Question

Find the digits p and q if p7q6 is divisible by 24

Answer 1

Answer:

Possible numbers are: 2736, 5736, 8736, 1776, 4776,7776

Step-by-step explanation:

p7q6 is divisible by 24. So it's divisible by both 8 & 3. Divisiblity of 8 test: Number is divisible by 8 if the number formed by last 3 digits is divisible by 8.

For 7q6 to be divisible by 8, q =3 or q = 7.

{By observation 736 & 776 are divisible by 8}.

Now number is divisible by 3 if it's sum of the digits is divisible by 3.

Number is p736: Digit sum is p+16. For divisible by 3, p should be 2,5,8.

Number can be 2736 or 5736 or 8736.

If number is p 776, then sum of digits is: p+20

For divisiblity by 3, p= 1 or 4 or 7.

Number is 1776 or 4776 or 7776.

Answer: p = 2 or 5 or 8 and q = 3.

p = 1 or 4 or 7 and q = 7.

{Possible numbers are: 2736, 5736, 8736, 1776, 4776,7776}.