When the even integer n is divided by 9, the remainder is 8. Which of

When the even integer n is divided by 9, the remainder is 8. Which of the following, when added to n, gives a sum that is divisible by 18?

The question is about "the even integer n" such that, when n is divided by 9, the remainder is 8.

So, the correct answer must work for every such integer.

To find the correct answer, we can't just use the answer choices. However, we don't have to do much more.

We can just, first, find any even number such that, when it is divided by 9, the remainder is 8 and, then, test each answer choice.

The easiest number to use for n is 8. After all, 8 is the smallest integer such that, when it is divided by 9, the remainder is 8.

Now, we just have to find an answer choice such that, when the choice is added to 8, the sum is divisible by 18.

A. 1

8 + 1 = 9 Not divisible by 18.

B. 4

8 + 4 = 12 Not divisible by 18.

C. 9

8 + 9 = 17 Not divisible by 18.

D. 10

8 + 10 = 18 Divisible by 18.

So, we're done

E. 17

The correct answer is (D).

Start with the given equation:
\[ \frac{n}{9} = Q + \frac{9}{8} \]

**Step 1:** Understand the Formula
- If the formula above seems confusing, it's a commonly used "tactic" to answer remainder questions.
- If you need more clarity feel free to PM me for a detailed explanation on how I got that.

**Step 2:** Simplify the Equation
- Simplify the given equation to:
\[ n = 9Q + 8 \]

**Step 3:** Consider the Even Nature of the Number
- The problem states the number is even. This implies \(Q\) must be a multiple of not only \(9\) but also \(2\), ensuring the total remains even due to the constant term \(+8\).
- Thus, we adjust the equation to:
\[ n = (2)(9)Q + 8 \]
\[ n = 18Q + 8 \]

**Step 4:** Final Adjustment
- For \(n = 18Q +8\) to be divisible by \(18\) transform the \(+8\) into a \(+18\), by simply adding \(10\).

**Conclusion:**
- The manipulation reveals the necessity to add \(10\) to align with the condition. This leads us to our final answer, d.