Allegation/Mixture 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 1:01 pm

Ian is paid an hourly wage, totaling $400 for h hours of work in a week, where h >0. If Ian's hourly wage increases by 25% and Ian decides to work 25% fewer hours each week, how much will Ian be paid in a week?

1.)$200
2.)$375
3.)$400
4.)$425
5.)$600

I can't help but think this is such a problem. I approached this problem by assuming he had $100 beforehand which goes up 25% and then and this was the problem...for the other 25%, would I have had to start from a hundred or just ninety? I'm thinking this in terms of principles apparently.

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Source: Beat The GMAT — Problem Solving | Mon Nov 10, 2014 1:01 pm

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

by Brent@GMATPrepNow » Mon Nov 10, 2014 1:10 pm

datonman wrote:Ian is paid an hourly wage, totaling $400 for h hours of work in a week, where h >0. If Ian's hourly wage increases by 25% and Ian decides to work 25% fewer hours each week, how much will Ian be paid in a week?

A) $200
B) $375
C) $400
D) $425
E) $600

Let's PLUG in some "nice" values and see what happens.

Ian is paid an hourly wage, totaling $400 for h hours of work in a week, where h > 0
Let's say that Ian works 100 hours per week AND he is paid $4/hour.
This gives us the total of $400 that he makes in a week.

If Ian's hourly wage increases by 25% and Ian decides to work 25% fewer hours each week, ...
25% of 4 = 1
So, Ian's $4/hour wage increases by $1 to $5/hour

25% of 100 = 25
So, the number of hours he works decreases by 25 to 75 hours

...how much will Ian be paid in a week?
In this scenario, Ian works 75 hours and earns $5/hour
(75)(5) = [spoiler]$375[/spoiler]

Answer: B

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Mon Nov 10, 2014 3:30 pm

Hi datonman,

I'm a big fan of TESTing VALUES (as Brent showed in his approach) and that's exactly how I would have solved this problem. It can also be solved with algebra (and a hint from the answers).

We're told that Ian is paid $400 for H hours of work, so....

H = number of hours of work
X = Pay/hour

(H)(X) = 400

We're told that Ian's hourly wage increases by 25% and the total number of hours he worlds decreases by 25%. This can be written as....

(.75H)(1.25X)

Multiplying these decimals might take awhile, so we can rewrite them as fractions:

(3/4)(H)(5/4)(X) =

(15/16)HX

From the beginning, we know that HX = 400

(15/16)(400)

Since 15/16 is less than 1, Ian's new pay will be a little less than $400. Looking at the answers, there's only one that's a little less than $400.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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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 4:22 am

Pay increase of 25% = 1.25 multiplier
Hourly decrease of 25% = 0.75 multiplier
$400 x 1.25 x 0.75 = $375

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

by ceilidh.erickson » Tue Nov 11, 2014 7:25 am

I approached this problem by assuming he had $100 beforehand which goes up 25% and then and this was the problem...for the other 25%, would I have had to start from a hundred or just ninety?

I'm not sure where you're getting the "ninety" here. If you're picking $100/hr as the original wage, then the wage would go up 25% to $125/hr.

An original total of $400 would mean that h = 4hrs originally. Therefore, a 25% decrease in hours would be 3 hours, according to the numbers you picked.

I think your question was - do we take the decrease from the original number of hours or the new number of hours? Since we're told that "Ian's hourly wage increases by 25% and Ian decides to work 25% fewer hours each week," it's implied that both the percent increase and the percent decrease are applied to the original values (of wage and hours, respectively).

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

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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 » Wed Nov 12, 2014 5:05 am

pooja181 wrote:i think ceilidh.erickson explain most correctly

Hi there Pooja,

Thanks for this link. I just tried the test there. It took 70 out of 75 minutes to answer the 45 maths questions, then the verbal reasoning test came up, which I randomly ticked to complete everything in the remaining 5 minutes. Assuming that I got 20% of the verbal correct by chance, that means that my maths score would be 192-9 = 183. Unfortunately, I have no idea what that means. The site doesn't tell you which questions were right or wrong, or what the maximum score is. In addition, 7 of the maths questions contained errors. Therefore, I wouldn't recommend this link to anyone. I feel like I've wasted 75 minutes of my life. Don't get me wrong, I enjoyed doing it and the experience of stress against the clock was worthwhile. If I had got the 7 misprinted questions right, I reckon my maths score would have been around 190. Is this good, bad or indifferent??? Thanks.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Nov 27, 2017 10:54 am

datonman wrote:Ian is paid an hourly wage, totaling $400 for h hours of work in a week, where h >0. If Ian's hourly wage increases by 25% and Ian decides to work 25% fewer hours each week, how much will Ian be paid in a week?

1.)$200
2.)$375
3.)$400
4.)$425
5.)$600

We can let the original number of hours worked = h and the original wage = w and we have:

wh = 400

After the 25% increase in wages and 25% decrease in number of hours, we have:

1.25w x 0.75h = 1.25 x 0.75 x wh

= 5/4 x 3/4 x 400

= 5/4 x 300

= $375

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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