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After the first week of training for an upcoming race

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After the first week of training for an upcoming race  [#permalink]

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New post 22 Apr 2017, 09:46
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After the first week of training for an upcoming race, Dinesh begins the second week of his training program by increasing his weekly running mileage by 50%. After three weeks, he catches a cold and has to reduce his current weekly mileage by 40% for the final week of training. By what percent did Dinesh's weekly mileage change from the first week to the final week.
    A)15% decrease
    B)10% decrease
    C)no change
    D)10% increase
    E)20% increase
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Re: After the first week of training for an upcoming race  [#permalink]

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New post 22 Apr 2017, 10:41
Fazil Nadeem Hussain wrote:
After the first week of training for an upcoming race, Dinesh begins the second week of his training program by increasing his weekly running mileage by 50%. After three weeks, he catches a cold and has to reduce his current weekly mileage by 40% for the final week of training. By what percent did Dinesh's weekly mileage change from the first week to the final week.
    A)15% decrease
    B)10% decrease
    C)no change
    D)10% increase
    E)20% increase



let 1st week mileage =100mph
then 2nd wee = 150mph
final week = 150*(1-40/100)
150 *60/100 =90mph
thus initial =100mph and final is 90mph
total 10Mph decrease or 10% decrease

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After the first week of training for an upcoming race  [#permalink]

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New post 22 Apr 2017, 10:45
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Fazil Nadeem Hussain wrote:
After the first week of training for an upcoming race, Dinesh begins the second week of his training program by increasing his weekly running mileage by 50%. After three weeks, he catches a cold and has to reduce his current weekly mileage by 40% for the final week of training. By what percent did Dinesh's weekly mileage change from the first week to the final week.
    A)15% decrease
    B)10% decrease
    C)no change
    D)10% increase
    E)20% increase


Method I - multiply successive multipliers

Let X = original number of miles per week
Increase of 50% in second week = (1.5)X
Decrease by 40% in final week = 1 - .40 = .60 of (1.5)X*

Or (.6)(1.5)(X) = .90 X

He ends up at 90% of his original miles per week, which is a 10% decrease. Answer B.

* it is not .60 multiplied by original X. He has increased his mileage from X to 1.5X. The second calculation (decrease by 40% = 60%) depends on the first, which has happened already.

Method II - plug in numbers and track on weeks [original miles = 10, derive 50% increase = 15, derive 40% decrease = 9]

1. Week 1, he runs \(10\) miles: -----------------------------------------------END WEEK 1
2. After week 1, he increases by 50% = \(15\) -------------------------------END WEEK 2
3. Nothing happens in week 3 --------------------------------------------------END WEEK 3
4. Week 4, final, decreases current mileage by 40%, .60(15)= \(9\) ----END WEEK 4

Percent change = \(\frac{Change}{original}\) x 100 => 10 - 9 = 1 (Change). Original is 10.
\(\frac{1}{10}\) x 100 = 10%, and because he went from 10 to 9, it's a 10% decrease
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Re: After the first week of training for an upcoming race  [#permalink]

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New post 08 May 2018, 10:33
helloSimba wrote:
After the first week of training for an upcoming race, Dinesh begins the second week of his training program by increasing his weekly running mileage by 50%. After three weeks, he catches a cold and has to reduce his current weekly mileage by 40% for the final week of training. By what percent did Dinesh's weekly mileage change from the first week to the final week.
    A)15% decrease
    B)10% decrease
    C)no change
    D)10% increase
    E)20% increase


If the first week was n, after the final week his mileage was 1.5(0.6)n = 0.9n.

Thus, the change was a decrease of 10%.

Answer: B
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Re: After the first week of training for an upcoming race &nbs [#permalink] 08 May 2018, 10:33
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