Smita04 wrote:
Z is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of Z, and y is the minimum value of the sum of k distinct members of Z, what is x + y?
(A) kn
(B) kn + k^2
(C) kn + 2k^2
(D) 2kn – k^2
(E) 2kn
Probably the easiest way to solve this question would be to assume some values for n and k.
Say n=3, so Z, the set of the first n positive odd numbers would be: Z={1, 3, 5};
Say k=1, so X, the maximum value of the sum of K distinct members of Z would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of Z would simply be 1.
X+Y=5+1=6.
Now, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1=6.
Answer: E.
Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.
Hope it helps.
but for the example that you have used - Z={1, 3, 5} - shouldn't the maximum value of the sum of K distinct members of Z be = 1+3+5 = 9 ?