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Math Expert V
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From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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Difficulty:   15% (low)

Question Stats: 80% (01:44) correct 20% (02:00) wrong based on 1034 sessions

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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

NEW question from GMAT® Official Guide 2019

(PS15957)

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Joined: 04 Aug 2010
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Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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1
Bunuel 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.

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Intern  B
Joined: 04 Feb 2013
Posts: 14
Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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1
Bunuel 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

NEW question from GMAT® Official Guide 2019

(PS15957)

5/4 x 4/3 (Population in 2000) = 100, solving we get X = 60
Intern  B
Joined: 21 May 2017
Posts: 40
Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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3
2

Let population in 2000 be x.
Let population in 2003 be y.
Population in 2006 is 100
2y/3 = 100
y = 150

Also, population in 2003 is 5x/4
So, 5x/4 = 150
x = 120
Intern  B
Joined: 03 Feb 2016
Posts: 10
Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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2
2
In 2000 Let employees x
In 2003 employees then 5x/4
In 2006 employees then (5x/4-5x/12)=10x/12
10x/12=100
X=120

Sent from my iPhone using GMAT Club Forum
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3230
Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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5
5

Solution

Given:
• From 2000 to 2003, the number of employees at a certain company increased by a factor of $$\frac{1}{4}$$
• From 2003 to 2006, the number of employees at this company decreased by a factor of $$\frac{1}{3}$$
• There were 100 employees at the company in 2006

To find:
• The number of employees in the company in 2000

Approach and Working:
Let us assume the number of employees in the company in 2000 is 12x [12 = LCM (4,3)]

Given that, from 2000 to 2003, the number of employees at a certain company increased by a factor of $$\frac{1}{4}$$
• Therefore, the number of employees in 2003 = $$12x + \frac{1}{4} * 12x = 12x + 3x = 15x$$

It is also given that, from 2003 to 2006, the number of employees at this company decreased by a factor of $$\frac{1}{3}$$
• Therefore, the number of employees in 2006 = $$15x – \frac{1}{3} * 15x = 15x – 5x = 10x$$

As there were 100 employees in 2006, we can write
• 10x = 100
Or, x = 10
Or, 12x = 10 * 12 = 120

Hence, the correct answer is option B.

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Intern  B
Joined: 02 Sep 2015
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Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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2
2000 -> 2003: x -> x + x/4
2003 -> 2006: (x + x/4) -> (x + x/4) - (x +x/4)/3
2006: 100

100 = (x + x/4) - (x +x/4)/3
x = 120

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Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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3
1
Bunuel 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

Letting x = the number of employees in 2000, we have:

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

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

x(10/12) = 100

x = 100(12/10)

x = 120

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Intern  B
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Concentration: Marketing, Human Resources
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From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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B is correct:

x+(1/4)x = (5/4)x
(5/4)x - (1/3)(5/4)x = (5/4)x[1 - 1/3] = (5/4)x.(2/3) = (5/6)x = 100

x = 120
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From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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Let no of employees in 2000 be x
2000 to 2003: increase of 25% (i.e. 1/4), 2003 to 2006 decrease of 33% (i.e. 1/3)
Hence,

x * 1.25 * (1-(1/3)) = 100
x = (100*3)/(2*1.25) = 120

Hence B
VP  P
Joined: 07 Dec 2014
Posts: 1230
Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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1
Bunuel 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

let x=number of employees in 2000
x*5/4*2/3=100
x=120
B
Intern  S
Joined: 09 Nov 2016
Posts: 49
Location: India
Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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1
It is a very simple problem.. Its straightforward X=120..
Option B.
Intern  B
Joined: 30 Aug 2018
Posts: 31
Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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1
Is it wise to use options here?
Like choose a middle option 'C' at first.

Option C: 100 so 100 + 1/4 of 100 = 125. Now 125- 125/3 = 125-41 = 84 (approx), but as of question 100 employes are there in 2006. So option C rejected.

Option B: 120, so 120+1/4 of 120 = 150. Now 150-150/3= 100. As of question, there are 100 employees in 2006. So Option B is correct.

Is it wise to solve the problem by this method of using options?
Intern  S
Joined: 09 Nov 2016
Posts: 49
Location: India
From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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prav04 wrote:
Is it wise to use options here?
Like choose a middle option 'C' at first.

Option C: 100 so 100 + 1/4 of 100 = 125. Now 125- 125/3 = 125-41 = 84 (approx), but as of question 100 employes are there in 2006. So option C rejected.

Option B: 120, so 120+1/4 of 120 = 150. Now 150-150/3= 100. As of question, there are 100 employees in 2006. So Option B is correct.

Is it wise to solve the problem by this method of using options?

Hi prav04

Yes you can. That sometimes helps to solve questions quickly where forming equations and solving them is time consuming.
This approach is fine.

Hope this helps! Please give +1 Kudos if you like this response!! Manager  S
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Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q50 V29
GPA: 3.8
WE: Engineering (Manufacturing)
Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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1
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
There were 100 employees at the company in 2006

So , let the employee be X in 2000 , so increased by 1/4 factor totals =(1+1/4)=5/4X
Now, in 2003 decreased by 1/3 =(1-1/3)=2/3 so total (5/4)*(2/3)X eaquals 100 employee in 2006
In 2006
(5/4)*(2/3)X=100

Solve for x
x=120

Thanks
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4228
Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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Top Contributor
Bunuel 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

Cheers,
Brent
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Location: United States
GMAT 1: 740 Q49 V42
From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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1
 Calculate Relative Values for Each Year

$$2000: x$$

$$2003: x + \frac{1}{4}x \rightarrow \frac{5}{4}x$$

$$2006: (x - \frac{1}{3}x) \times \frac{5}{4}x \rightarrow \frac{2}{3}x \times \frac{5}{4}x \rightarrow \frac{5}{6}x$$

 Solve

$$\frac{5}{6}x = 100$$
$$x = 100 \times \frac{6}{5}$$
$$x = 120$$

Manager  S
Joined: 23 Apr 2018
Posts: 164
Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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shouri wrote:
Bunuel 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

NEW question from GMAT® Official Guide 2019

(PS15957)

5/4 x 4/3 (Population in 2000) = 100, solving we get X = 60

hey, when you decrease something by a factor of 1/3, the number will be multiplied by 2/3 (1-1/3 = 2/3) and not 4/3, that's why you get 60 as an answer, whereas the answer is 120 (B)
Manager  B
Joined: 24 Sep 2018
Posts: 117
Location: India
Re: From 2000 to 2003, the number of employees at a certain company increa  [#permalink]

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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) Re: From 2000 to 2003, the number of employees at a certain company increa   [#permalink] 17 Jan 2020, 03:45
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