How many books in a certain library have more than 250 pages

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Oct 06, 2019 6:17 pm

How many books in a certain library have more than 250 pages?

(1) Average number of pages per book is equal to the number of pages in the book with least number of pages

(2) The median number of pages in the book in the library is 240.

OA C

Source: e-GMAT

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Source: Beat The GMAT — Data Sufficiency | Sun Oct 06, 2019 6:17 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Sun Oct 06, 2019 9:23 pm

BTGmoderatorDC wrote:How many books in a certain library have more than 250 pages?

(1) Average number of pages per book is equal to the number of pages in the book with least number of pages

(2) The median number of pages in the book in the library is 240.

OA C

Source: e-GMAT

Let's take each statement one by one.

(1) Average number of pages per book is equal to the number of pages in the book with least number of pages

Note that for unequal numbers, the average (arithmetic mean) is always greater than the least number. Since it is given that the average number of pages per book is equal to the number of pages in the book with the least number of pages, each book has the same number of pages. However, we cannot ascertain the number of books in a certain library. Insufficient.

(2) The median number of pages in the book in the library is 240.

The statement means that upon arranging the books in ascending order of the number of pages, the middle-most book has 240 pages. However, we cannot ascertain the number of books in a certain library. Insufficient.

(1) and (2) together

From (1), we know that all books have the same number of pages; thus, from (1) and (2) together, we know that each book has 240 pages. Thus, we know that NO book has more than 250 pages. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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