Word problem

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datonman: Senior | Next Rank: 100 Posts; Posts: 53; Joined: Wed May 28, 2014 9:36 pmFollowed by: 1 member

by datonman » Mon Nov 10, 2014 10:23 am

Each employee of company x works in exactly one of the departments 'G' and 'H'. Currently, there are 1,500 employees at company X and 60% of the employees at company x works in department 'G'.

If every employee currently at company x remains at company x and remains in the department they are in, then what is the number of new employees who must be hired to work in department 'G' so that 85% of the employees working in company x work in department 'G'?

A)1,275
B)1,700
C)2,500
D)3,750
E)4,000

I got lost right after i realized and i could be wrong here...that the 1500 employees times the 60 percent would equal 900 and the 600 together would constitute the 1500. But then in the second paragraph, i'd have to realize which part: department G or company x would have the 600 or 900 and then multiply by 85%. Again i could be wrong here.

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Source: Beat The GMAT — Problem Solving | Mon Nov 10, 2014 10:23 am

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Mon Nov 10, 2014 10:54 am

Let's take it step by step:

1500 employees
60% of 1500 = 900 in G
40% of 1500 = 600 in H

Now suppose that G hires n new employees. We want (900 + n) to be 85% of the total, which is now (1500 + n).

This gives us (900 + n) = .85 * (1500 + n), which I'd solve on test day as follows:

900 + n = .85*1500 + .85n
subtract from both sides:: .15n = .85*1500 - 900
multiply both sides by 100:: 15n = 85*1500 - 90000
divide both sides by 15:: n = 85*100 - 6000 = 8500 - 6000 = 2500

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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 » Mon Nov 10, 2014 11:32 am

datonman wrote:Each employee of company x works in exactly one of the departments 'G' and 'H'. Currently, there are 1,500 employees at company X and 60% of the employees at company x works in department 'G'.

If every employee currently at company x remains at company x and remains in the department they are in, then what is the number of new employees who must be hired to work in department 'G' so that 85% of the employees working in company x work in department 'G'?

A)1,275
B)1,700
C)2,500
D)3,750
E)4,000

Current number of employees who work in G = 60% of 1500 = 900.
We can PLUG IN THE ANSWERS, which represent the number of new employees who must be hired to work in G.
When the correct answer choice is plugged in, (new total employees in G)/(new total employees) = 85/100 = 17/20.

Since percent problems on the GMAT tend to involve very round numbers, the correct answer choice is probably B, C or E.
Start with the middle value.

Answer choice C: 2500
If 2500 employees are hired to work in G, we get:
(new total G employees)/(new total employees) = (900+2500)/(1500+2500) = (9+25)/(15+25) = 34/40 = 17/20.
Success!

The correct answer is C.

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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 » Mon Nov 10, 2014 11:42 am

datonman wrote:Each employee of company x works in exactly one of the departments 'G' and 'H'. Currently, there are 1,500 employees at company X and 60% of the employees at company x works in department 'G'.

If every employee currently at company x remains at company x and remains in the department they are in, then what is the number of new employees who must be hired to work in department 'G' so that 85% of the employees working in company x work in department 'G'?

A)1,275
B)1,700
C)2,500
D)3,750
E)4,000

An alternate approach is to treat this as a MIXTURE problem.

Of the CURRENT employees, the percentage who work in G = 60%.
Of the NEW employees, the percentage who will work in G = 100%. (Since all of the new employees will work in G.)
When the two groups are combined to form a MIXTURE, the percentage who work in G = 85%.

Let C = current employees and N = new employees.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for C and N on the ends and the percentage for the mixture in the middle.
C 60%-----------85%-----------100% N

Step 2: Calculate the distances between the percentages.
C 60%----25-----85%----15-----100% N

Step 3: Determine the ratio in the mixture.
The required ratio of C to N is equal to the RECIPROCAL of the distances in red.
C:N = 15:25 = 1500:2500.

Since C:N = 1500:2500, the 1500 current employees must be combined with 2500 new employees.

The correct answer is C.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Tue Nov 11, 2014 4:31 am

Using abbreviations:
t = total number of employees = 1500
g = number of employees in dept G = 0.6 x 1500 = 900
h = number of employees in dept H = 0.4 * 1500 = 600

Capital letter denote new values
N = number of new employees:

T = 1500 + N
G = 900 + N = 0.85 x (1500 + N)
H = h = 600

Using G above:
900 + N = 1275 + 0.85N
0.15N = 1275 - 900 = 375
N = 375/0.15 = 2500

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Tue Nov 11, 2014 4:34 am

Or even simpler:

Dept G has 0.6 x 1500 = 900 staff

900 + N = 0.85 x (1500 + N)

Solving for N gives: N = 2500

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KristenH88: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Wed Feb 20, 2013 8:35 pm; Thanked: 1 times

by KristenH88 » Tue Nov 11, 2014 8:31 am

MUCH BETTER! You should see how much space and time I used with the back solve and reduction method. No way. Thank you.

Mathsbuddy wrote:Or even simpler:

Dept G has 0.6 x 1500 = 900 staff

900 + N = 0.85 x (1500 + N)

Solving for N gives: N = 2500

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