# . The largest prime factor of n is

A book is published in three volumes, the pages being numbered from 1 onwards. The page numbers are continued from the first volume to the second volume to the third. The number of pages in the second volume is 50 more than that in the first volume, and the number pages in the third volume is one and a half times that in the second. The sum of the page numbers on the first pages of the three volumes is 1709. If n is the last page number, the largest prime factor of n is

A. 11
B. 13
C. 17
D. 23

Solution |||

Let the number of pages in 1st volume be x

And the number of pages in the 2nd volume will be x + 50

The number of pages in the 3rd volume will be 3/2 (x + 50)

= 3/2x + 75

1st page of 1st volume = 1

1st page of 2nd volume = x + 1

1st page of 3rd volume = x + x + 50 + 1 = 2x + 51

1 + x + 1 + 2x + 51 = 1709

3x + 53 = 1709

3x = 1656 (we subtracted 1709 and 53)

x = 552 (we divided 1656 by 3)

So, the last page number = (3/2) x + 75 + x + x + 50

= (3/2) x 552 + 75 + 1154

= 828 + 75 + 1154

= 2057

Prime factorising we get 2057 = 11 × 11 × 17

Thus, the largest prime factor is 17.