Tom read a 480-page book by reading a fixed number of pages each day.

Question

Tom read a 480-page book by reading a fixed number of pages each day. If he had read 16 pages more each day, he would have finished the book 5 days earlier. How many days did Tom spend reading the book?

A. 10 
 B. 12 
 C. 15 
 D. 16 
 E. 18

Bunuel · Accepted Answer

Tom read a 480-page book by reading a fixed number of pages each day. If he had read 16 pages more each day, he would have finished the book 5 days earlier. How many days did Tom spend reading the book?

A. 10
B. 12
C. 15
D. 16
E. 18

Let's assume that Tom spent  d  days reading the 480-page book. Therefore, he read an average of  \frac{480}{d}  pages per day.

If he had increased his reading speed by 16 pages per day, he would have finished the book in  d-5  days, which means he would have read an average of  \frac{480}{d-5}  pages per day.

Since we know that the second reading speed is 16 pages per day faster than the first one, we can set up the equation  \frac{480}{d}=\frac{480}{d-5}-16 . At this point, it would be more effective to substitute the answer choices rather than attempting to solve for the value of  d .

After testing answer choices, we find that option C, which corresponds to  d=15 , satisfies the equation:  \frac{480}{15}=\frac{480}{15-5}-16 . Therefore, Tom spent 15 days reading the book.

Answer: C

samsonfred76 · Answer

See Img for a back up method.

VeritasPrepRon · Answer

I like this approach a lot, but on the GMAT it is a little math intensive. Seeing that 480 is divisible by 48 is trivial, but seeing that it's not divisible by 64 might take a little bit longer.

Great approach that works well on these types of questions, and works particularly well on ratio questions. I'd advise using this concept if you're quick at math and don't like setting up algebraic formulae. All roads lead to Rome, as I like to say.

Thanks!
-Ron

mau5 · Answer

Let the rate of reading the book(the number of pages being read each day) be p and the total number of days be d. Thus, r*d = 480. Also, (r+16)*(d-5) = 480. Thus, both d and (d-5) have to be a factor of 480. That eliminates options B,D,E. Left with A and C. Pick up any one and try plugging in. In any case, you plug-in only once.

C.

Enael · Answer

Started writing the equation and it took too long.

Then realized it's pretty easy using values:

Started with B: 
12 days = 40 pages a day
7 days (i.e. 12 - 5) wouldn't yield 56 pages a day to reach 480 total. It would yield 7*56 = 392 (still missing 78 pages)

Went to C:
15 days = 32 pages a day
10 days = 48 pages a day (32 + 16).

Equation holds, so it is the answer.

Hope it helps.

KarishmaB · Answer

Algebra is one way of doing it. Another is by plugging in values. As usual, we start with the middle value so that we can go up or down depending on whether the days are short or in excess.

Say number of days = 15
The Tom reads 480/15 = 32 pages everyday.

In 5 days, he reads 32*5 pages which when split equally across the rest of the days such that each day gets 16 pages gives us 32*5/16 = 10 days

These 10 days are 5 less than 15 and hence everything fits.

Answer (C)

Of course, we could have needed to do this calculation once again in case (C) did not fit.

For example, trying (B), 480/12 = 40 pages
So in 5 days, the pages read = 40*5. When we try to split them equally among the leftover days such that each day gets 16 pages, we do not get an integral number of days. Hence this will not be the answer.

GMATGuruNY · Answer

All of the values in the problem are INTEGERS.
Implication:
The correct combination of times -- the ACTUAL number of days and the HYPOTHETICAL number of days if Tom finishes 5 days earlier -- will almost certainly divide cleanly into the amount of reading work (480 pages).

The answer choices imply the following options for the actual time and the hypothetical time of 5 fewer days:
 A: 10 days --> 5 days 
B: 12 days --> 7 days
 C: 15 days --> 10 days 
D; 16 days --> 11 days
E: 18 days --> 13 days

Only A and C offer combinations that divide cleanly into 480.
 He would have finished the book 5 days earlier by reading 16 pages a day more. 
When the correct answer is plugged in, the rate for the hypothetical time must be 16 pages greater than the rate for the actual time.

Test C:
Rate for the actual time  = \frac{pages}{days} = \frac{480}{15} = 32  pages per day
Rate for the hypothetical time of 5 fewer days  = \frac{pages}{days }= \frac{480}{10} = 48  pages per day
Rate difference = 48-32 = 16 pages per day
Success!

C

bumpbot · Answer

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Tom read a 480-page book by reading a fixed number of pages each day.

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