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

It is currently 20 Feb 2019, 15:44

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Prep Hour

     February 20, 2019

     February 20, 2019

     08:00 PM EST

     09:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST
  • Online GMAT boot camp for FREE

     February 21, 2019

     February 21, 2019

     10:00 PM PST

     11:00 PM PST

    Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Director
Director
avatar
Joined: 11 Jun 2007
Posts: 863
Tom read a book containing 480 pages by reading the same num  [#permalink]

Show Tags

New post Updated on: 02 Apr 2013, 14:30
4
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

69% (02:50) correct 31% (03:22) wrong based on 216 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, 06:18.
Last edited by Bunuel on 02 Apr 2013, 14:30, edited 1 time in total.
Edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53020
Re: Tom read a book containing 480 pages by reading the same num  [#permalink]

Show Tags

New post 02 Apr 2013, 14:30
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: \(\frac{480}{15}=32=\frac{480}{15-5}-16\).

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1340
Re: quad eqn  [#permalink]

Show Tags

New post 30 Oct 2007, 06:48
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
Intern
avatar
Joined: 30 Oct 2007
Posts: 7
  [#permalink]

Show Tags

New post 30 Oct 2007, 06:53
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
Intern
avatar
Joined: 10 Apr 2012
Posts: 22
Concentration: Finance, Economics
GMAT 1: 760 Q50 V44
Re: Tom read a book containing 480 pages reading the same number  [#permalink]

Show Tags

New post 02 Apr 2013, 14:21
6
1
See Img for a back up method.
Attachments

Note_20130401_173652_05.jpg
Note_20130401_173652_05.jpg [ 111.42 KiB | Viewed 6657 times ]

Veritas Prep GMAT Instructor
User avatar
Joined: 11 Dec 2012
Posts: 312
Re: Tom read a book containing 480 pages reading the same number  [#permalink]

Show Tags

New post 02 Apr 2013, 14:25
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
_________________

Ron Awad
Veritas Prep | GMAT Instructor
Save $100 on Veritas Prep GMAT Courses and Admissions Consulting Services
Veritas Prep Reviews

Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 611
Premium Member
Re: Tom read a book containing 480 pages by reading the same num  [#permalink]

Show Tags

New post 02 Apr 2013, 20:43
1
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.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1694
Concentration: Finance
GMAT ToolKit User
Re: Tom read a book containing 480 pages by reading the same num  [#permalink]

Show Tags

New post 13 Nov 2013, 06:10
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.
If you start with C the answer should pop in 40 seconds tops.

Cheers
J :)
Intern
Intern
avatar
Joined: 13 Dec 2013
Posts: 36
GMAT 1: 620 Q42 V33
GMAT ToolKit User
Re: Tom read a book containing 480 pages by reading the same num  [#permalink]

Show Tags

New post 18 Jul 2014, 17:25
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
User avatar
D
Joined: 16 Oct 2010
Posts: 8888
Location: Pune, India
Re: Tom read a book containing 480 pages by reading the same num  [#permalink]

Show Tags

New post 18 Sep 2017, 04:09
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.

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.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9869
Premium Member
Re: Tom read a book containing 480 pages by reading the same num  [#permalink]

Show Tags

New post 11 Oct 2018, 09:37
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: Tom read a book containing 480 pages by reading the same num   [#permalink] 11 Oct 2018, 09:37
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.