An awesome logical question!!

Level 2

A book is published in 3 3 volumes, the pages being numbered from 1 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 50 more than that in the first volume. And the number of pages in the third volume is one and a half times of that in the second. The sum of the page numbers on the first page of the 3 3 volumes is 1709 1709 . If n n is the last page number, what is the largest prime factor of n n ?

23 13 17 19

Prem Chebrolu by Prem Chebrolu , 17, India

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1 solution

X X
Aug 29, 2018

Let the first volume be x x pages, second be y y pages, third be z z pages.

Obviously, y = 50 + x , z = 1.5 y , 1709 = 1 + ( x + 1 ) + ( x + y + 1 ) y=50+x,z=1.5y,1709=1+(x+1)+(x+y+1)

So x = 552 , y = 602 , z = 903 , x + y + z = 2057 = 1 1 2 × 17 x=552, y=602,z=903,x+y+z=2057=11^2\times17

Hence the answer is 17 17

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