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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Pat is reading a book that has a total of 15 chapters. Has [#permalink]

Show Tags

14 Nov 2009, 07:24

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

55% (02:10) correct
45% (01:03) wrong based on 216 sessions

HideShow timer Statictics

Pat is reading a book that has a total of 15 chapters. Has Pat read at least 1/3 of the pages in the book?

(1) Pat has just finished reading the first 5 chapters. (2) Each of the first 3 chapters has more pages than each of the other 12 chapters in the book..

I am able to get the answer by putting numbers but I am unable to frame up an algebraic expression. Also, its taking almost 2 mins for me to solve this type of question which I think is relatively easy. So should I be worried because I got my G-date in next week. Please give an opinion. Thanks a lot friends.

Re: Pat is reading a book that has a total of 15 chapters. Has [#permalink]

Show Tags

14 Nov 2009, 19:49

I can create the equations, but stuck at solving them

From the question (i.e. from choice (2)) Let x - Total no. of pages of Chapter 1 to 3 y - Total no. of pages of Chapter 3 to 15 Total no. of pages = 3x + 12y

Let Z = No. of chapters Pat completed reading. Question is Is Z >= 1/3(3x+12y)?

1. Z = 3x + 2y Not sufficient (No information on no. of pages per chapter)

2. x > y

Combining both 1. and 2, question becomes Is (3x+2y) >= 1/3(3x+12y) given x>y?

I tried Bunuel's suggestion on the other thread "Remember we can add inequalities when their signs are in the same direction and subtract inequalities when their signs are in the opposite direction." Still struggling...

Re: Pat is reading a book that has a total of 15 chapters. Has [#permalink]

Show Tags

15 Nov 2009, 04:51

1

This post received KUDOS

Statement 1:

Completely useless. Each of the first five chapters can be just 1 page long, or they can each be 50 pages long.

We just don't know: INSUFFICIENT

Statement 2:

Let just say the first three chapters each has 20 pages in the book and the rest of the chapters have only 19:

60/(300-12) is much less than 1/3

But if we say that each of the first three chapters has 100 pages and the rest of the 12 chapters has only 1: 300/(300+12) is much greater than 1/3

So still INSUFFICIENT

Statements 1 and 2

Because no exact relationship between the number of pages and the chapters are defined, we can still come up with scenarios in which Pat reads more or less than 1/3rd of the book while still satisfying Statements 1 and 2:

Less than 1/3:

(100+100+100+1+1)/(100+100+100+1+1+10*99)=23% (less than 33.3%)

More than 1/3:

(100+100+100+99+99)/(100+100+100+12*99)=33.4% (more than 33.3%)

we can further prove this: 5*x/(15*x) = 1/3 BUT (3*y+3*x)/(15*x) is greater than 1/3 if we definte y>x BUT (3*y+3*1)/(15*x) is less than 1/3 if x is greater than 1 and y is greater than x

Re: Pat is reading a book that has a total of 15 chapters. Has [#permalink]

Show Tags

15 Nov 2009, 04:57

2

This post received KUDOS

1

This post was BOOKMARKED

Hi,

There is no need to form equations and try and solve this as it will be very time consuming.

Just look at it logically.

Question stem : Has Pat read 1/3 the pages in a book containing 15 chapters?

Therefore we have to know something about how many pages he has read as well as the total number of pages in the book (or the number of pages per chapter which would give us the total number of pages).

St. (1) : He has read 5 chapters.

This does not tell us how many pages he has read therefore Insufficient.

St. (2) : Each of the first 3 chapters has more pages than each of the other 12 chapters in the book.

This tells us something about the structure of the book but does not tell us anything about how many pages Pat might have read.

This is where I disagree with the OA and think the answer should be E.

Now, St. (1) and (2) together :

If all the remaining 12 chapters have equal number of pages and the first three have more than those many pages per chapter, then Pat would most certainly have read more than 1/3 of the book had he read the first five chapters.

BUT we are not told anything about the relationship between the other chapters of the book. Therefore we cannot conclude this.

If the first 3 chapters have 10 pages each, the next two have 1 page each, and the last 10 have 8 pages each, the ratio of the pages read to total pages (considering he has read 5 chapters) would be : 32/112.

Now compare this to 1/3 , which can also be written as 32/96.

Since 32/112 is smaller we can safely say that he has not read 1/3 of the pages.

Thus even together, the statements are insufficient.

Re: Pat is reading a book that has a total of 15 chapters. Has [#permalink]

Show Tags

15 Nov 2009, 06:30

Good question this is. The original poster should not be worried about not solving this question, it is a bit tricky. Keep up the confidence.

