If 13 99 - 19 93 is divided by 162, then the remainder is
Text Solution
Verified by ExpertsD
0
13 99 - 19 93 = odd number - odd number = even number
It is divisible by 2.
Also, 13 99 = (1 + 12) 99 - 1 + 99 C1 . 12 + 99 C 2 . 12 2 + 99 C 3 . 12 3 + 99 C 4 . 12 4 +....
= 1 + 99 x 12 + 99 x 49 . 12 2 + 3 x 11 x 49 x 97 x 12 3 + 81I 1
= 1 + 99 x 12 + 81 {11 x 49 x 16 + 11 x 49 x 97 x 64 + I 1 }
13 99 = 1 + 99 x 12 + 81I 2
19 93 = (1 + 18) 93 = 1 + 93 C 1 . 18 + 93 C 2 . 18 2 +.. . .
= 1 + 93 x 18 + 81I 3
13 99 - 19 93 = 99 x 12 - 93 x 18 + 81 (I 2 - I 3 )
= 27 {11 x 4-31 x 2} + 81I 4
= 27 (44 - 62) + 81I 4 = 27 x (-18) + 81I 4
=81{-6 + I 4 } = 81I 5
Hence, it is also divisible by 81.
So, it is divisible by 162 => Remainder = 0.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems