The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were

by Vincen » Wed Jun 24, 2020 2:14 am

Timer

00:00

Your Answer

Global Stats

The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by \(w\) feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of \(w?\)

(A) 25
(B) 50
(C) 75
(D) 100
(E) 200

[spoiler]OA=B[/spoiler]

Source: Official Guide

Quote

Source: Beat The GMAT — Problem Solving | Wed Jun 24, 2020 2:14 am

GMAT/MBA Expert

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

Re: The smaller rectangle in the figure above represents the original size of a parking lot before its length and width

by Scott@TargetTestPrep » Fri Apr 16, 2021 8:06 am

Vincen wrote: ↑
Wed Jun 24, 2020 2:14 am
2015-10-16_0901.png

The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by \(w\) feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of \(w?\)

(A) 25
(B) 50
(C) 75
(D) 100
(E) 200

[spoiler]OA=B[/spoiler]

Source: Official Guide

Solution:

We are given a diagram, which represents a parking lot with a smaller rectangle inside a larger rectangle. The dimensions of the smaller rectangle are 100 ft. by 150 ft., and the dimensions of the larger rectangle are (100 + w) ft. by (150 + w) ft. Since the area of the larger rectangle is twice that of the smaller rectangle, we can create the following area equation:
(w + 100)(w + 150) = 2(100 x 150)
w^2 + 250w + 15,000 = 30,000
w^2 + 250w – 15,000 = 0
(w + 300)(w – 50) = 0
w = -300 or w = 50
Since w must be positive, w must be 50.
Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]