Question

When H is divided by 10 , the remainder is 9 . What is the remainder when H is divided by 5 ? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

Answer 1

Answer: 4

Step-by-step explanation

q = some quotient

H/10 = q + 9/10

H = 10(q + 9/10)

H = 10q + 9

The value H is 9 more than a multiple of 10.

Let's divide H over 5.

H = 10q + 9

H/5 = (10q + 9)/5

H/5 = 2q + 9/5

H/5 = 2q + (5+4)/5

H/5 = 2q + 5/5 + 4/5

H/5 = 2q + 1 + 4/5

H/5 = (2q+1) + 4/5

The portion 2q+1 is the new quotient. We don't care about the quotient and focus entirely on the remainder only. The remainder is 4 since it's the numerator of the fractional portion 4/5.

Or alternatively we can rewrite things a bit like so

H/5 = (2q+1) + 4/5

5*H/5 = 5*( (2q+1) + 4/5)

H = 5(2q+1) + 4

H = 5*(some integer) + 4

H = (multiple of 5) + 4

It shows us that H is 4 more than a multiple of 5.

This is another way to see that the remainder of H/5 is 4.

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Let's look at an example.

H = 19

H/10 = 19/10 = 1 remainder 9

H/5 = 19/5 = 3 remainder 4