When $ x $ is divided by 5, the remainder is 4. When $ x $ is divided by 9, the remainder is 0. Which of the following is a possible value for $ x $?

Option 1: 14
Option 2: 23
Option 3: 27
Option 4: 36

Question

13-03-2025
Mathematics

High School

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When $ x $ is divided by 5, the remainder is 4. When $ x $ is divided by 9, the remainder is 0. Which of the following is a possible value for $ x $?

Option 1: 14
Option 2: 23
Option 3: 27
Option 4: 36

Answer :

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Final answer:

For an integer x to satisfy the conditions of leaving a remainder of 4 when divided by 5, and a remainder of 0 when divided by 9, it must conform to the structure of both 5n+4 = x and 9m = x, where n and m are integers. Out of the given options, only 36 meets both conditions.

Explanation:

The question is asking us for a possible value of x such that it satisfies the conditions: when divided by 5 the remainder is 4, and when divided by 9, the remainder is 0. Thus, x should conform to the structure of both 5n+4 = x and 9m = x, where n and m are integers. Looking at the given options, we can examine each one. The number 14 leaves a remainder of 4 when divided by 5 but a remainder of 5 when divided by 9, hence it does not satisfy both conditions. The numbers 23 and 27 do not satisfy the condition of leaving a remainder of 0 when divided by 9 either. However, 36 satisfies both conditions: it leaves a remainder of 4 when divided by 5 (because 5*7+4 = 36) and 36 divided by 9 is exactly 4 with a remainder of 0. Therefore, among the given options, 36 is the correct answer.

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When \( x \) is divided by 5, the remainder is 4. When \( x \) is divided by 9, the remainder is 0. Which of the following is a possible value for \( x \)?Option 1: 14 Option 2: 23 Option 3: 27 Option 4: 36

Answer :

Final answer:

Explanation:

Learn more about Division with Remainders here:

Other Questions

When \( x \) is divided by 5, the remainder is 4. When \( x \) is divided by 9, the remainder is 0. Which of the following is a possible value for \( x \)?

Option 1: 14
Option 2: 23
Option 3: 27
Option 4: 36