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# A part-time employee whose hourly wage was increased by 25

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Intern
Joined: 30 May 2005
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A part-time employee whose hourly wage was increased by 25 [#permalink]  12 Jul 2007, 18:51
A part-time employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?

A) 12.5%
B) 20%
C) 25%
D) 50%
E) 75%
Manager
Joined: 08 Jul 2007
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[#permalink]  12 Jul 2007, 19:12

This is probably not the best way to do the problem but I just plug in variables.

If the employee's wage is initially $4/hr then a 25% increase means his wage is now$5/hr.

If he is working 20 hours/week then initially he made $80/week. 4x=80. So x=20. Now, 5x=80 so x=16. % decrease=20/16=1.25, or C, 25%. Director Joined: 12 Jun 2006 Posts: 536 Followers: 1 Kudos [?]: 29 [0], given: 1 Re: Parts of Numbers Q5 [#permalink] 12 Jul 2007, 19:55 700dreamer wrote: A part-time employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced? A) 12.5% B) 20% C) 25% D) 50% E) 75% why not B? h(w) = hw (5/4h)(4/5w) = hw ... 80% decrease in working hours Manager Joined: 05 Jul 2007 Posts: 55 Followers: 0 Kudos [?]: 3 [0], given: 0 [#permalink] 12 Jul 2007, 20:11 The answer is B! I agree with ggarr I tried this using various numbers,$8 & $10,$9 and $11.25, etc. Then I used a variety of different hours/week. If you figure$8 before raise at 30 hrs/wk=$240/wk Then take the weekly wage$240 and divide it by the new hourly wage ($8*1.25=$10) and you have
240/10=24
Then use the comparison
24/30=.8, then 1-.8=.2= 20% reduce in workload.
I think it's B

Using briks123's example, you have to remember it's a decrease in workload, not an increase, so you take 16/20=.8, and subtract that from 1 to give you .2 or 20%, not 20/16. (BTW 20/16 gives you how much she would have to increase her workload to maintain the same income level after a cut in pay), but you were on the right track!

However, if anyone knows a way to figure this out using a special rule, please let me know! I need to work on speed and pacing, so I know I won't have time to plug in experimental numbers during the real GMAT!
Manager
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[#permalink]  12 Jul 2007, 20:27
TRUE! Silly me. Too much math.

Anyways, without using experimental numbers, you could solve it this way:

The employee's income is initially i=$x/hr. With the increase, his income is i=$1.25x/hr. So letting h1=the number of hours worked before the increase and h2=the number of hours worked after the increase, we get xh1=i and 1.25xh2=i.

h1=i/x
h2=i/1.25x

So h2/h1=x/1.25x=4/5. So the decrease is 1-4/5=1/5.

Sorry about the earlier mistake!
Manager
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[#permalink]  12 Jul 2007, 21:49
It is B ........
Let the person works for 100 days and earns 100 per hour.......
then the over all salary per 100 days is 100*100=10000.

Now,the income per hour increases by 25%.therefore the income becomes 125 per hour.Now he reduces the number of working hours do let that be X then the over all income should not change..therefore 10000/125=80.
therefore the number of days reduces by 20%..........
[#permalink] 12 Jul 2007, 21:49
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# A part-time employee whose hourly wage was increased by 25

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