GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jul 2018, 08:31

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Tom read a book containing 480 pages by reading the same num

Author Message
TAGS:

### Hide Tags

Director
Joined: 11 Jun 2007
Posts: 891

### Show Tags

Updated on: 02 Apr 2013, 15:30
4
2
00:00

Difficulty:

65% (hard)

Question Stats:

67% (02:24) correct 33% (03:02) wrong based on 190 sessions

### HideShow timer Statistics

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
Joined: 02 Sep 2009
Posts: 47037

### Show Tags

02 Apr 2013, 15:30
3
4
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: $$\frac{480}{15}=32=\frac{480}{15-5}-16$$.

_________________
##### General Discussion
VP
Joined: 10 Jun 2007
Posts: 1397

### Show Tags

30 Oct 2007, 07:48
1
1
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: 8

### Show Tags

30 Oct 2007, 07:53
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

### Show Tags

02 Apr 2013, 15:21
5
1
See Img for a back up method.
Attachments

Note_20130401_173652_05.jpg [ 111.42 KiB | Viewed 5043 times ]

Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 313

### Show Tags

02 Apr 2013, 15:25
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
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 619

### Show Tags

02 Apr 2013, 21:43
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.
_________________
SVP
Joined: 06 Sep 2013
Posts: 1869
Concentration: Finance

### Show Tags

13 Nov 2013, 07:10
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: 38
Schools: Fuqua (I), AGSM '16
GMAT 1: 620 Q42 V33

### Show Tags

18 Jul 2014, 18:25
1
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.
GMAT Club Legend
Joined: 16 Oct 2010
Posts: 8124
Location: Pune, India

### Show Tags

18 Sep 2017, 05:09
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.
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Re: Tom read a book containing 480 pages by reading the same num   [#permalink] 18 Sep 2017, 05:09
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.