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# Derek can read x pages in 5 minutes. At this rate, how long will it

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Math Expert
Joined: 02 Sep 2009
Posts: 43810
Derek can read x pages in 5 minutes. At this rate, how long will it [#permalink]

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02 Dec 2015, 05:51
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Difficulty:

15% (low)

Question Stats:

80% (00:24) correct 20% (00:35) wrong based on 95 sessions

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Derek can read x pages in 5 minutes. At this rate, how long will it take him to read p pages?

A. 5p/x
B. 5x/p
C. p/(5x)
D. 5/(px)
E. px/5
[Reveal] Spoiler: OA

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Joined: 11 Mar 2015
Posts: 18
GPA: 3.4
Re: Derek can read x pages in 5 minutes. At this rate, how long will it [#permalink]

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02 Dec 2015, 05:55
As given
x pages in 5 min, so pages per min = x/5
for P pages time = No .of pages /Pages per min
=p/x/5
=5p/x

Hence A
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Re: Derek can read x pages in 5 minutes. At this rate, how long will it [#permalink]

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02 Dec 2015, 06:13
Bunuel wrote:
Derek can read x pages in 5 minutes. At this rate, how long will it take him to read p pages?

A. 5p/x
B. 5x/p
C. p/(5x)
D. 5/(px)
E. px/5

x page in 5 mins

i.e. 1 page in 5/x mins

i.e. p pages in (5/x)*p

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Re: Derek can read x pages in 5 minutes. At this rate, how long will it [#permalink]

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02 Feb 2018, 11:25
Bunuel wrote:
Derek can read x pages in 5 minutes. At this rate, how long will it take him to read p pages?

A. 5p/x
B. 5x/p
C. p/(5x)
D. 5/(px)
E. px/5

The rate for Derek is x/5, is it takes Derek p/(x/5) = 5p/x minutes.

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Joined: 22 May 2016
Posts: 1329
Derek can read x pages in 5 minutes. At this rate, how long will it [#permalink]

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02 Feb 2018, 14:43
Bunuel wrote:
Derek can read x pages in 5 minutes. At this rate, how long will it take him to read p pages?

A. 5p/x
B. 5x/p
C. p/(5x)
D. 5/(px)
E. px/5

Another approach: assign values. Pick values that prevent your having to work with fractions less than 1 (e.g. don't pick x = 1 and p = 2)

Let x = 10 pages
Let p = 20 pages

Derek reads $$\frac{10pgs}{5mins}$$. How long to read 20 pages?

Mental math:
Twice as many pages, twice as much time = 10 minutes, OR

$$\frac{10pgs}{5mins}=\frac{20pgs}{X mins}$$
$$10 * X = 5 * 20$$
$$10X = 100$$
$$X = 10$$
minutes

Use x = 10, p = 20. Find the answer that yields 10.

Eliminate D and E immediately. Look at numerators and denominators. D is too small and E is too large.

A. 5p/x
$$\frac{(5*20)}{10}= \frac{100}{10} = 10$$ MATCH

B. 5x/p
$$\frac{(5*10)}{20}= \frac{50}{20}=\frac{5}{2}$$ NOT A MATCH

C. p/(5x)
$$\frac{20}{5*10}= \frac{20}{50}$$ NOT A MATCH

D. 5/(px) - dismiss. It's tiny.

E. px/5 - dismiss. It's huge.

*With this method, you must check all answers that you cannot eliminate immediately, such as D and E here. If more than one answer yields 10 (rare), pick a new set of numbers.
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Derek can read x pages in 5 minutes. At this rate, how long will it   [#permalink] 02 Feb 2018, 14:43
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