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# 20 books, each on a different subject, are placed on a shelf

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Retired Moderator
Joined: 22 Aug 2013
Posts: 1435
Location: India
20 books, each on a different subject, are placed on a shelf  [#permalink]

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24 Feb 2018, 00:12
00:00

Difficulty:

65% (hard)

Question Stats:

60% (01:53) correct 40% (01:52) wrong based on 40 sessions

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20 books, each on a different subject, are placed on a shelf from left to right. The books are labelled numerically from '1' to '20' respectively in increasing order from left to right, such that the leftmost book is labelled number '1' while the rightmost book is labelled number '20'. Out of these 20 books, there is also a Physics book, a Mathematics book and a Philosophy book. What is the label number on the Mathematics book?

(1) Exactly 1 book is placed between the Physics book and the Philosophy book, while exactly 2 books are placed between the Philosophy book and the Mathematics book. Physics book has label number '15'.

(2) Philosophy book has label number '17'.
examPAL Representative
Joined: 07 Dec 2017
Posts: 1074
20 books, each on a different subject, are placed on a shelf  [#permalink]

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24 Feb 2018, 02:59
amanvermagmat wrote:
20 books, each on a different subject, are placed on a shelf from left to right. The books are labelled numerically from '1' to '20' respectively in increasing order from left to right, such that the leftmost book is labelled number '1' while the rightmost book is labelled number '20'. Out of these 20 books, there is also a Physics book, a Mathematics book and a Philosophy book. What is the label number on the Mathematics book?

(1) Exactly 1 book is placed between the Physics book and the Philosophy book, while exactly 2 books are placed between the Philosophy book and the Mathematics book. Physics book has label number '15'.

(2) Philosophy book has label number '17'.

We'll use a drawing to help us understand the different arrangements.
This is an Alternative approach.

(1) So, putting the math book on different sides of the philosophy book we can have
15:Physics 16:? 17:Philosophy 18:? 19:? 20:Math or
14:Math 15:Physics 16:? 17:Philosophy.
Insufficient!

(2) This is clearly insufficient as it says nothing about the math book.
Insufficient!

Combined:
We still can't separate between the two options given above.
Insufficient.

_________________
20 books, each on a different subject, are placed on a shelf   [#permalink] 24 Feb 2018, 02:59
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