If $$x = 300 - y - z,$$ what is the value of $$x?$$

This topic has expert replies
Legendary Member
Posts: 1622
Joined: 01 Mar 2018
Followed by:2 members

If $$x = 300 - y - z,$$ what is the value of $$x?$$

by Gmat_mission » Tue Nov 10, 2020 8:19 am

00:00

A

B

C

D

E

Global Stats

If $$x = 300 - y - z,$$ what is the value of $$x?$$

(1) $$y = \dfrac{x + z}2$$

(2) $$x = \dfrac{y + z}2$$

Source: Manhattan GMAT

GMAT/MBA Expert

GMAT Instructor
Posts: 16084
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770

Re: If $$x = 300 - y - z,$$ what is the value of $$x?$$

by [email protected] » Wed Mar 30, 2022 8:33 am

00:00

A

B

C

D

E

Global Stats

Gmat_mission wrote:
Tue Nov 10, 2020 8:19 am
If $$x = 300 - y - z,$$ what is the value of $$x?$$

(1) $$y = \dfrac{x + z}2$$

(2) $$x = \dfrac{y + z}2$$

Source: Manhattan GMAT
Given: x = 300 − y − z
STRATEGY: In order to solve one of the equations below for x, I'll need to eliminate the variables y and z (and leave only x's).
So, I'm going to begin by solving the given equation for a variable other than x.

Let's solve the equation for y by first adding y to both sides of the equation to get: x + y = 300 − z
Now subtract x from both sides of the equation: y = 300 − z - x

Target question: What is the value of x?

Statement 1: y = (x + z)/2
Replace y with 300 − z - x to get: 300 − z - x = (x + z)/2
It appears that we still we're unable to eliminate the variable z. But to be extra safe, let's ensure that is the case.
First, multiply both sides of the equation by 2 to get: 600 − 2z - 2x = x + z
At this point, we can see that the variable z remains, which means there are infinitely many solutions to this linear equation.
As such, statement 1 is NOT SUFFICIENT

Statement 2: x = (y + z)/2
Replace y with 300 − z - x to get: x = (300 − z - x + z)/2
Multiply both sides of the equation by 2 to get: 2x = 300 − z - x + z
Simplify the right side: 2x = 300 - x
Add x to both sides: 3x = 300
We can see that x = 100
Since we can answer the target question with certainty, statement 2 is SUFFICIENT