For the set of positive, distinct integers \(v, w, x, y, z\)

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

For the set of positive, distinct integers \(v, w, x, y, z\)

by BTGmoderatorLU » Wed Jul 31, 2019 4:49 pm

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Source: Princeton Review

For the set of positive, distinct integers \(v, w, x, y, z,\) the median is 10. What is the minimum value of \(v+w+x+y+z\)?

A. 25
B. 32
C. 36
D. 40
E. 50

The OA is C

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Source: Beat The GMAT — Problem Solving | Wed Jul 31, 2019 4:49 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Thu Aug 01, 2019 12:46 am

BTGmoderatorLU wrote:Source: Princeton Review

For the set of positive, distinct integers \(v, w, x, y, z,\) the median is 10. What is the minimum value of \(v+w+x+y+z\)?

A. 25
B. 32
C. 36
D. 40
E. 50

The OA is C

Since there are five (Odd numbers of) integers, one of \(v, w, x, y, z,\) is the median. Say \(v, w, x, y, z,\) are arranged in ascending order; thus, x = median = 10. Since we want the minimum value of \(v+w+x+y+z\), the minimum possible value of v = 1 and w = 2. Again, since x < y < z, the minimum possible values of y = 11 and z = 12.

Thus, the minimum value of \(v+w+x+y+z\) = 1 + 2 + 10 + 11 + 12 = 36.

The correct answer: C

Hope this helps!

-Jay
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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 Aug 04, 2019 10:28 am

BTGmoderatorLU wrote:Source: Princeton Review

For the set of positive, distinct integers \(v, w, x, y, z,\) the median is 10. What is the minimum value of \(v+w+x+y+z\)?

A. 25
B. 32
C. 36
D. 40
E. 50

The OA is C

We need to make the numbers as small as possible. Notice that the smallest possible values for the two integers smaller than the median are 1 and 2; and the smallest possible values for the two integers greater than the median are 11 and 12.

Thus, the minimum value is:

1 + 2 + 10 + 11 + 12 = 36

Answer: C

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