Today was Catherine´s birthday. She turned 24. Catherine is twice as old as Ryan was when Catherine was as old as Ryan now. How old is Ryan now?..................
Application of test of divisibility over other methods
Find the least number of five digits which is exactly divisible by 12,15 & 18.
A. 10005 B. 10010 C. 10020 D. 10080
Options:
A. 3 B. 9 C. 11 D. 10
Method used to find the solution :
Least no of five digits = 10000
L.C.M of 12,15 & 18 is 180.
Dividing 10000 by 180, remainder is 80.
The least possible number exactly divisible by 12,15 & 18 = 10000 +(180 -100) = 10080.
Answer is Option D.
Alternate method using test of divisibility:
The given divisors are :12,15 & 18.
For 18, 9 is a divisor.
For a number to be exactly divisible by 18, it should be divisible by 9.
Out of the given options, applying test of divisibility by 9 , only 10080 is exactly divisible by 9.
(Application of divisibility : 1+0+0+8+0 = 9. 9 is divisible by 9. Therefore 10080 is divisible by 9.
None of the other given options pass this test.)
Therefore 10080 is the answer.
By using the test of divisibility, we can easily find solutions for this type of problems without finding the LCM or dividing every no by the divisors given.
