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Set S consists of integers 7, 8, 10, 12, and 13. If integer n is included in the set, the average (arithmetic
mean) of set S will increase by 20%. What is the value of integer n?
mean) of set S will increase by 20%. What is the value of integer n?
- a)10
- b)12
- c)16
- d)22
- e)24
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Set S consists of integers 7, 8, 10, 12, and 13. If integer n is inclu...
First, let’s use the average formula to find the current mean of set S: Current mean of set S = (sum of the terms)/(number of terms): (sum of the terms) = (7 + 8 + 10 + 12 + 13) = 50 (number of terms) = 5 50/5 = 10
Mean of set S after integer n is added = 10 × 1.2 = 12 Next, we can use the new average to find the sum of the elements in the new set and compute the value of integer n. Just make sure that you remember that after integer n is added to the set, it will contain 6 rather than 5 elements. Sum of all elements in the new set = (average) × (number of terms) = 12 × 6 = 72 Value of integer n = sum of all elements in the new set – sum of all elements in the original set = 72 – 50 = 22 The correct answer is D.
Mean of set S after integer n is added = 10 × 1.2 = 12 Next, we can use the new average to find the sum of the elements in the new set and compute the value of integer n. Just make sure that you remember that after integer n is added to the set, it will contain 6 rather than 5 elements. Sum of all elements in the new set = (average) × (number of terms) = 12 × 6 = 72 Value of integer n = sum of all elements in the new set – sum of all elements in the original set = 72 – 50 = 22 The correct answer is D.
Most Upvoted Answer
Set S consists of integers 7, 8, 10, 12, and 13. If integer n is inclu...
Understanding the Problem
The problem states that including an integer n in set S will increase the average of the set by 20%. We need to find the value of n from the options provided.
Calculating the Current Average
1. Elements of Set S: {7, 8, 10, 12, 13}
2. Number of Elements: 5
3. Sum of Elements: 7 + 8 + 10 + 12 + 13 = 50
4. Current Average: 50 / 5 = 10
Finding the New Average
1. Increase in Average: 20% of 10 = 2
2. New Average: 10 + 2 = 12
Setting Up the Equation
When we include n in the set, the new average becomes:
1. New Sum: 50 + n
2. New Number of Elements: 5 + 1 = 6
3. Equation for New Average: (50 + n) / 6 = 12
Simplifying the Equation
1. Multiply both sides by 6:
- 50 + n = 72
2. Solve for n:
- n = 72 - 50 = 22
Conclusion
The value of integer n that increases the average by 20% is 22.
Thus, the correct answer is option d) 22.
The problem states that including an integer n in set S will increase the average of the set by 20%. We need to find the value of n from the options provided.
Calculating the Current Average
1. Elements of Set S: {7, 8, 10, 12, 13}
2. Number of Elements: 5
3. Sum of Elements: 7 + 8 + 10 + 12 + 13 = 50
4. Current Average: 50 / 5 = 10
Finding the New Average
1. Increase in Average: 20% of 10 = 2
2. New Average: 10 + 2 = 12
Setting Up the Equation
When we include n in the set, the new average becomes:
1. New Sum: 50 + n
2. New Number of Elements: 5 + 1 = 6
3. Equation for New Average: (50 + n) / 6 = 12
Simplifying the Equation
1. Multiply both sides by 6:
- 50 + n = 72
2. Solve for n:
- n = 72 - 50 = 22
Conclusion
The value of integer n that increases the average by 20% is 22.
Thus, the correct answer is option d) 22.
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Set S consists of integers 7, 8, 10, 12, and 13. If integer n is included in the set, the average (arithmeticmean) of set S will increase by 20%. What is the value of integer n?a)10b)12c)16d)22e)24Correct answer is option 'D'. Can you explain this answer?
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