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

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Senior Manager
Joined: 12 Mar 2006
Posts: 349
Schools: Kellogg School of Management
Pat is reading a book that has a total of 15 chapters. Has  [#permalink]

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15 Jan 2007, 20:12
1
3
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:25) correct 43% (01:53) wrong based on 213 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..
VP
Joined: 21 Mar 2006
Posts: 1046
Location: Bangalore

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15 Jan 2007, 23:49
I plugged in numbers and got C.

first 3 chapters = 11 pages each (minimum more than last 7 chapters)
next 2 chapters = 1 page each (minimum possible)
Last 7 chapters = 10 pages each (maximum possible less than 1st 3 chapters)

From one => Pat has finished reading a minimum of 11*3 + 1*2 = 35 pages
Total pages = 11*3 +1*2 + 10*7 = 105 pages

Fraction pf pages read by Pat = 35/105 = 1/3. this is the minimum possible value under the given conditions (or at least I think so!)

So he has read ATLEAST 1/3 of the pages. So C
Intern
Joined: 15 Jan 2007
Posts: 38

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16 Jan 2007, 19:35
1
E.
plug in these numbers : 2*1page + 8 * 10page + 2 * 12page + 3 * 13page=146pgs

so if read 3*13 + 2*1 = 41
and ur example gives the other way. so E.

kripalkavi wrote:
I plugged in numbers and got C.

first 3 chapters = 11 pages each (minimum more than last 7 chapters)
next 2 chapters = 1 page each (minimum possible)
Last 7 chapters = 10 pages each (maximum possible less than 1st 3 chapters)

From one => Pat has finished reading a minimum of 11*3 + 1*2 = 35 pages
Total pages = 11*3 +1*2 + 10*7 = 105 pages

Fraction pf pages read by Pat = 35/105 = 1/3. this is the minimum possible value under the given conditions (or at least I think so!)

So he has read ATLEAST 1/3 of the pages. So C
VP
Joined: 21 Mar 2006
Posts: 1046
Location: Bangalore

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16 Jan 2007, 20:46
svas wrote:
E.
plug in these numbers : 2*1page + 8 * 10page + 2 * 12page + 3 * 13page=146pgs

so if read 3*13 + 2*1 = 41
and ur example gives the other way. so E.

kripalkavi wrote:
I plugged in numbers and got C.

first 3 chapters = 11 pages each (minimum more than last 7 chapters)
next 2 chapters = 1 page each (minimum possible)
Last 7 chapters = 10 pages each (maximum possible less than 1st 3 chapters)

From one => Pat has finished reading a minimum of 11*3 + 1*2 = 35 pages
Total pages = 11*3 +1*2 + 10*7 = 105 pages

Fraction pf pages read by Pat = 35/105 = 1/3. this is the minimum possible value under the given conditions (or at least I think so!)

So he has read ATLEAST 1/3 of the pages. So C

Shoot! I've taken the number of chapters as 12... Pretty dumb
Director
Joined: 13 Nov 2003
Posts: 767
Location: BULGARIA

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17 Jan 2007, 02:41
Think it is C)

From A we can not conclude anything
FromB again we can not conclude anything
from both:
If each chapter has same number of pages , then Pat must have read 5/15 of the pages or 1/3 of them. But B) says that first 3 chapters have more pages than the other 12. So Pat have read >1/3 of the pages
Senior Manager
Joined: 19 Jul 2006
Posts: 334

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17 Jan 2007, 06:57
1
E

scenario 1:

first 3 chapters = 10 pages each
next 12 chapters = 9 page each (maximum possible)

total no. of pages in 15 chapters = (3*10) + ( 12*9) = 138

no of pages in first 5 chapters = 30 + 18 = 48

% of pages in first 45 chapters = (48/138)*100 = 34.7 % > 1/3

scenarion 2:

first 3 chapters = 10 pages each
next 2chapters = 1 page each
next 12 chapters = 9 page each (maximum possible)

total no. of pages in 15 chapters = (3*10) + (2*1)+( 10*9) = 122

(32/122)*100 = 26% < 1/3
SVP
Joined: 06 Sep 2013
Posts: 1720
Concentration: Finance
Re: Pat is reading a book that has a total of 15 chapters. Has  [#permalink]

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14 Sep 2013, 06:40
Good one.

Statement 1: 5 chapters read doesn't give us anything since we don't know the # of pages per chapter.
Statement 2: Tells us that the # of pages read is >1/5 (assuming that the total # of pages in the first 3 chapters is slightly higher than in the others) , but we don't know whether the total is more than 1/3.

Statement 1 and 2 together: Doesn't help since we don't know # of pages in 4th and 5th chapter. So we are not sure if it will be >1/3 assuming that the # of pages is just slightly above 1/5 from Statement 2.

Just to elaborate more picking some numbers

Obviously each statement alone is NOT sufficient

Now we have the following,

Say that there are 2 pages in each of the first 3 chapters, and we have 1 page for each of the remaining 12 chapters

We would then have a total of 6+2 =8 over a total of 18

8/18>=1/3? Yes, so this answers part of the question

Now we can try different numbers for the pages in each chapter. Thing is, as we have larger numbers then the fraction (8/18 in the first case) will decrease as the number of pages in the first 3 chapters will be a smaller part of the total number of pages. Therefore, from here we can already infer that we will also have a NO answer to this statement, and hence answer will be E

Hope it is now crystal clear
Cheers
J
Director
Joined: 04 Jun 2016
Posts: 571
GMAT 1: 750 Q49 V43
Re: Pat is reading a book that has a total of 15 chapters. Has  [#permalink]

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01 Aug 2016, 22:53
prude_sb wrote:
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..

(1) Pat has just finished reading the first 5 chapters.
Each chapter can have variable number of pages. The number of pages in each chapter is not same
INSUFFICIENT

(2) Each of the first 3 chapters has more pages than each of the other 12 chapters in the book..
Good to know but how does it helps us. The number of pages can be X in the first 3 chapters and Y in the next 12 chapters
We cannot reach a a definite number to deduce what is 1/3 of (x+y)
INSUFFICIENT

MERGING BOTH STATEMENT
Again insufficient , because we still not know the total number of pages in the book

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

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26 Jun 2018, 02:52
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Re: Pat is reading a book that has a total of 15 chapters. Has &nbs [#permalink] 26 Jun 2018, 02:52
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