Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
Find the number of digits in the smallest number which is made up of digits 1 and 0 only and is divisible by 225.
Answer
Answer (as printed):
Explanation
225 = 9 × 25, where 9 and 25 are co-primes. Clearly, a number is divisible by 225 if it is divisible by both 9 and 25. Now, a number is divisible by 9 if the sum of its digits is divisible by 9 and a number is divisible by 25 if the number formed by the last two digits is divisible by 25. \ The smallest number which is made up of digits 1 and 0 and divisible by 225 = 11111111100. Hence, number of digits = 11.
Explanation as extracted from the printed page; notation may be imperfect.