The average of 5 numbers is 24. If one number is removed, the average becomes 20. What is the removed number?

Appeared in: AIIMS Delhi NO- 2019

Explanation

The sum of the original 5 numbers is their average (24) multiplied by the count (5), which equals 120.
After removing one number, the sum of the remaining 4 numbers is their new average (20) multiplied by the new count (4), which equals 80.
The removed number is the difference between the original sum (120) and the new sum (80), which is 40.

Option A: If 36 were removed, the new sum would be 120 - 36 = 84. The average of the remaining 4 numbers would be 84 / 4 = 21, not 20.
Option C: If 44 were removed, the new sum would be 120 - 44 = 76. The average of the remaining 4 numbers would be 76 / 4 = 19, not 20.
Option D: If 48 were removed, the new sum would be 120 - 48 = 72. The average of the remaining 4 numbers would be 72 / 4 = 18, not 20.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating a removed value from a change in average (mean) as background academic context rather than a clinical decision trigger.
Understanding how to work with averages is a fundamental skill for interpreting data sets, which is common in many fields, including analyzing patient data or research results.
This concept is crucial for data sufficiency and interpretation questions that frequently appear in competitive exams.
What if the average increased to 25 after removing a number? This would indicate that a number smaller than the original average was removed. The removed number would be 120 - (4 × 25) = 120 - 100 = 20.

How to Approach the Question

Identify the key information given: the initial average and count (24 for 5 numbers), and the final average and count (20 for 4 numbers).
Recall the formula for the sum of a set of numbers: Sum = Average × Count.
Calculate the initial total sum before the number was removed (5 × 24).
Calculate the final total sum after the number was removed (4 × 20).
The difference between the initial sum and the final sum is the value of the number that was removed.

Concept Tested & Keywords

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