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If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?
- a)(Q - 1)/2 + 120
- b)Q/2 + 119
- c)Q/2 + 120
- d)(Q + 119)/2
- e)(Q + 120)/2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If Q is an odd number and the median of Q consecutive integers is 120,...
Understanding the Problem
To find the largest integer in a set of Q consecutive integers where Q is an odd number and the median is 120, we start by defining the series of integers.
Defining the Integers
- Let the consecutive integers be represented as:
(x, x+1, x+2, ..., x+Q-1)
- Since Q is odd, the median is the middle integer:
Median = x + (Q-1)/2
Setting the Median
- Given that the median is 120, we can set up the equation:
x + (Q-1)/2 = 120
Solving for x
- Rearranging gives us:
x = 120 - (Q-1)/2
x = 120 - Q/2 + 1/2
x = 120 + 1/2 - Q/2
Finding the Largest Integer
- The largest integer in the set is:
x + (Q - 1) = (120 - (Q-1)/2) + (Q - 1)
= 120 + (Q - 1)/2
- Simplifying this, we have:
= (Q - 1)/2 + 120
Conclusion
- Therefore, the largest of these integers is given by:
(Q - 1)/2 + 120
- This matches option 'A', confirming that it is indeed the correct answer.
To find the largest integer in a set of Q consecutive integers where Q is an odd number and the median is 120, we start by defining the series of integers.
Defining the Integers
- Let the consecutive integers be represented as:
(x, x+1, x+2, ..., x+Q-1)
- Since Q is odd, the median is the middle integer:
Median = x + (Q-1)/2
Setting the Median
- Given that the median is 120, we can set up the equation:
x + (Q-1)/2 = 120
Solving for x
- Rearranging gives us:
x = 120 - (Q-1)/2
x = 120 - Q/2 + 1/2
x = 120 + 1/2 - Q/2
Finding the Largest Integer
- The largest integer in the set is:
x + (Q - 1) = (120 - (Q-1)/2) + (Q - 1)
= 120 + (Q - 1)/2
- Simplifying this, we have:
= (Q - 1)/2 + 120
Conclusion
- Therefore, the largest of these integers is given by:
(Q - 1)/2 + 120
- This matches option 'A', confirming that it is indeed the correct answer.
Community Answer
If Q is an odd number and the median of Q consecutive integers is 120,...
If Q is an odd number and the median of Q consecutive integers is 120, we can determine the largest of these integers using the properties of odd numbers.
Let's consider the median of Q consecutive integers. Since Q is an odd number, the median will be the middle number. In this case, the median is given as 120.
We know that the median is the average of the two middle numbers when Q is an odd number. Therefore, we can represent the two middle numbers as 120 and 120.
To find the largest integer, we need to determine the number that comes after the second middle number. Since the consecutive integers are evenly spaced, the difference between each integer is 1.
Therefore, the largest integer can be obtained by adding (Q - 1)/2 to the second middle number, which is 120.
Hence, the largest integer is (Q - 1)/2 + 120.
Therefore, the correct answer is A: (Q - 1)/2 + 120.
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