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

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14 Nov 2009, 07:24

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A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

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

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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]

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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]

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15 Nov 2009, 04:51

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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]

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15 Nov 2009, 04:57

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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]

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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]

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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]

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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]

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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]

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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]

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