If 31z5 is a multiple of 9, where z is a digit, what is the value of 2? Explain why there are two answers to this problem. Class 8

If 31z5 is a multiple of 9, where z is a digit, what is the value of 2? Explain why there are two answers to this problem. Class 8

Question 1.

If 31z5 is a multiple of 9, where z is a digit, what is the value of 2? Explain why there are two answers to this problem. Class 8

Solution:

3 + 1 +z + 5 = 9 + z

For a multiple of 9, (9 + 2) must be multiple of 9. For this the values of z can be 0 or 9.

Question 2.

“I take a number that leaves a remainder of 8 when divided by 12.1 take another number which is 4 short of a multiple of 12. Their sum will always be a multiple of 8”, claims Snehal. Examine his claim and justify your conclusion. Class 8

Solution:

Let first number be 12x + 8 and second number be 12y - 4.

Their sum = 12x + 8 + 12y - 4

= 12x + 12y + 4.

For x = 3 and y = 5, the value of 12x + 12y + 4 = 36+ 60+ 4= 100, which is not a multiple of 8. So, Snehal claim is not correct.

Note : For some values of x and y, it might be correct.