Directions: Solve the question below and select the correct option.

The mean score of 9 assessments in a course is 50. If the average score of the first 5 assessments is 46 and the average score of the last 5 assessments is 56, what is the score obtained in the 5th assessment?

The correct option is 60.

Step-by-step explanation:

Step 1: Calculate the total sum of all 9 assessments.

Given that the mean score of 9 assessments is 50, the total sum of scores for all 9 assessments is:

$\text{Total sum of 9 assessments}=9\times 50=450$

Step 2: Calculate the total sum of the first 5 assessments.

The average score of the first 5 assessments is 46, so their sum is:

$\text{Sum of first 5 assessments}=5\times 46=230$

Step 3: Calculate the total sum of the last 5 assessments.

The average score of the last 5 assessments is 56, so their sum is:

$\text{Sum of last 5 assessments}=5\times 56=280$

Step 4: Find the score obtained in the 5th assessment.

Adding the sum of the first 5 assessments and the sum of the last 5 assessments counts the 5th assessment twice (since it is included in both groups):

$\text{Sum of first 5}+\text{Sum of last 5}=\text{Total sum of 9 assessments}+\text{Score of 5th assessment}$

$230+280=450+\text{Score of 5th assessment}$

$510=450+\text{Score of 5th assessment}$

$\text{Score of 5th assessment}=510-450=60$

Therefore, the score obtained in the 5th assessment is 60.