A student's mean score on 5 tests was 84. The student's mean score on the first 4 of these tests was 87. What was the student's score on the fifth of these tests ?

Options

A. 68
B. 72
C. 75
D. 81

Explanation

To find the student's score on the fifth test, we can follow these steps:

### Step 1: Understand the Mean Score
The mean score of 5 tests is given as 84. The mean is calculated by dividing the total score by the number of tests. Therefore, we can express this as:
\[ \text{Mean} = \frac{m_1 + m_2 + m_3 + m_4 + m_5}{5} = 84 \]
Where \(m_1, m_2, m_3, m_4, m_5\) are the scores of the 5 tests.

### Step 2: Calculate the Total Score for 5 Tests
From the mean score, we can find the total score for the 5 tests:
\[ m_1 + m_2 + m_3 + m_4 + m_5 = 84 \times 5 = 420 \]

### Step 3: Understand the Mean Score of the First 4 Tests
The mean score of the first 4 tests is given as 87. We can express this as:
\[ \text{Mean of first 4 tests} = \frac{m_1 + m_2 + m_3 + m_4}{4} = 87 \]

### Step 4: Calculate the Total Score for the First 4 Tests
From this mean, we can find the total score for the first 4 tests:
\[ m_1 + m_2 + m_3 + m_4 = 87 \times 4 = 348 \]

### Step 5: Set Up the Equation for the Fifth Test Score
Now we have the total score for all 5 tests and the total score for the first 4 tests. We can find the score of the fifth test (\(m_5\)) using:
\[ m_5 = (m_1 + m_2 + m_3 + m_4 + m_5) - (m_1 + m_2 + m_3 + m_4) \]
Substituting the values we found:
\[ m_5 = 420 - 348 \]

### Step 6: Calculate the Score of the Fifth Test
Now we can calculate \(m_5\):
\[ m_5 = 420 - 348 = 72 \]

### Conclusion
The student's score on the fifth test is **72**.

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