a book is published in three volumes the pages being numbers from 1 onwards the page numbers the continued from the first volume to the third volume.the number of pages in the second volume is 15 more than the first volume and the number of pages in the third volume is one and a half times that in the second volume the sum of 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
Answers
y - x = x + 50
2x - y = -50 ----(1)
z - y = 1.5 (y-x)
z = 2.5 y - 1.5x ---(3)
1+x+1+y+1 = 1709
x + y = 1706
We will solve the linear equations and will substitute the values of x and y in the equation 3
x = 552
y = 1154
z = 2057
So the last page number, n = z = 2057
= 11 x 11 x 17
for this the prime factors of 2057 = 11, 11, 17
Largest prime factor of n will be 17
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