Question

13. Let s be the sum of the digits of the number
15^2×5^18 in base 10. Then find the range in which s belong​

Answer 1

6 ≤ s < 140   s is sum of digits of 15² * 5¹⁸

Step-by-step explanation:

15² * 5¹⁸

= 3² * 5² * 5¹⁸

= 9  * 5²⁰

= 9 * 5²⁰ * 2²⁰ /  2²⁰

= 9 * 10²⁰ / (2¹⁰)²

= 9 * 10²⁰ / ( 1024)²

≈ 9 * 10²⁰ / ( 1000)²

= 9 * 10¹⁴

Number of digit would be 15

each digit maximum can be 9

so maximum sum  =  15 * 9 = 135

as number has only 5 & 3 as factor

so number would end with 5 hence sum of digits would be atleast 5

also as 3 is a factor so sum of digits should be divisible by 3

Hence 6 would be minimum sum of digits

6 ≤ s ≤ 135

as options provides has   6 ≤ s < 140

so  6 ≤ s < 140