Data Sufficiency

If set s consists of the numbers 1,5,-2,8 and n, is 0<n<7 ?

(1) The median of the numbers in S is less than 5

(2) The median of the numbers in S is greater than 1

Ans C

moneyman wrote:If set s consists of the numbers 1,5,-2,8 and n, is 0<n<7 ?

(1) The median of the numbers in S is less than 5

(2) The median of the numbers in S is greater than 1

Ans C

In the given set of numbers the median will be the middle number after it has been arranged in an ascending order. So the given numbers can be arranged as -2,1,5,8 with n depending upon its value falling in somewhere between.

Let us consider 3 cases for n (1) it is less than 0 (2) it is greater than 7 (3) it is between 0 and 7 (which is our question).

The first statement says that the median is less than 5. Now if n is <0 e.g -4 the median would be 1 (which is less than 5) as the series would become -4,-2,1,5,8. If n is equal to 3 then the series would become -2,1,3,5,8 in which case the median is 3 (<5> 7, e.g. 15, then the series would become -2,1,5,8,15 in which case the median would be 5 (which is equal to 5 and hence negates the statement) which mean n cannot be greater than 7. So as we can see the n can be < 0 i.e. outside the range of numbers 0<n<7 and also assume a value within the range 0<n<7 and still satisfy statement 1. Hence this statement is not sufficient.

The second statement says the median is greater than 1. Using the same reasoning as above we will see that n can assume values within the range 0<n<7 and values greater than 7 and still satisfy statement 2. So this statement is also insufficient.

Combine both the statements and we have that the median is between 1 and 5. Now as there is no other number between 1 and 5 in the series the median will be n and it will assume a value of 2,3,4 which means that n will be between 0 and 7. So both the statements combined are sufficient. Let me know if any doubts.

Crystal clear

(C)

~AJ

moneyman wrote:If set s consists of the numbers 1,5,-2,8 and n, is 0<n<7 ?

(1) The median of the numbers in S is less than 5

(2) The median of the numbers in S is greater than 1

I received a PM requesting that I comment.

In ascending order, set S without n = -2, 1, 5, 8.
In the cases below, red value = median.

Is 0 < n < 7?

Statement 1:
Case 1: n=1, with the result that S = -2, n=1, 1, 5, 8.
Case 2: n=0, with the result that S = -2, n=0, 1, 5, 8.
Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2:
Case 3: n=6, with the result that S = -2, 1, 5, n=6, 8.
Case 4: n=7, with the result that S = -2, 1, 5, n=7, 8.
Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statements combined:
Case 2 (n=0) yields a median of 1, which does not satisfy Statement 2.
If n<0, then the median will either remain 1 or become smaller, with the result that Statement 2 will remain unsatisfied.

Case 4 (n=7) yields a median of 5, which does not satisfy Statement 1.
If n>7, then the median will either remain 5 or become greater, with the result that Statement 1 will remain unsatisfied.

Implication:
No value of n such that n≤0 or n≥7 will satisfy both statements.
Thus:
To satisfy both statements, 0<n<7.
SUFFICIENT.

The correct answer is C.

GMATGuruNY wrote:

moneyman wrote:If set s consists of the numbers 1,5,-2,8 and n, is 0<n<7 ?

(1) The median of the numbers in S is less than 5

(2) The median of the numbers in S is greater than 1

I received a PM requesting that I comment.

In ascending order, set S without n = -2, 1, 5, 8.
In the cases below, red value = median.

Is 0 < n < 7?

Statement 1:
Case 1: n=1, with the result that S = -2, n=1, 1, 5, 8.
Case 2: n=0, with the result that S = -2, n=0, 1, 5, 8.
Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2:
Case 3: n=6, with the result that S = -2, 1, 5, n=6, 8.
Case 4: n=7, with the result that S = -2, 1, 5, n=7, 8.
Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statements combined:
Case 2 (n=0) yields a median of 1, which does not satisfy Statement 2.
If n<0, then the median will either remain 1 or become smaller, with the result that Statement 2 will remain unsatisfied.

Case 4 (n=7) yields a median of 5, which does not satisfy Statement 1.
If n>7, then the median will either remain 5 or become greater, with the result that Statement 1 will remain unsatisfied.

Implication:
No value of n such that n≤0 or n≥7 will satisfy both statements.
Thus:
To satisfy both statements, 0<n<7.
SUFFICIENT.

The correct answer is C.

Dear GMAtGUrur,

Both cases 1 & 2 do not satisfy both statements, so it must be that 1 < n <5?

Am I correct?

Mo2men wrote:Dear GMAtGUrur,

Both cases 1 & 2 do not satisfy both statements, so it must be that 1 < n <5?

Am I correct?

Correct!
Both statements are satisfied only if n is the median such that 1<n<5, as follows:
-2, 1, 1<n<5, 5, 8.