If the crime rate in a certain region dropped by 28% last

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

by BTGmoderatorDC » Sat Jul 27, 2019 5:36 pm

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If the crime rate in a certain region dropped by 28% last year to a rate of 500 crimes per 100,000 citizens, what was the approximate rate before the drop?

A. 500 crimes per 128,000 citizens

B. 640 crimes per 128,000 citizens

C. 695 crimes per 128,000 citizens

D. 640 crimes per 100,000 citizens

E. 695 crimes per 100,000 citizens

OA E

Source: Veritas Prep

Source: Beat The GMAT — Problem Solving | Sat Jul 27, 2019 5:36 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jul 28, 2019 2:55 am

BTGmoderatorDC wrote:If the crime rate in a certain region dropped by 28% last year to a rate of 500 crimes per 100,000 citizens, what was the approximate rate before the drop?

A. 500 crimes per 128,000 citizens

B. 640 crimes per 128,000 citizens

C. 695 crimes per 128,000 citizens

D. 640 crimes per 100,000 citizens

E. 695 crimes per 100,000 citizens

Since the rate dropped by 28%, the current rate is equal to 72% of the previous rate:
500/100,000 = 72/100 * x
x = (500*100)/(72*100,000)
x ≈ (7*100)/100,000
x ≈ 700 per 100,000

The correct answer is E.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Aug 06, 2019 4:48 pm

BTGmoderatorDC wrote:If the crime rate in a certain region dropped by 28% last year to a rate of 500 crimes per 100,000 citizens, what was the approximate rate before the drop?

A. 500 crimes per 128,000 citizens

B. 640 crimes per 128,000 citizens

C. 695 crimes per 128,000 citizens

D. 640 crimes per 100,000 citizens

E. 695 crimes per 100,000 citizens

OA E

Source: Veritas Prep

Let x be the number of crimes per 100,000 citizens, before the drop. We can create the equation:

0.72x = 500

x ≈ 695

Alternate Solution:

We can use the percent change formula: (New - Old)/Old x 100%. Since the % change was a decrease, we consider it as -28%:

(500 - Old)/Old x 100 = -28

(500 - Old)/Old = -0.28

Letting Old = x, we have:

(500 - x)/x = -0.28

500 - x = -0.28x

500 = 0.72x

694.4 = x

695 = x

Thus, the previous rate was 695 crimes per 100,000.

Answer: E

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