaving city A.(2) Car Y arrives in Town A at the same time Car X arrived in Town B.(P meeting point). Question: is (1) Car X arrives in Town B 90 minutes after leaving city A. No info about car Y. Not sufficient.(2) Car Y arrives in Town A at the same time Car X arrived in Town B --> X needs 15 min longer than Y to cover the same distance (as Y starts 15 min after X) --> rate of X < rate of Y(m<n). Also, after they meet X and Y will need the same time to get to their respective destinations (as they arrived at the same time) --> the distance covered by Y after they meet (PA=nt) at higher speed, will obviously be more than the distance covered by X after they meet (PB=mt) at lower speed (or algebraically as m<n, mt<nt --> ). So . Sufficient.Answer: B.Discussed at:
?
44. Number PropertiesIs product 2*x*5*y an even integer?