If 3p7q8 is divisible by 44, list all possible pairs of values for p and q. Class 8

If 3p7q8 is divisible by 44, list all possible pairs of values for p and q. Class 8

Question 1.

If 3p7q8 is divisible by 44, list all possible pairs of values for p and q. Class 8

Solution:

3p7q8 : For divisibility by 44, it must be divisible by 4 and 11.

For divisibility by 4, q must be 0 or 2 or 4 or 8.

Now, alternate sums are 3 + 7 + 8 = 18 and p + q.

18 - (p + q) must be divisible by 11.

So, for q = 0, we have 18 - p — 0 = 18 - p.

So, p = 7.

For q = 2, we have 18 - p - 2 = 16 - p.

So, p = 5.

For q = 4, we have 18 - p - 4 = 14 - p.

So, p = 3.

For q = 8, we have 18 - p - 8 = 10 - p.

From no value of p is possible.

So, required pairs of p and q are 7 and 0, 5 and 2 and 3 and 4 respectively.