Z is the set of the first n positive odd numbers, where ....

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

Z is the set of the first n positive odd numbers, where ....

by Vincen » Wed Jan 24, 2018 8:13 am

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

The OA is the option E.

How can I solve this PS question? I'm really confused here.

Experts, can you give me some help?

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Source: Beat The GMAT — Problem Solving | Wed Jan 24, 2018 8:13 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Fri Jan 26, 2018 12:43 pm

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

The OA is the option E.

How can I solve this PS question? I'm really confused here.

Experts, can you give me some help?

Hi Vincen,
Let's take a look at your question.

We will solve this question by assuming some random values for the set Z.
Let n = 5, therefore, the set Z has first 5 positive odd numbers. i.e.
$$Z=\left\{1,\ 3,\ 5,\ 7,\ 9\right\}$$

Let k = 2,
then x is the is the maximum value of the sum of k=2 distinct members of Z.
We can see that the two values of set Z, that will give the maximum sum are the last two values, i.e. 7 and 9. Therefore,
$$x=7+9=16$$

y is the is the minimum value of the sum of k=2 distinct members of Z.
We can see that the two values of set Z, that will give the minimum sum are the first two values, i.e. 1 and 3. Therefore,
$$y=1+3=4$$

Now, we can find x+y:
$$x+y=16+4=20$$

We had: n = 5 and k = 2
So 20 will be equal to:
$$2\times5\times2=2nk$$

Therefore, option E is correct.

Hope it helps.
I am available if you'd like any follow up.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jul 28, 2019 8:41 am

Vincen 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

The OA is the option E.

How can I solve this PS question? I'm really confused here.

Experts, can you give me some help?

We can let n = 5 and k = 3. Thus Z = {1, 3, 5, 7, 9}, x = 5 + 7 + 9 = 21, y = 1 + 3 + 5 = 9 and hence x + y = 21 + 9 = 30.

Now let's check the given answer choices (note: we will be looking for the one that is equal to 30):

A) kn = 5(3) = 15 â†’ This is not 30.

B) kn + k^2 = 5(3) + 3^2 = 15 + 9 = 24 â†’ This is not 30.

C) kn + 2k^2 = 5(3) + 2(3)^2 = 15 + 18 = 33 â†’ This is not 30.

D) 2kn - k^2 = 2(5)(3) - 3^2 = 30 - 9 = 21 â†’ This is not 30.

E) 2kn = 2(5)(3) = 30 â†’ This is 30

Answer: E

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