If the average of 21, 25, 24, 20, A and B is 26 then what is the average of A and B?

Appeared in: CIP Ranchi 2023

Explanation

The average of a set of numbers is their total sum divided by the count of the numbers.
The question states the average of 6 numbers (21, 25, 24, 20, A, B) is 26. Therefore, the total sum of these numbers is 26 × 6 = 156.
The sum of the four known numbers is calculated as 21 + 25 + 24 + 20 = 90.
To find the sum of the two unknown numbers (A + B), subtract the sum of the known numbers from the total sum: 156 - 90 = 66.
The average of A and B is their sum (66) divided by their count (2), which results in 66 / 2 = 33.

Option A: This value would imply that the sum of A and B is 70 (35 × 2), which is incorrect. The actual sum is 66.
Option C: This value would imply that the sum of A and B is 72 (36 × 2), which is incorrect. This might result from miscalculating the sum of the known numbers as 84 instead of 90.
Option D: This value would imply that the sum of A and B is 74 (37 × 2), which is incorrect. The actual sum is 66.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating averages and finding missing values in a dataset as background academic context rather than a clinical decision trigger.
While this is a general aptitude question, the concept of averages is vital in nursing practice.
Nurses use averages to monitor trends in vital signs (e.g., average heart rate over an hour), interpret lab results (e.g., mean corpuscular volume), and calculate fluid balance over a shift.
Understanding how to work with averages is also essential for evidence-based practice, as research studies often report findings using mean values.

How to Approach the Question

First, identify the key information given: the list of items (including unknowns), the total count of items (6), and the overall average (26).
Recall the formula for an average: Average = Sum / Count. Rearrange it to find the total sum: Sum = Average × Count.
Calculate the total sum of all six numbers by multiplying the average (26) by the count (6).
Calculate the sum of the known numbers (21, 25, 24, 20).
Subtract the sum of the knowns from the total sum to isolate the sum of the unknowns (A + B).
Finally, calculate the average of the unknowns by dividing their sum by their count (2).

Concept Tested & Keywords

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Practise the full CIP Ranchi 2023

Attempt every question from this paper in a timed mock, then review the full solution for each one.