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

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

by BTGmoderatorDC » Wed Jul 13, 2022 12:34 am

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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?

Options

a) -10
b) -6
c) -5
d) 5
e) 10

OA C

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### Re: A set of 51 different integers has a median of 30 and a range of 60. What is the value of the least possible

by swerve » Sun Jul 24, 2022 2:40 pm
BTGmoderatorDC wrote:
Wed Jul 13, 2022 12:34 am
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?

Options

a) -10
b) -6
c) -5
d) 5
e) 10

OA C

Source: e-GMAT
The median is $$30$$ which is the $$26\text{th}$$ number in the series.
In order to minimize the lowest number, we need to minimize the maximum number.
Because
$$(X)(\text{smallest highest number}) - (Y)(\text{least negative number}) = 60 (\text{to minimize}\,Y)$$

The smallest highest number possible for this series is $$55$$. Because $$30+25=55$$. $$25$$ different integers ahead of the median.

Therefore,

$$55−x=60 \; \Longrightarrow \; x=-5$$

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### Re: A set of 51 different integers has a median of 30 and a range of 60. What is the value of the least possible

by [email protected] » Fri Dec 30, 2022 8:06 am
BTGmoderatorDC wrote:
Wed Jul 13, 2022 12:34 am
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?

Options

a) -10
b) -6
c) -5
d) 5
e) 10

OA C

Source: e-GMAT
Since 30 is the median of the 51 distinct integers, there must be 25 integers greater than 30 and another 25 integers less than 30. Thus, the smallest possible value of the largest integer is 30 + 25 = 55. Since the range is 60, the least possible integer is 55 - 60 = -5.