Brent@GMATPrepNow wrote: ↑Wed Mar 04, 2020 3:40 pm
W and X are points on the number line, and W < X < 0. If X is the midpoint of line segment WY, and W is the midpoint of line segment YZ, then what is the value of Z in terms of W and X?
A) -2X - 3W
B) 2W - 3X
C) 3W - 2X
D) 3X - 2W
E) 2X - 3W
Answer:
C
Source:
www.gmatprepnow.com
APPROACH #1: Plot the points on the number line
X is the midpoint of line segment WY
We get:
W is the midpoint of line segment YZ
We get:
At this point let's add a midpoint between Z and W
Now recognize that
X-W = the distance between W and X
Furthermore, since every pair of successive points are equidistant, we can have the following distances.
What is the value of Z in terms of W and X?
If we start from point W, we must move TWO SPACES to the left to get to point Z
So, Z = W - (
X-W) - (
X-W)
= W - X + W - X + W
= 3W - 2X
Answer: C
------------------------------------------
APPROACH #2: Use the INPUT-OUTPUT strategy
First find values of W, X, Y and Z that satisfy the given information.
Here's one possible set of values:
We can see that, when
W = -3,
X = -2 and
Y = -1, the answer to the question (What is the value of Z?) is
-5
In other words, when we INPUT
W = -3 and
X = -2, the resulting OUTPUT is Z =
-5
From here we need to check all 5 answers choices to see which one yields and OUTPUT of
-5 when we INPUT
W = -3 and
X = -2
A) -2X - 3W = -2(
-2) - 3(
-3) =
13. No good. We want
-5.
B) 2W - 3X = 2(
-3) - 3(
-2) =
0. No good. We want
-5.
C) 3W - 2X = 3(
-3) - 2(
-2) =
-5. PERFECT!
D) 3X - 2W = 3(
-2)- 2(
-3) =
0. No good. We want
-5.
E) 2X - 3W = 2(
-2) - 3(
-3) =
5. No good. We want
-5.
Answer: C
