P is a set of all integers between x and y, inclusive, and Q is a set

Question

P is a set of all integers between x and y, inclusive, and Q is a set of all integers between x and z, inclusive, where x, y and z are integers. The median of set P is (5/6)*y. The median of set Q is (2/3)*z. If R is a set of all integers between y and z, inclusive, what fraction of z is the median of set R?
A. ½
B. 7/12
C. 2/3
D. ¾
E. 3/2

gmatophobia · Answer

We can assume numbers to solve the question

Assume y = 6

Median of set P = 5/6 * 6 = 5

P = {4,5,6}

Median of Q is (2/3)*z

Assume z = 12

Median = 2*4 = 8

Q = { 4, 5, 6, 7, 8, 9, 10, 11, 12}

R = {6, 7, 8, 9, 10, 11, 12}

Median of R = 9

Ratio =  \frac{9 }{ 12} = \frac{3}{4}

Option D

KarishmaB · Answer

x, y and z are integers and P, Q and R are sets of consecutive integers.

Take one statement at a time:

The median of set P is (5/6)*y

Median is the middle value. 
Median of x...y is (5/6)y. The easiest case of this would be when median is 5 and y = 6 
Then x...y must be 4, 5, 6.

The median of set Q is (2/3)*z. 
Set Q is x...z so as per our case, x = 4. So Q is 4...??
Since median is (2/3)z, z is a multiple of 3. 
If z is 9, median of 4, 5, 6, 7,8 9 is 6.5 which is not valid. 
If z is 12, median of 4, 5, 6 ,7, 8, 9, 10, 11, 12 is 8 which is (2/3)z. Hence, z = 12

what fraction of z is the median of set R? 
Since y = 6 and z = 12, R is 6, 7, 8, 9, 10, 11, 12 for which median is 9.
Fraction = 9/12 = 3/4

Answer (D)

KumarRishav · Answer

I took P - 1,5,6 and Q - 1,2,3.... All criteria is getting satisfied but still wrong answer I am getting

Krunaal · Answer

"P is a set of  all integers between x and y,  inclusive." -  you cannot take set P as 1, 5, 6; similarly for other sets. Since, the sets have consecutive integers, the median = mean. (x+y)/2 = (5/6)y => 3x=2y. You can take x = 4 and y = 6. Set P = {4, 5, 6}. From here you can solve further using similar logic to form other sets.

P is a set of all integers between x and y, inclusive, and Q is a set

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P is a set of all integers between x and y, inclusive, and Q is a set

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