Question 1

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General aptitude tests frequently challenge candidates with problems involving averages, requiring a blend of arithmetic skill and logical reasoning. This classic problem, where the average shifts upon removal of a number, serves as an excellent exercise to sharpen your quantitative abilities.

Understanding the Core Concept of Averages

Averages, or means, are fundamental in statistics and everyday calculations, representing the central value of a dataset. They are pivotal in aptitude exams for assessing numerical proficiency.

Definition and Formula

Accepted Answer

The average of a set of numbers is calculated by summing all values and dividing by the count. For instance, with five numbers, the sum is five times the average, a key insight for solving such problems.

Question 2

Importance in Aptitude Testing

Accepted Answer

Averages are commonly tested because they evaluate basic arithmetic and problem-solving skills under time constraints. Many competitive exams include them to filter candidates efficiently.

Question 3

Step 1: Calculate the Total Sum Initially

Accepted Answer

Using the average formula, the sum of the five numbers is ##5 	imes 28 = 140##. This total is crucial for finding the removed number later in the solution.

Question 4

Step 2: Find the Sum After Removal

Accepted Answer

After removing one number, the average of the remaining four is 30, so their sum is ##4 	imes 30 = 120##. This step isolates the effect of the removal on the total.

Question 5

Step 3: Determine the Removed Number

Accepted Answer

Subtract the sum after removal from the original sum: ##140 &#8211; 120 = 20##. Thus, the removed number is 20, a straightforward arithmetic result.

Question 6

Step 4: Verify the Solution

Accepted Answer

To ensure accuracy, check if removing 20 from the set of five numbers with sum 140 leaves a sum of 120 for four numbers, yielding an average of 30, which confirms the answer.

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