From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4. From 2003 to 2006, the num

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

by Vincen » Sun Apr 25, 2021 10:31 am

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From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4. From 2003 to 2006, the number of employees at this company decreased by a factor of 1/3. If there were 100 employees at the company in 2006, how many employees were there at the company in 2000?

A. 200

B. 120

C. 100

D. 75

E. 60

Answer: B

Source: Official Guide

Source: Beat The GMAT — Problem Solving | Sun Apr 25, 2021 10:31 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4. From 2003 to 2006, the

by Brent@GMATPrepNow » Fri May 21, 2021 7:13 am

Vincen wrote: ↑
Sun Apr 25, 2021 10:31 am
From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4. From 2003 to 2006, the number of employees at this company decreased by a factor of 1/3. If there were 100 employees at the company in 2006, how many employees were there at the company in 2000?

A. 200

B. 120

C. 100

D. 75

E. 60

Answer: B

Source: Official Guide

From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4
Let x = the number of employees in 2000
So, the number of employees in 2003 = x + (1/4)x
= (5/4)x

From 2003 to 2006, the number of employees at this company decreased by a factor of 1/3
(5/4)x = the number of employees in 2003
So, the number of employees in 2006 = (5/4)x - (1/3)((5/4)x
= (5/4)x - (5/12)x
= (15/12)x - (5/12)x
= (10/12)x
= (5/6)x

If there were 100 employees at the company in 2006, how many employees were there at the company in 2000 ?
We can write: (5/6)x = 100
Multiply both sides by 6 to get; 5x = 600
Solve: x = 600/5 = 120

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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