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Shawana made a schedule for reading books during 4 weeks

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Shawana made a schedule for reading books during 4 weeks

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Shawana made a schedule for reading books during 4 weeks (28 days) of her summer vacation. She has checked out 12 books from the library. The number of pages in each book and the order in which she plans to read the books are shown in the table above. She will read exactly 50 pages each day. The only exception will be that she will never begin the next book on the same day that she finishes the previous one, and therefore on some days she may read fewer than 50 pages. At the end of the 28th day, how many books will Shawana have finished?

A. 7
B. 8
C. 9
D. 10
E. 11

The OA is B.

Source: Official Guide

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The easiest (though perhaps not the most elegant) way to approach this problem is to chart it out.

For each book, divide the number of pages by 50, then round up if there is a remainder. For example, 253/50 = 5 remainder 3 --> round up to 6 days total.

Book #:----Days to read:---Total days:
1-------------------6-----------------6
2-------------------3-----------------9
3-------------------3-----------------12
4-------------------4-----------------16
5-------------------4-----------------20
6-------------------1-----------------21
7-------------------5-----------------26
8-------------------2-----------------28

On the 28th day, she has finished exactly 8 books. The answer is B.

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EdM in Mind, Brain, and Education
Harvard Graduate School of Education


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swerve wrote:


Shawana made a schedule for reading books during 4 weeks (28 days) of her summer vacation. She has checked out 12 books from the library. The number of pages in each book and the order in which she plans to read the books are shown in the table above. She will read exactly 50 pages each day. The only exception will be that she will never begin the next book on the same day that she finishes the previous one, and therefore on some days she may read fewer than 50 pages. At the end of the 28th day, how many books will Shawana have finished?

A. 7
B. 8
C. 9
D. 10
E. 11

The OA is B.


In the figure above, we consider the numbers presented in red, so that we may "run the reading days without worries"...

Hence:

(1) 300/50 = exactly 6 days needed till the end of first book
(2) 150/50 = exactly 6+3 days needed till the end of second book
(3) 150/50 = exactly 6+3+3 = 12 days needed till the end of third book

And we found the rule... using vulgar induction we may "re-start our reasoning" to proceed much quicker:

Oriented by the minimum value (7) among the alternative choices, we calculate

(300+150+150+200+200+50+250)/50 = 6+3+3+4+4+1+5 = 26 days needed till the end of the 7th book (days available, because 26 is not more than 28)

To read till the end of the 8th book, 26 + 100/50 = 28 days would be needed, exactly what Sawana had available. That´s our answer.

The above follows the notations and rationale taught in the GMATH method.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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swerve wrote:


Shawana made a schedule for reading books during 4 weeks (28 days) of her summer vacation. She has checked out 12 books from the library. The number of pages in each book and the order in which she plans to read the books are shown in the table above. She will read exactly 50 pages each day. The only exception will be that she will never begin the next book on the same day that she finishes the previous one, and therefore on some days she may read fewer than 50 pages. At the end of the 28th day, how many books will Shawana have finished?

A. 7
B. 8
C. 9
D. 10
E. 11

The OA is B.

Source: Official Guide
Since 253/50 = 5 R 3, Shawana will finish the first book in 6 days.

Since 110/50 = 2 R 10, she will finish the second book in 3 days, and thus she will have taken a total of 9 days to finish the first 2 books.

Since 117/50 = 2 R 17, she will finish the third book in 3 days, and thus she will have taken a total of 12 days to finish the first 3 books.

Since 170/50 = 3 R 20, she will finish the fourth book in 4 days, and thus she will have taken a total of 16 days to finish the first 4 books.

Since 155/50 = 3 R 5, she will finish the fifth book in 4 days and thus she will have taken a total of 20 days to finish the first 5 books.

Since 50/50 = 1, She will finish the sixth book in only 1 day, and thus she will have taken a total of 21 days to finish the first 6 books.

Since 205/50 = 4 R 5, she will finish the seventh book in 5 days and thus she will have taken a total of 26 days to finish the first 7 books.

Since 70/50 = 1 R 20, she will finish the eighth book in 2 days and thus she will have taken a total of 28 days to finish the first 8 books.

Answer: B

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Founder and CEO
scott@targettestprep.com



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