Problem Solving

If T divided by B equals 8.12 what is a possible remainder?

A. 2
B. 8
C. 9
D. 26
E. 44

The OA is C.

With the decimal being 12/100, the simplest form is 3/25.

If the divisor is a multiple of 25, the remainder must be a multiple of 3.

The only number that is so is 9. Answer C.

Has anyone another approach to solve this PS question? Regards!

Hello AAPL.

I would solve it as follows:

We know that T divided by B equals 8.12, then $$\frac{T}{B}=8.12\ \ \ \Rightarrow\ T=8.12\ B\ \ \Rightarrow\ \ T=\left(8+0.12\right)B\ \ \Rightarrow\ \ T=8B\ +\ \frac{12}{100}B$$ $$\Rightarrow\ \ \ T=8B\ +\ \frac{3}{25}B$$ $$\Rightarrow\ \ \ 25T=200B\ +\ 3B$$ Here we see that the remainder (3B) is a multiple of 3.

The unique multiple of 3 is [spoiler]C=9[/spoiler].

If t is divided by b,
ie t/b = 8.12
ie 8.12

8[12][/100] = 8[3][/5] ie 8 + 3/5
so, it means thats t/b = 3/25
ie t = 3b+25 where t is teh reaminder.

So, it means the remainder is the multiple of 3.
In these options, only 9 is a multiple of 3.
So the answer is C.

Regards!