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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Basics of Mathematics

Olympiad workbook · IOQM · Basics of Mathematics

A book is published in three volumes, the pages being numbered from...

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 nn is the last page number, what is the largest prime factor of n ?

Correct answer

17

Step-by-step solution

Let the number of pages in volume-1 be x ∴\therefore Number of pages in second volume =x+50=\mathrm{x}+50 ∴\therefore Number of pages in third volume =32(x+50)=\frac{3}{2}(x+50) Moreover 1+(x+1)+(2x+51)=17091+(x+1)+(2 x+51)=1709 ⇒3x+53=1709=⇒x=552\Rightarrow 3 x+53=1709=\Rightarrow x=552 So n=552+602+903=2057\mathrm{n}=552+602+903=2057 So n=112×17\mathrm{n}=11^2 \times 17 Hence largest prime factor of n=17\mathrm{n}=17
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