GMAT Official Guide 2019 From 2000 to 2003, the number

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

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

by GMATGuruNY » Sun Jul 01, 2018 2:03 am

BTGmoderatorDC wrote: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

We can PLUG IN THE ANSWERS, which represent the number of employees in 2000.

Since the number of employees increases by 1/4 and then decreases by 1/3, the correct answer must be divisible by 4 and 3.
In other words, the correct answer must be a MULTIPLE OF 12.
Eliminate A, C and D.

Since the decrease (1/3) is greater than the increase (1/4), the number of employees must DECREASE from 2000 to 2006.
Implication:
The number of employees in 2000 must be GREATER than the number of employees in 2006 (100).
Eliminate E.

The correct answer is B.

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pm; Thanked: 1443 times; Followed by:247 members

by ceilidh.erickson » Mon Jul 02, 2018 10:58 am

Another strategy is to solve algebraically.

Let x = the # of employees in 2000.

An increase of 1/4 would mean that we would have 1 + 1/4 --> 5/4. A decrease of 1/3: 1 - 1/3 = 2/3.

(original #)(1/4 increase)(1/3 decrease) = number in 2006
x(5/4)(2/3) = 100
x(5/6) = 100
x = 100(6/5)
x = 120

The answer is B.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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Shahrukh_mbabreakspace: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Mon Jul 02, 2018 1:56 am; Followed by:2 members

by Shahrukh_mbabreakspace » Tue Jul 03, 2018 1:45 am

If 1/3 left between 2003 to 2006, this means 100 is 2/3 of people in 2003. This means in 2003, there were 150 people.
Now, 150 is after 1/4 increase. this means, it is 5/4 of 2000, so, it means there were 120 people.

________________________________________

Shahrukh Moin Khan
QA Mentor at Breakspace
https://www.mbabreakspace.com
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B.Tech IIT Roorkee

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Scott@TargetTestPrep: GMAT Instructor; Posts: 7243; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jul 04, 2018 6:28 pm

BTGmoderatorDC wrote: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

We can let x = the number of employees in 2000 and create the following equation:

x(1 + 1/4)(1 - 1/3) = 100

x(5/4)(2/3) = 100

x(10/12) = 100

x = 100(12/10)

x = 120

Answer: B

Scott Woodbury-Stewart
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[email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Jan 16, 2019 8:15 am

BTGmoderatorDC wrote: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

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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Bijaya Krushna Mohapatra: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Jul 23, 2019 8:52 pm

Re: GMAT Official Guide 2019 From 2000 to 2003, the number

by Bijaya Krushna Mohapatra » Fri Jan 17, 2020 2:47 am

2000- 2003 : 1/4 increase

Let in 2000 employees = X

so increased 1/4 means increased x/4 so total = x+ x/4 = 5x/4

2003-- 2006 : decrease by 1/3 So decrease from 5x/4

(5x/4)* 1/3 = 5x/12 (decreased value)

so remaining : 5x/4 - 5x/12 = 10x/12

This 10x/12 =100 employee's

So x = 120. ( so in 2000 total 120 employees were there

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