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
GMAT Official Guide 2019 From 2000 to 2003, the number
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We can PLUG IN THE ANSWERS, which represent the number of employees in 2000.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
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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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.
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.
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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.
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Now, 150 is after 1/4 increase. this means, it is 5/4 of 2000, so, it means there were 120 people.
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We can let x = the number of employees in 2000 and create the following equation: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
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
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From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4BTGmoderatorDC 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 = 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
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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
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