Question

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, what is the largest prime factor of

n

Answer 1

Let the number of pages in volume-1 be x
Number of pages in second volume = x + 50
Number of pages in third volume =
3
2
(x + 50)
Moreover 1 + (x + 1) + (2x + 51) = 1709
3x + 53 = 1709 = x = 552
So n = 552 + 602 + 903 = 2057
So n = 11×11
× 17
Hence largest prime factor of n = 17

Answer 2

Answer: 17

Step-by-step explanation: 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 = 1659 (we subtracted 1709 from 53)

x = 552 (we divided 1659 by 3)

So the last number of page = 3/2 x + 75 + x + x + 50

= 3/2 x 552 + 75 + 1154

= 828 + 75 + 1154

= 2057

We will take LCM of this

and we will get the  LARGEST PRIME FACTOR WHICH IS 17