If w + 2x = 150, 2w + 3y = 100, and x + 3z = 50, what is the

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

If w + 2x = 150, 2w + 3y = 100, and x + 3z = 50, what is the

by BTGmoderatorDC » Fri Dec 14, 2018 5:51 pm

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If w + 2x = 150, 2w + 3y = 100, and x + 3z = 50, what is the value of w + x + y + z?

A. 12.5
B. 20
C. 50
D. 100
E. It cannot be determined from the information provided.

OA D

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Fri Dec 14, 2018 5:51 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Sun Dec 16, 2018 11:40 am

Add all 5 equations
$$w+2x+2w+3y+x+3z=150+100+50$$
collect the like terms
$$\left(w+2w\right)+\left(2x+x\right)+\left(3y\right)+\left(3z\right)=300$$
$$3\left(w+x+y+z\right)=300$$
divide both sides by 3
$$\frac{3\left(w+x+y+z\right)}{3}=\frac{300}{3}$$
$$w+x+y+z=\ 100$$
$$answer\ is\ Option\ D$$

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Mar 14, 2019 3:55 pm

BTGmoderatorDC wrote:If w + 2x = 150, 2w + 3y = 100, and x + 3z = 50, what is the value of w + x + y + z?

A. 12.5
B. 20
C. 50
D. 100
E. It cannot be determined from the information provided.

OA D

Source: Princeton Review