Question
For what number of values of 'z' is the number 1269zq
divisible by 15?Solution
ATQ,
Divisible by 15 ⇒ divisible by 5 and 3
Divisible by 5 ⇒ q = 0 or 5
Divisible by 3 ⇒ sum divisible by 3
Case 1: q = 0
Sum = 1 + 2 + 6 + 9 + z + 0 = z + 18
Divisible by 3 ⇒ z = 0, 3, 6, 9
Case 2: q = 5
Sum = 1 + 2 + 6 + 9 + z + 5 = z + 23
Divisible by 3 ⇒ z = 1, 4, 7
Total values of z: 4 + 3 = 7
Determine the smallest four-digit number that is evenly divisible by 12, 22, and 42.
Three natural numbers X,Y,Z are pairwise co-prime and satisfy the following conditions, the least common multiple (LCM) of X and ...
The smallest natural number that must be added to 1212 to make it a perfect square is:
There are three numbers 'u', 'v' and 'w' (u < v < w) such that 'v' is equal to the average of 'u' and 'w'. 80% of 'w' is equal to 'u' and the difference...
If 893x2 is divisible by 56, and x > 6, find x.
Consider three numbers whose total is 294. The first and second numbers are in a ratio of 5:7, and the second and third numbers are in a ratio of 7:9. D...
- If 246x179y is divisible by 72, find the value of (x + 2y).
Find the sum of the first 30 natural numbers.
A number is initially increased by 37.5% and then reduced by 40%. The final value obtained after these changes is 6,270. Determine 80% of the original n...
