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What is the median of 10 numbers?

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What is the median of 10 numbers?  [#permalink]

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New post 30 Jul 2018, 23:42
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[Math Revolution GMAT math practice question]

What is the median of 10 numbers?

1) 6 of the ten numbers are less than or equal to 10.
2) 6 of the ten numbers are greater than or equal to 10.

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Re: What is the median of 10 numbers?  [#permalink]

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New post 30 Jul 2018, 23:56
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the median of 10 numbers?

1) 6 of the ten numbers are less than or equal to 10.
2) 6 of the ten numbers are greater than or equal to 10.



Since the numbers are even in total that is 10 numbers..
Median will be average of 5th and 6th

1) 6 of the ten numbers are less than or equal to 10.
If numbers are 0,0,0,0,0,0,0,0.. median is 0
If 8,9,9,9,9,9,10,20,... Median is 9
Insufficient

2) 6 of the ten numbers are greater than or equal to 10.
Similarly here too we can have median anything equal or greater than 10
Insufficient

Combined..
Statement I tells us that 5th and 6th number cannot be >10
And statement II tells us that 5th and 6th number cannot be <10
Only possibility is if both are 10, thus the median is 10
Sufficient

C
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Re: What is the median of 10 numbers?  [#permalink]

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New post 31 Jul 2018, 02:08
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the median of 10 numbers?

1) 6 of the ten numbers are less than or equal to 10.
2) 6 of the ten numbers are greater than or equal to 10.


median of 10 numbers = 10/2 (5th number when arranged in ascending order)

1) 6 of the ten numbers are less than or equal to 10.
There is now way to line up the numbers
clearly insufficient
2) 6 of the ten numbers are greater than or equal to 10
again insufficient.

combining both

say we have the following numbers
a,b,c,d,e,f,g,h,i,j
from statement 1 and 2
e will always be 10
sufficient
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Re: What is the median of 10 numbers?  [#permalink]

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New post 31 Jul 2018, 05:28
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the median of 10 numbers?

1) 6 of the ten numbers are less than or equal to 10.
2) 6 of the ten numbers are greater than or equal to 10.


Statement 1:
Case 1: X, X, X, X, 10, 10, X, X, X, X
Here, the 6 blue values are all less than or equal to 10.
In this case, the median = (10+10)/2 = 10
Case 2: X, X, X, X, 8, 10, X, X, X, X
Here, the 6 red values are all less than or equal to 10.
In this case, the median = (8+10)/2 = 9.
Since the median can be different values, INSUFFICIENT.

Statement 2:
Case 1 also satisfies Statement 2.
Case 1: X, X, X, X, 10, 10, X, X, X, X
Here, the 6 blue values are all greater than or equal to 10.
In this case, the median = 10.
Case 3: X, X, X, X, 10, 12, X, X, X, X
Here, the 6 red values are all greater than or equal to 10.
In this case, the median = (10+12)/2 = 11.
Since the median can be different values, INSUFFICIENT.

Statements 1 and 2:
Only Case 1 satisfies both statements.
In Case 1, the median = 10.
SUFFICIENT.


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Re: What is the median of 10 numbers?  [#permalink]

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New post 01 Aug 2018, 23:36
=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Let x1, x2, … , x10 be the 10 numbers, written in increasing order: x1 ≤ x2 ≤ … ≤ x10.
The median of 10 numbers is the average of the 5th number, x5 and the 6th number, x6.

By condition 1), x5 ≤ x6 ≤ 10, and by condition 2), 10 ≤ x5 ≤ x6.
Thus, x5 = x6 = 10.
The median is ( x5 + x6 ) / 2 = 10.
Both conditions together are sufficient.

Therefore, the answer is C.

Answer: C
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