# Problem of the Day

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

(1) (2) D. Each statement alone is sufficient.

See the Solution

### 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.