The average of four numbers is 61. The largest number among them is 85 and the smallest number is 21. What will be the larger of the remaining two numbers if their difference is 26?

1. A

   56

2. B

   65

3. C

   82

4. D

   74

Appeared in: BHU NO - 12 April 2024

Explanation

• The sum of the four numbers is the average multiplied by the count (61 × 4 = 244).
• Subtracting the known numbers (85 and 21) from the total sum gives the sum of the two remaining numbers (244 - 106 = 138).
• With the sum (x + y = 138) and difference (x - y = 26) of the two unknown numbers, a system of linear equations can be solved.
• Adding the two equations (2x = 164) directly yields the value of the larger number, x = 82.

Why Other Options Were Wrong

• Option A: This is the value of the smaller of the two remaining numbers (y), not the larger one (x).
• Option B: This value is incorrect and likely results from a calculation error, such as miscalculating the sum or difference of the numbers.
• Option D: This value is incorrect and likely results from a calculation error. For instance, incorrectly adding or subtracting during the equation-solving process might lead to a wrong result.

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Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a word problem involving averages and systems of linear equations as background academic context rather than a clinical decision trigger.
• While this is a general mathematics question, the underlying skill of using averages and solving for unknowns is crucial in nursing for tasks like calculating drug dosages, interpreting patient fluid balance charts, and analyzing vital sign trends over time.
• What if the difference between the remaining two numbers was 10? Then the equations would be x + y = 138 and x - y = 10. Solving this gives 2x = 148, so x = 74. The larger number would be 74.

How to Approach the Question

• First, identify all the given numerical values: the average (61), the count of numbers (4), the largest number (85), the smallest number (21), and the difference between the other two (26).
• Calculate the total sum of all four numbers by multiplying the average by the count (61 × 4).
• Find the sum of the two unknown numbers by subtracting the two known numbers from the total sum.
• Set up two algebraic equations. Let the unknown numbers be 'x' and 'y'. The first equation is their sum (x + y = ?), and the second is their difference (x - y = 26).
• Solve this system of two equations to find the values of 'x' and 'y'.
• Read the question again to ensure you are providing the requested value (the larger of the two numbers).

Concept Tested & Keywords

• Concept Tested: Solving a word problem involving averages and systems of linear equations.
• Stem keywords: average, four numbers, largest number, smallest number, difference
• Lead-in keywords: What will be the larger

Question ID

Q_moGX_Mz6PeXGp2tnrNnY

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