If 56x32y is divisible by 18, find the least value of y.
Solution:
If 56x32y is divisible by 18 it means that it is divisible by 9 and 2, because 18 = 9 × 2
The number is divisible by 2 if y is even.
A number is divisible by 9 if the sum of its digits is divisible by 9.
Therefore,
5 + 6 + x + 3 + 2 + y = 16 + x + y
For 16 + x + y to be divisible x + y has to be at least 2.
Therefore x and y can assume values:
(a) x = 2, y = 0
(b) x = 1, y = 1 but y = 1 therefore it is not even and not divisible by 2
(c) x = 0; y = 2
From the above three values of x and y the least value of y = 0.
✦ Try This: If 45x21y is divisible by 12, find the least value of x + y.
If a number is divisible by 12 then the number is also divisible by 3 and 4 because 12 = 4 × 3
For the number to be divisible by 4 the number formed last two digits 1y has to be divisible by 4. The least number divisible by 4 is 12 which implies y = 2. (1)
For the number to be divisible by 3 the sum of its digits should be divisible by 3. Therefore 4 + 5 + x + 2 + 1 + y = 12 + x + y has to be divisible by 3. The least number divisible by 3 will be:
12 + x + y = 12 + 0 + 0 = 12
But if y = 0 then 10 will be last two digits and that will not be divisible by 4.
If y = 2
Then the least value x + y will be 6.
Since y = 2, x = 4
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 16
NCERT Exemplar Class 8 Maths Chapter 13 Problem 74
If 56x32y is divisible by 18, find the least value of y.
Summary:
If 56x32y is divisible by 18, the least value of y = 0.
☛ Related Questions:
visual curriculum