P - m members
Q - n members
R - m+n members

To evaluate Case 1 also combine choices that are different from case 2
Case 1)
The smallest number in list Q is greater than the largest number in list P and m > n, and m < n

m>n
P= 1,1,1 -> median =1
Q= 2 -> median = 2
R= 1,1,1,2 -> median =1
is the median of list R greater than the median of list P ? no

m<n
P= 1, -> median =1
Q= 2,2 -> median = 2
R= 1,2,2 -> median =2
is the median of list R greater than the median of list P ? yes
because we have a yes and a no, statement is insufficient


To evaluate Case 2 also combine choicew that are different from case 1
Case 2)
m = n and The smallest number in list Q is less than the largest number in list P and The smallest number in list Q is equal the largest number in list P


The smallest number in list Q is less than the largest number in list P
P= 2, 2, 2-> median =1
Q= 1,1,1 -> median = 1
R= 1, 1, 1, 2,2,2 -> median =1.5
is the median of list R greater than the median of list P ? yes

The smallest number in list Q is equal the largest number in list P
P= 1,1,1 -> median =1
Q= 1,1,1 -> median = 1
R= 1,1,1,1,1,1 -> median =1
is the median of list R greater than the median of list P ? no
because we have a yes and a no, statement is insufficient

Combing both equations
m = n and The smallest number in list Q is greater than the largest number in list P
P= 1,1,1 -> median =1
Q= 2,2,2 -> median = 2
R= 1,1,1,2,2,2 -> median =2
is the median of list R greater than the median of list P ? yes

combination is sufficent to answer the question of yes or no
answer = c

j_shreyans wrote:List P contains m numbers; list Q contains n numbers. If the two lists are combined to produce list R, containing m + n numbers, is the median of list R greater than the median of list P ?

(1) The smallest number in list Q is greater than the largest number in list P.

(2) m = n

Statement 1: The smallest number in list Q is greater than the largest number in list P.
Test an EASY CASE that satisfies BOTH statements.
Case 1: P = {0} and Q = {1}, implying that R = {0, 1}.
Median of P = 0.
Median of R = 1/2.
In this case, median of R > median of P, so the answer to the question stem is YES.

Test an easy case that satisfies ONLY STATEMENT 1.
Case 2: P = {0, 0} and Q = {1}, implying that R = {0, 0, 1}.
Median of P = 0.
Median of R = 0.
In this case, median of R = median of P, so the answer to the question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2: m=n
Case 1 satisfies statement 2.
In Case 1, the answer to the question stem is YES.

Test a case that satisfies ONLY STATEMENT 2.
Case 3: P = {0} and Q = {0}, implying that R = {0, 0}.
Median of P = 0.
Median of R = 0.
In this case, median of R = median of P, so the answer to the question stem is NO.

Since the answer is YES in Case 1 but NO in Case 3, INSUFFICIENT.

Statements combined:
Let P = {a, b, c}, where a≤b≤c.
Let Q = {d, e, f}, where d≤e≤f.

Statement 1 indicates that d > c.
Thus:
R = {a, b, c, d, e, f}, where a ≤ b ≤ c < d ≤ e ≤ f}.

Adding together c≥b and d>b, we get:
c+d > 2b
(c+d)/2 > b.

Since the median of R = (c+d)/2, and the median of P = b, the resulting inequality implies that the median of R > median of P.
SUFFICIENT.

The correct answer is C.