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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Tom read a book containing 480 pages by reading the same num

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Director  Joined: 11 Jun 2007
Posts: 618

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Difficulty:   65% (hard)

Question Stats: 69% (02:53) correct 31% (03:19) wrong based on 172 sessions

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Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book?

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

m15 q20

so i was able to set up the equation correctly

[480 / x] = [480 / (x+16)] + 5
the working it out
[480 / x] = [480 + 5(x + 16)] / (x+16)
480x + 7680 = 5x^2 + 560x
5x^2 + 80x -7680
finally dividing by 5
x^2 + 16x - 1536

my question is without a calculator on the test what is the easiest way/ best plan of attack to realize that
x^2 + 16x - 1536 is...
(x + 48) (x - 32)
x = 32

then finally 480/x = 480/32 = 15 which is the answer

there was no way i was able to do this within 2 minutes.. too much factorizing and room for error.. for those larger quadratic equations. would backsolving be a good option here? please advise, thanks.

Originally posted by beckee529 on 30 Oct 2007, 07:18.
Last edited by Bunuel on 02 Apr 2013, 15:30, edited 1 time in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 60579

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m15 q20

Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book?
A. 10
B. 12
C. 15
D. 16
E. 18

Say the number of days Tom spent reading the book was $$d$$. Then:

The number of pages he read per day would be $$\frac{480}{d}$$;
The number of pages he would read per day with an increased speed would be $$\frac{480}{d-5}$$;

We are told that the number of pages for the second case was 16 pages per day more, so $$\frac{480}{d}=\frac{480}{d-5}-16$$. At this point it's much better to plug answer choices rather than solve for $$d$$. Answer choice C fits: $$\frac{480}{15}=32=\frac{480}{15-5}-16$$.

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VP  Joined: 10 Jun 2007
Posts: 1002

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beckee529 wrote:
Tom read a book containing 480 pages reading the same number of pages each day. If he had read 16 pages a day more, he would have finished the book 5 days earlier. How many days did Tom spend reading the book?

10
12
15
16
18

so i was able to set up the equation correctly

[480 / x] = [480 / (x+16)] + 5
the working it out
[480 / x] = [480 + 5(x + 16)] / (x+16)
480x + 7680 = 5x^2 + 560x
5x^2 + 80x -7680
finally dividing by 5
x^2 + 16x - 1536

my question is without a calculator on the test what is the easiest way/ best plan of attack to realize that
x^2 + 16x - 1536 is...
(x + 48) (x - 32)
x = 32

then finally 480/x = 480/32 = 15 which is the answer

there was no way i was able to do this within 2 minutes.. too much factorizing and room for error.. for those larger quadratic equations. would backsolving be a good option here? please advise, thanks.

If I get to a point where the equation takes too long to solve, I would just start plugging in the answer choices...
Intern  Joined: 30 Oct 2007
Posts: 5

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1
Actually u can set up 2 equation
P--stands for the pages
D--stands for the days

1) P*D=480 (we want to find the Days, so P=480/D)
2) (P+16)(D-5)=480 => PD-5P+16D-80=480

as the 1) stated u can put 1) into 2)
=> 480-5P+16D-80=480 => 16D-5P=80
put the bold one into it => 16D-5(480/D)=80

the we get the final equation 16D^2-2400=80D (divide 16)

=> D^2-5D-150=0
(D-15)(D+10)=0 so D=15 days
Intern  Joined: 10 Apr 2012
Posts: 22
Concentration: Finance, Economics
GMAT 1: 760 Q50 V44

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1
See Img for a back up method.
Attachments Note_20130401_173652_05.jpg [ 111.42 KiB | Viewed 8451 times ]

Veritas Prep GMAT Instructor Joined: 11 Dec 2012
Posts: 312

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samsonfred76 wrote:
See Img for a back up method.

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
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Joined: 10 Oct 2012
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beckee529 wrote:
Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book?

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

m15 q20

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.
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SVP  Joined: 06 Sep 2013
Posts: 1525
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beckee529 wrote:
Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book?

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

m15 q20

so i was able to set up the equation correctly

[480 / x] = [480 / (x+16)] + 5
the working it out
[480 / x] = [480 + 5(x + 16)] / (x+16)
480x + 7680 = 5x^2 + 560x
5x^2 + 80x -7680
finally dividing by 5
x^2 + 16x - 1536

my question is without a calculator on the test what is the easiest way/ best plan of attack to realize that
x^2 + 16x - 1536 is...
(x + 48) (x - 32)
x = 32

then finally 480/x = 480/32 = 15 which is the answer

there was no way i was able to do this within 2 minutes.. too much factorizing and room for error.. for those larger quadratic equations. would backsolving be a good option here? please advise, thanks.

For these questions Backsolving is definetely the best approach.

Cheers
J Intern  Joined: 13 Dec 2013
Posts: 34
GMAT 1: 620 Q42 V33

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2
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.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10004
Location: Pune, India

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beckee529 wrote:
Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book?

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

m15 q20

so i was able to set up the equation correctly

[480 / x] = [480 / (x+16)] + 5
the working it out
[480 / x] = [480 + 5(x + 16)] / (x+16)
480x + 7680 = 5x^2 + 560x
5x^2 + 80x -7680
finally dividing by 5
x^2 + 16x - 1536

my question is without a calculator on the test what is the easiest way/ best plan of attack to realize that
x^2 + 16x - 1536 is...
(x + 48) (x - 32)
x = 32

then finally 480/x = 480/32 = 15 which is the answer

there was no way i was able to do this within 2 minutes.. too much factorizing and room for error.. for those larger quadratic equations. would backsolving be a good option here? please advise, thanks.

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.

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.
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