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What is the median of m, n and 5?

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What is the median of m, n and 5?  [#permalink]

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New post 24 Apr 2018, 05:54
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A
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C
D
E

Difficulty:

  45% (medium)

Question Stats:

54% (01:02) correct 46% (00:47) wrong based on 79 sessions

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[GMAT math practice question]

What is the median of \(m, n\) and \(5\)?

\(1) m+n=10\)
\(2) m=5\)

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Re: What is the median of m, n and 5?  [#permalink]

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New post 24 Apr 2018, 09:50
Statement 1: m+n=10
we don't know the values of m and n
Not Sufficient

Statement 2: m=5
the no. 5 is duplicated, so the numbers can be arranged as n, 5, 5 or 5,5,n
So, the median will be 5, in either case.
Hence, Sufficient
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Re: What is the median of m, n and 5?  [#permalink]

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New post 24 Apr 2018, 10:30
What is the median of m,n and 5?

Stat:1) m+n=10 : Mean (m,n) can have values (1,9), (2,8), (3,7), (4,6) and (5,5) or opposite. In this case we know that 5 will always be in the middle. so median will be 5. (Sufficient)

Stat 2)m=5 : Means out of three 2 are 5 so we need to find median of (5,5,n) whatever the value n holds median will always be 5. (Sufficient)

Both statement alone are sufficient to ans.
Ans: D
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Re: What is the median of m, n and 5?  [#permalink]

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New post 25 Apr 2018, 06:48
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MathRevolution wrote:
[GMAT math practice question]

What is the median of \(m, n\) and \(5\)?

\(1) m+n=10\)
\(2) m=5\)


Target question: What is the median of m, n and 5?

Statement 1: m + n = 10
Let's examine the ONLY TWO possible cases: m and n are equal and m and n are NOT equal
Case a: m and n are equal. That is m = 5 and n = 5. In this case, the set = {5, 5, 5 }, in which case the answer to the target question is the median is 5
Case b: m and n are NOT equal. This means one value is greater than 5, and one value is less than 5. In this case, the set = {a number less than 5, 5, a number greater than 5 }, in which case the answer to the target question is the median is 5
Since there are only 2 possible cases, and since the answer to the target question is the SAME in each case, we can conclude that there's only ONE possible answer to the target question: the median is 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: m = 5
So, the set = {n, 5, 5}
Since two of the three values are 5, the median MUST be 5. Here's why:
If n is less than 5, then set set = {a number less than 5, 5, 5}, in which case the median is 5
If n = 5, then set set = {5, 5, 5}, in which case the median is 5
If n is greater than 5, then set = {5, 5, a number greater than 5 }, in which case the median is 5
So, the median MUST BE 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

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Re: What is the median of m, n and 5?  [#permalink]

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New post 26 Apr 2018, 01:18
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2) together:
Since \(m + n = 10\) and \(m = 5\), we have \(m = n = 5\).
Thus, the median of \(m, n\) and \(5\) is \(5\).

Both conditions together are sufficient.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1): \(m + n = 10\)
If one of \(m\) and \(n\) is less than \(5,\) the other one must be greater than \(5\). For example, if \(m < 5\), then \(n > 5\).
If one of \(m\) and \(n\) is \(5\), the other must also equal \(5\). For example, if \(m = 5\), then \(n = 5\).
In both cases, the median is \(5\).
Condition 1) is sufficient.

Condition 2) : \(m = 5.\)
If \(n > 5\), the numbers are \(5, 5, n\) in ascending order.
If \(n < 5\), the numbers are \(n, 5, 5\) in descending order.
If \(n = 5\), the numbers are \(5, 5, 5\).
In each of the possible cases, the median is \(5\).
Condition 2) is sufficient.

Therefore, D is the answer.

Answer: D

Note: The VA approach tells us that the answer is most likely to be D, since this is a CMT(Common Mistake Type) 4B question.
Condition 1) is easy to check, but condition 2) is more difficult to work with. If you can’t figure out condition 2), you should choose D as the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

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Re: What is the median of m, n and 5?  [#permalink]

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New post 11 May 2018, 23:36
For median we need to arrange numbers in ascending order and then see middle value

I)m+n=10
M and n can both be 5 here , so for series
5,5,5 5 is median

Otherwise for sum to be 10 and values are other than 5
Then one value would be less than 5 and other would be greater than 5

So middle value i.e. median will always be 5
Eg 4,5,6
Or 4.5,5,5.5

II)m=5
Two values among 3 are 5
So 3rd value can be either greater than or less than 5
i.e 3,5,5. Or 5,5,6
In both cases 5 is median
Sufficient

D is answer

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Re: What is the median of m, n and 5? &nbs [#permalink] 11 May 2018, 23:36
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