Problem Solving

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

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,

\(55−x=60 \; \Longrightarrow \; x=-5\)