[Math Revolution GMAT math practice question]
The average of the maximum and the minimum of a data set is x and its maximum is 40. The range of the set is 10 greater than x. What is the minimum of the set in terms of x?
A. x - 20
B. 2x - 40
C. 2x
D. 20 - x
E. 40 - 2x
The median of a data set is x and its maximum is 40. The ran
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- Max@Math Revolution
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Last edited by Max@Math Revolution on Sun Aug 26, 2018 11:11 am, edited 1 time in total.
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The range of the set is 2 times 40 - x, since 40 - x is the distance between the median and the maximum. The minimum is the median minus the distance between the median and the maximum, which is x - ( 40 - x ) = 2x - 40.
Therefore, the answer is B.
Answer : B
The range of the set is 2 times 40 - x, since 40 - x is the distance between the median and the maximum. The minimum is the median minus the distance between the median and the maximum, which is x - ( 40 - x ) = 2x - 40.
Therefore, the answer is B.
Answer : B
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Median is middle value of a ranked order of numbers. Let's pick some:
40 has to be the largest number. Let's try the following:
40 20 20 10 10
The median here is 20. The range is 40-10 = 30, which is 10 greater than the median of 20. So this satisfies the problem statement.
The minimum of this set is 10. The suggested answer of 2 x median - 40 would suggest the minimum is 0, which isn't the case.
Using algebra: 40 - minimum = median + 10
So minimum = 30 - median. Let's test this on the numbers above
30 - 20 = 10 = minimum. Yes
Answer not among the choices
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GIVEN: The median of a data set is x, and its MAXIMUM is 40Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
The median of a data set is x and its maximum is 40. The range of the set is 10 greater than the median. What is the minimum of the set in terms of x?
A. x - 20
B. 2x - 40
C. 2x
D. 20 - x
E. 40 - 2x
The range of the set is 10 greater than the median
So, the range = x + 10
Let N = the MINIMUM value
We can write: MAXIMUM value - MINIMUM value = range
Rewrite as: 40 - N = x + 10
What is the minimum of the set in terms of x?
So, we must solve the above equation for N
Take: 40 - N = x + 10
Subtract 40 from both sides to get: -N = x - 30
Multiply both sides by -1 to get: N = -x + 30, which is the same as N = 30 - x
The answer is not among the answer choices.
Cheers,
Brent
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Max@Math Revolution wrote: The range of the set is 2 times 40 - x, since 40 - x is the distance between the median and the maximum.
Your suggestion that range = 2(maximum value - median) is not always true
In fact, the only time the range = 2(maximum value - median) is when the median is the average of the minimum and maximum value.
For example, in the set {1, 9, 17}, the range = 17 - 1 = 16, which is equal to 2(maximum value - median)
However, the rule does not work when the median is NOT the average of the minimum and maximum value.
For example, the set {-9, 39, 40} satisfies the given information
Here, x = 39, the maximum value is 40, and the range (of 49) is 10 greater than the median (39)
In this case, minimum value (-9) does NOT equal 2x - 40
Cheers,
Brent
- Max@Math Revolution
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The question should be changed to the following.
It is fixed now.
The average of the maximum and the minimum of a data set is x and its maximum is 40. The range of the set is 10 greater than x. What is the minimum of the set in terms of x?
It is fixed now.
The average of the maximum and the minimum of a data set is x and its maximum is 40. The range of the set is 10 greater than x. What is the minimum of the set in terms of x?
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