Question

A book is published in 3 volumes, the pages being numbered from 1 onwards. The page numbers are continued from the 1st volume to the 2nd volume to the 3rd. The number of pages in the 2nd volume is 50 more than that in the 1st volume and the number of pages in the 3rd volume is 3/2 times that in the 2nd.The sum of the page numbers on the 1st pages of each volume is 1709. If 'n' is the last page number, what is the largest factor of n?

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Answer 1

Question: A book is published in 3 volumes, the pages being numbered from 1 onwards. The page numbers are continued from the 1st volume to the 2nd volume to the 3rd. The number of pages in the 2nd volume is 50 more than that in the 1st volume and the number of pages in the 3rd volume is 3/2 times that in the 2nd.The sum of the page numbers on the 1st pages of each volume is 1709. If 'n' is the last page number, what is the largest factor of n?

Solution: volume 1: page 1 to page 552;        volume 2: page 553 to page 1154;       volume 3: page 1154 to page 2056.

Logic: Let us assume that there are x number of pages in Volume 1.

So the page numbers will be: 1,2,3....x

Acc to the question, Volume 2 has 50 pages more than that in volume 1 i.e. x+50 pages.

So the page numbers will be: x+1,x+2,x+3.........2x+50.

Again, Volume 3 has 1.5 times pages of volume 2.

So the page numbers will be: 2x+51,2x+52,2x+53,.......

Acc to the condition, the sum of the page numbers on the 1st pages of each volume is 1709.

i.e. 1 + x+1 + 2x+51 = 1709.

or, 3x+53 = 1709

or, 3x = 1656

or, x = 552.

Therefore, the below solution holds true.

Volume 1: page 1 to page 552;  (page count = 552)

Volume 2: page 553 to page 1154;   (page count = 602)

Volume 3: page 1154 to page 2057.      (page count = 903)

Thus, the last page number is 2057.

The factors of 2057 = 11×11×17

Therefore, the largest factor is 17. [Ans]

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