Question
Find the smallest number which when divided by 7, 9 and
12 leaves a remainder 5 in each case.Solution
Let the number be N. N ≡ 5 (mod 7), (mod 9), (mod 12) ⇒ N − 5 is divisible by 7, 9 and 12 LCM(7, 9, 12): 7 = 7 9 = 3² 12 = 2² × 3 LCM = 2² × 3² × 7 = 4 × 9 × 7 = 252 So N − 5 = 252 ⇒ N = 252 + 5 = 257
Find the sum of all natural numbers less than 500 which are divisible by 7.
In a two digit positive number, the digit in the unit’s place is equal to the square of the digit in ten’s place, and the difference between...
- The average of five consecutive prime numbers is 11. Find the third number.
The digits of a two-digit number ‘N’ are reversed to form a new number ‘M’. If M < N and N – M = 27, then which of the following maybe ‘N’...
Find the third proportion of 28 and 14.
What is the smallest number that should be added to 673 so that the sum becomes exactly divisible by 9?
A number ‘N’ is the greatest 3-digit number which gives a remainder of 2 when divided by 7, 10, and 12. Find the minimum number to be added to it to...
If the sum of two numbers is 45, and their difference is 9, what are the two numbers?
A monkey climbs a tower of height 60 m. It climbs 5m above in 1st minute and 4m below in 2nd minute. In how many minutes monkey wi...
Which pair of these numbers is cop rime?
Relevant for Exams:
