The sum of five numbers is 655. The average of the first two numbers is 76 and the third number is 128. Find the average of the remaining two numbers.

1. A

   204

2. B

   205

3. C

   188.5

4. D

   187.5

Appeared in: Bihar NHM CHO-2025

Explanation

• The problem requires a multi-step calculation involving sums and averages.
• First, calculate the sum of the first two numbers: Average × Count = 76 × 2 = 152.
• Next, find the sum of the first three numbers by adding the third number: 152 + 128 = 280.
• Then, determine the sum of the remaining two numbers by subtracting the sum of the first three from the total sum: 655 - 280 = 375.
• Finally, calculate the average of these two remaining numbers by dividing their sum by their count: 375 / 2 = 187.5.

Why Other Options Were Wrong

• Option A: The value 204 is incorrect. This result might be obtained through a calculation error, such as incorrectly subtracting the sum of the first three numbers from the total sum.
• Option B: The value 205 is incorrect. This is likely a result of an arithmetic mistake during one of the subtraction or division steps.
• Option C: The value 188.5 is incorrect. It is very close to the correct answer and likely results from a minor calculation error, such as miscalculating the sum of the remaining numbers as 377 instead of 375.

Related Visual

• Visual 1: Flowchart: A flowchart illustrating the step-by-step process: Start with Total Sum -> Calculate Sum of First 2 -> Add 3rd Number -> Subtract from Total Sum -> Divide by 2 to get Final Average. This visual would clarify the logical sequence of calculations.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating Averages and Sums as background academic context rather than a clinical decision trigger.
• While this is a mathematics question, strong numeracy skills are fundamental in nursing for accurate medication dosage calculations, interpreting lab results, and managing fluid intake and output records.
• A nurse must be able to perform multi-step calculations quickly and accurately to ensure patient safety.
• What if the average of the first two numbers was 80 instead of 76? The sum of the first two numbers would be 160. The sum of the first three would be 160 + 128 = 288. The sum of the last two would be 655 - 288 = 367. The average would then be 367 / 2 = 183.5.

How to Approach the Question

• Identify all the given values: the total sum, the count of numbers, the average of a subset, and the value of another number.
• Use the formula 'Sum = Average × Count' to find the sum of the first two numbers.
• Add the value of the third number to this sum to get the total sum of the first three numbers.
• Subtract this partial sum from the total sum of all five numbers to find the sum of the remaining two numbers.
• Divide the sum of the remaining two numbers by 2 to find their average.
• Double-check your arithmetic at each step to avoid simple errors.

Concept Tested & Keywords

• Concept Tested: Calculating Averages and Sums
• Stem keywords: sum, five numbers, average, first two numbers, third number, remaining two numbers
• Lead-in keywords: Find

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Q46I6gT6PEuzFEw74kAS2h

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