Question

The median of a list of $99$ consecutive integers is $60$. What is the greatest integer in the list?

• A. $108$
• B. $109$
• C. $110$
• D. $98$

Answer 1

Answer: (B)

$109$

Median is the 'middle' value in a sorted list of numbers.

To find the median, we need to sort the list in a numerical order.

Here, we have ${}^{\prime }{99}^{\prime }$ list of consecutive numbers.

Consecutive numbers are integers that follow each other in order. They have a difference of $1$ between two consecutive numbers.

Median of this list is ${}^{\prime }{60}^{\prime }$ which means there are $(\frac{99}{2}=49)$ integers after ${}^{\prime }{60}^{\prime }$ in this list.

The greatest number in the list is the last number of this list.

As consecutive numbers differ by ${}^{\prime }{1}^{\prime }$ and the last number is ${}^{\prime }{49}^{\prime }$ numbers far from the median.

Last number $=$ (Median) $+$ $(49$ $\times$ $1)$

$=$ $60$ $+$ $49$

$=$ $109$

Therefore, the greatest integer in the list is $109$.