Answer should be C.

stmt1. Pat has finished first 5 chapters. We do not know how many pages are there per chapter and hence the total number of pages. Insuff.

stmt2: Let p be the number of pages in each of the last 12 chapters. Let x be the 'extra' pages in each of the first 3 chapters. So, we have, 3(p+x) pages in first three chapters and 12p pages in last 12 pages.

Total number of pages in the book = 3(p+x)+12p = 3p+3x+12p = 15p+3x

Here, we do not how many pages Pat has read. Insuff

Combining, Pat has read 3(p+x) + 2p pages = 3p+3x+2p = 5p+3x pages. 1/3 of total pages is (1/3)*(15p+3x) = 5p+x. Now, x>0 because Pat has read some pages/chapters. So, 5p+3x > 5p+x. Hence, proved. Sufficient.

Re: Pat is reading a book that has a total of 15 chapters. Has [#permalink]

Show Tags

15 Nov 2009, 06:39

Quote:

Let p be the number of pages in each of the last 12 chapters. Let x be the 'extra' pages in each of the first 3 chapters. So, we have, 3(p+x) pages in first three chapters and 12p pages in last 12 pages.

Total number of pages in the book = 3(p+x)+12p = 3p+3x+12p = 15p+3x

I disagree.

Nowhere does it say that the each of the last 12 chapters have the same number of pages. Nor for that matter does it say that each of the first three chapters have the same number of pages.

All it says is that each of the first three chapters has more pages than each of the last 12.

Hence it will be incorrect to assume that each of the last 12 chapters has 'p' pages and that each of the first 3 have the same number of extra pages 'x'. _________________

Re: Pat is reading a book that has a total of 15 chapters. Has [#permalink]

Show Tags

15 Nov 2009, 07:48

sriharimurthy wrote:

Quote:

Let p be the number of pages in each of the last 12 chapters. Let x be the 'extra' pages in each of the first 3 chapters. So, we have, 3(p+x) pages in first three chapters and 12p pages in last 12 pages.

Total number of pages in the book = 3(p+x)+12p = 3p+3x+12p = 15p+3x

I disagree.

Nowhere does it say that the each of the last 12 chapters have the same number of pages. Nor for that matter does it say that each of the first three chapters have the same number of pages.

All it says is that each of the first three chapters has more pages than each of the last 12.

Hence it will be incorrect to assume that each of the last 12 chapters has 'p' pages and that each of the first 3 have the same number of extra pages 'x'.

Even if take the worst case scenario...

say the 1st 3 chapters have 3 pages each and the rest 12 chapters have 2 pages each.

total = 9 + 24 = 33.

1/3 *33 = 11.

so 3*3 + 2*2 = 13 (1st 5 chapters) which is greater than 11.

The other case which you are talking about is different number of pages in each of the 3 chapters.This is the best case scenario

Re: Pat is reading a book that has a total of 15 chapters. Has [#permalink]

Show Tags

15 Nov 2009, 08:05

Quote:

Even if take the worst case scenario...

say the 1st 3 chapters have 3 pages each and the rest 12 chapters have 2 pages each.

This is not the worst case scenario... In fact I am not even sure what the worst case scenario would refer to in this question. Anyway.. that doesn't matter. All we have to see is whether it is possible to get conflicting suggestions or not.

The case you have considered is just one of the possibilities that tells us that he has read more than 1/3 of the pages.

However, there are possibilities which satisfy both St. (1) and St. (2), yet tell us that he has not read even 1/3 of the pages. (refer to my earlier post for an example).

Thus we can conclude that both together are also insufficient.

If you face any further difficulty in my reasoning, just let me know. I will be more than happy to help you out.

Re: Pat is reading a book that has a total of 15 chapters. Has [#permalink]

Show Tags

16 Nov 2009, 04:26

Hello,

I got stuck on the same question, the answer key says E is correct ..

thank you for the explanations!! I got mislead concluding that the rest of the 12 chapters have the equal amount of pages, which is not stated anywhere!

Re: Pat is reading a book that has a total of 15 chapters. Has [#permalink]

Show Tags

29 Dec 2014, 05:37

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. _________________

So, my final tally is in. I applied to three b schools in total this season: INSEAD – admitted MIT Sloan – admitted Wharton – waitlisted and dinged No...

HBS alum talks about effective altruism and founding and ultimately closing MBAs Across America at TED: Casey Gerald speaks at TED2016 – Dream, February 15-19, 2016, Vancouver Convention Center...