Problem Solving

BTGModeratorVI wrote: ↑

Fri Jul 03, 2020 7:00 am

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: GMAT Prep Now

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
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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

BTGModeratorVI wrote: ↑

Fri Jul 03, 2020 7:00 am

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

Solution:

We see that both W and X are negative. Let’s let W = -2 and X = -1. So Y = 0 (notice that -1 is the midpoint of -2 and 0) and Z = -4 (notice that -2 is the midpoint of 0 and -4). Now, let’s check which answer choice yields the value of Z = -4.

A) -2X - 3W = 2 + 3 = 5 → No

B) 2W - 3X = -4 + 3 = -1 → No

C) 3W - 2X = -6 + 2 = -4 → Yes

If we can also show that neither choice D nor E yields -4, the choice C must be the correct answer. Otherwise, we need to use different values for W and X.

D) 3X - 2W = -3 + 4 = 1 → No

E) 2X - 3W = -2 + 6 = 4 → No

Answer: C