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stormbind
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When the even integer n is divided by 9, the remainder is 8. Which of Updated on: 08 Nov 2023, 07:52
Originally posted by stormbind on 25 Apr 2013, 15:31.
Last edited by Bunuel on 08 Nov 2023, 07:52, edited 2 times in total.
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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?

A. 1
B. 4
C. 9
D. 10
E. 17

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D
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Bunuel
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When the even integer n is divided by 9, the remainder is 8. Which of 25 Apr 2013, 15:50
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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?

A. 1
B. 4
C. 9
D. 10
E. 17

Given that \(n=9q+8\) and n is even, n could be 8, 26, 44, ...

What number from answer choices when added to 8 (for example) yields a multiple of 18? It's 10!

Answer: D.
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When the even integer n is divided by 9, the remainder is 8. Which of 30 Jan 2024, 10:13
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Thib33600
Is there a way to use answer choices?
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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).
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When the even integer n is divided by 9, the remainder is 8. Which of 30 Jan 2024, 09:16
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Bunuel
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?

A. 1
B. 4
C. 9
D. 10
E. 17

Given that \(n=9q+8\) and n is even, n could be 8, 26, 44, ...

What number from answer choices when added to 8 (for example) yields a multiple of 18? It's 10!

Answer: D.
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Is there a way to use answer choices?
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When the even integer n is divided by 9, the remainder is 8. Which of 29 Feb 2024, 12:05
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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.
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When the even integer n is divided by 9, the remainder is 8. Which of 15 May 2024, 06:42
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­Classic remainder problem. N= 9k + 8 and also its even so gotta add 10:

­
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When the even integer n is divided by 9, the remainder is 8. Which of 22 May 2025, 04:15
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