Out of four numbers, the average of first 3 is 15 and the average of last 3 is 16. If the last number is 19, find the first number.?

1. A

   19

2. B

   15

3. C

   16

4. D

   18

Appeared in: HPSSC - 2015

Explanation

• The problem provides the average of two overlapping sets of three numbers and the value of the last number.
• From the average of the last three numbers (16) and the value of the last number (19), we can find the sum of the middle two numbers. The calculation is: (Sum of last 3 = 16 × 3 = 48), so (Sum of middle two = 48 - 19 = 29).
• Using the sum of the middle two numbers (29) and the average of the first three numbers (15), we can find the first number. The calculation is: (Sum of first 3 = 15 × 3 = 45), so (First number = 45 - 29 = 16).

Why Other Options Were Wrong

• Option A: This is the value of the last number, which is given in the problem statement. The question asks for the first number.
• Option B: This is the average of the first three numbers, not the value of the first number itself.
• Option D: This value is incorrect and likely results from a calculation error, such as subtracting an incorrect value from the sum of the first three numbers.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Average and algebraic manipulation as background academic context rather than a clinical decision trigger.
• Aptitude questions involving averages are common in the General Intelligence and Reasoning sections of nursing entrance exams.
• This type of problem tests logical reasoning and the ability to translate word problems into mathematical equations, a skill useful for tasks like calculating medication dosages or interpreting patient data trends.
• What if the last number was 16 instead of 19? The sum of the middle two numbers would be 48 - 16 = 32. The first number would then be 45 - 32 = 13.

How to Approach the Question

• Identify the given information: the total count of numbers, the averages of different subsets, and the value of one specific number.
• Translate the word problem into algebraic equations. Let the numbers be variables (e.g., a, b, c, d).
• Use the formula: Sum = Average × Number of items.
• Create two main equations: one for the first three numbers (a + b + c = 15 × 3) and one for the last three (b + c + d = 16 × 3).
• Substitute the known value (d = 19) into the second equation to find the sum of the overlapping numbers (b + c).
• Substitute this sum back into the first equation to isolate and solve for the unknown first number (a).

Concept Tested & Keywords

• Concept Tested: Average and algebraic manipulation
• Stem keywords: four numbers, average, first 3, last 3, last number
• Lead-in keywords: find the first number

Question ID

Qo17_dehDtwHkSs5XgiyBj

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