# Problem of the Day

When is divided by , the remainder is . What is the remainder when is divided by ?

(1)

(2)

Reveal Answer

### Solution

[latexpage]

Statement 1: Knowing the value of $y$ is clearly sufficient to calculate the remainder when $y$ is divided by 6. SUFFICIENT.

Statement 2: This tells us that the remainder when $y^2$ is divided by 6 is 3. The question then is whether this is sufficient to determine the remainder when $y$ is divided by 6. Let’s look at some values of $y$, their remainders when divided by 6, and the corresponding remainders of $y^2$ when divided by 6.

As you can see, a remainder of 3 with $y^2$ always corresponds to a remainder of 3 with $y$. But notice that if the remainder had been 4, that might correspond to a remainder of 2 or 4 with $y$. So, in this case we can say for sure that if the remainder when $y^2$ divided by 6 is 3, then the remainder when $y$ is divided by 6 is also 3. But this is a special case, and you should consider future problems on a case by case basis.

Comments are closed.