Out of four numbers, the average of first 3 is 15 and the average of the last 3 is 16. if the last number is 19, the first number is :

Appeared in: RRB Staff Nurse Delhi-2015

Explanation

The problem is solved by creating two algebraic equations from the definition of average (sum of values divided by the number of values).
The average of the first three numbers (a, b, c) is 15, so their total sum is a + b + c = 15 × 3 = 45.
The average of the last three numbers (b, c, d) is 16, meaning their total sum is b + c + d = 16 × 3 = 48.
Given that the last number (d) is 19, we can find the sum of the middle two numbers: b + c = 48 - 19 = 29.
By substituting the sum of (b + c) into the first equation, we can find the first number (a): a + 29 = 45, which gives a = 16.

Option A: This is the value of the last number (d), which was given in the problem statement. The question asks for the first number (a).
Option B: This is the average of the first three numbers, not the value of the first number itself. The first number is only one component of this average.
Option D: This value is incorrect and likely results from a calculation error, such as subtracting 29 from 47 instead of 45.

Visual 1: Flowchart - A flowchart illustrating the step-by-step algebraic solution. It would show how to set up the two initial equations, substitute the known value of the last number, solve for the intermediate sum, and finally substitute that sum to find the first number.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating a missing value in a series using the properties of arithmetic mean (average) as background academic context rather than a clinical decision trigger.
While this is a general mathematics question, the underlying skill of logical problem-solving is crucial in nursing.
Nurses frequently use analytical skills for tasks like calculating medication dosages, interpreting vital signs and lab values, and managing patient intake/output, all of which require precision.
This type of problem strengthens the logical reasoning needed to assess patient data and make sound clinical judgments.

How to Approach the Question

First, carefully read the problem to identify all the given information and what needs to be found.
Assign variables to the unknown quantities. In this case, let the four numbers be a, b, c, and d.
Translate the word statements into mathematical equations using the formula for average: Average = (Sum of values) / (Number of values).
This will give you two main equations: (a+b+c)/3 = 15 and (b+c+d)/3 = 16.
Use the given value (d=19) to substitute into one of the equations and simplify.
Solve the system of equations through substitution to find the value of the required variable (a).

Concept Tested & Keywords

Concept Tested: Calculating a missing value in a series using the properties of arithmetic mean (average).
Stem keywords: four numbers, average, first 3, last 3, last number, first number
Lead-in keywords: the first number is

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