Question : What is the sum of the digits of the least number which when divided by 15,18, and 36 leaves the same remainder 9 in each case and is divisible by 11?
Option 1: 15
Option 2: 16
Option 3: 18
Option 4: 17
Correct Answer: 18
Solution : The least number which leaves the same remainder when divided by 15, 18, and 36 is the least common multiple (LCM) of these numbers plus the remainder. 15 = 3 × 5 18 = 2 × 3 2 36 = 2 2 × 3 2 The LCM of 15, 18, and 36 = 2 2 × 3 2 ×5 = 180 When divided by these numbers, the least number that leaves a remainder of 9 is 180k + 9, where k is some positive integer. However, this number must also be divisible by 11. The smallest number of 180k + 9 divisible by 11 is 1089. The sum of the digits of 1089 is 1 + 9 + 8 = 18. Hence, the correct answer is 18.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : What is the least number which when divided by 15, 18 and 36 leaves the same remainder 9 in each case and is divisible by 11?
Question : Let $x$ be the least number which when divided by 8, 9, 12, 14 and 36 leaves a remainder of 4 in each case, but $x$ is divisible by 11. The sum of the digits of $x$ is
Question : Let $x$ be the least number of 4 digits that when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If $x$ lies between 2000 and 2500, then what is the sum of the digits of $x$?
Question : Find the least number which when divided by 4, 9, 12, and 15, leaves the remainder 3 in each case.
Question : Let $x$ be the least 4-digit number which when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If $x$ lies between 2800 and 3000, then what is the sum of the digits of $x$?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile