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The median of a data set is x and its maximum is 40. The ran

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The median of a data set is x and its maximum is 40. The ran

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[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

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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

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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. 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
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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Max@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
GIVEN: The median of a data set is x, and its MAXIMUM is 40

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

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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?

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