Allegation/Mixture problem?

[datonman]

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.

[Brent@GMATPrepNow]

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

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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

[Mathsbuddy]

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

[ceilidh.erickson]

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).

[Mathsbuddy]

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.

[Jeff@TargetTestPrep]

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