A set of 51 different integers has a median of 30 and a

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AAPL: Moderator; Posts: 2644; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Wed Mar 13, 2019 2:59 am

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e-GMAT

A set of 51 different integers has a median of 30 and a range of 60. What is the value of the least possible integer in this set?

A. -10
B. -6
C. -5
D. 5
E. 10

OA C

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Source: Beat The GMAT — Problem Solving | Wed Mar 13, 2019 2:59 am

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by GMATGuruNY » Wed Mar 13, 2019 6:28 am

AAPL wrote:e-GMAT

A set of 51 different integers has a median of 30 and a range of 60. What is the value of the least possible integer in this set?

A. -10
B. -6
C. -5
D. 5
E. 10

Range = biggest - smallest
Smallest = biggest - range

Since the range = 60, we get:
Smallest = biggest - 60

To minimize the smallest integer, we must minimize the biggest integer.
Since the median of the 51 distinct integers = 30, there must be 25 integers above 30, with the other 25 integers below 30.
Implication:
The least possible value for the biggest integer = 30+25 = 55.

Substituting biggest = 55 into the blue equation above, we get:
Smalest = 55-60 = -5.

The correct answer is C.

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by Scott@TargetTestPrep » Fri Mar 15, 2019 6:50 am

AAPL wrote:e-GMAT

A set of 51 different integers has a median of 30 and a range of 60. What is the value of the least possible integer in this set?

A. -10
B. -6
C. -5
D. 5
E. 10

OA C

Since the median is 30 and there are 51 terms, we see that 25 terms must be below the median and 25 above. So the least value of the largest number in the set is 30 + 25 = 55. Since the range is 60, the value of the smallest number in the set is 55 - 60 = -5.

Answer: C

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