# Quantitative Reasoning – Pages and Sum!

PSA 2014_XI_Q20. In a 100 page book, pages 2 and 3 face each other. Similarly, pages 4 and 5 and 6 and 7 face each other. This pattern is repeated to the end of the book. The sum of two facing pages could be
(1) 99

(2) 90

(3) 95

(4) 97

Ans: Every sum of two facing pages is evidently sum of two consecutive numbers with the first page being the even number and the second one an odd number:

(1) 99 -> 49 + 50 [Rejecting as first is odd].

(2) 90 -> Rejecting this as the sum should be an odd number. [Even + Odd= Odd].

(1) 95 -> 47 + 48 [Rejecting as first is odd].

(1) 97 -> 48 + 49 [Correct option].

Second method:

We can closely observe the sum of pages to be in AP:

5, 9, 11, 13, 17, …

Common difference= 4.

Second property that can be used is: Every term of the AP when divided by the common difference gives the same remainder. Here, the remainder is 1 always.

Let us find out the individual remainders when the options are divided by 4.

(1) 99 divided by 4 leaves a remainder 3.

(2) 90 divided by 4 leaves a remainder 2.

(3) 95 divided by 4 leaves a remainder 3.

(4) 97 divided by 4 leaves a remainder 1. Correct Option.