Theory

➡ Average = Sum of all the Values / Total Number of Values
➡ Sum of All the values = Average * Total Number of Values
➡ Median is the middle value of the set (after arranging the set in ascending or descending order)

Given that Average = $140 and Median price is $120 and there are 15 items which are purchased.
Since, median is $120 and there are odd number of values (15) so middle term, which is the \(8^{th}\) term, will be the median.
=> \(8^{th}\) term = Median = $120

Quantity A

The minimum price at which the most expensive item could be purchased

Now, for the maximum price to be minimum

➡ All the values greater than median should be equal and should be least
➡ All the values less than median should be equal and should be greatest => should be equal to Median

=> First 7 values = Median = $120
=> Sum of First 7 values = 7*$120 = $840

Last Seven values are equal, let each values is x
=> Sum of last 7 values = 7x

Total Sum = Average * 15 = $140*15 = $2100
=> Sum of First 7 values + $120 + Sum of last 7 values = $2100
=> $840 + $120 + 7x = $2100
=> 7x = $2100 - $960 = $1140
=> x = \(\frac{$1140}{7}\) ~ $162
=> Minimum value of Maximum purchase price = $162

=> Quantity A ($162) > Quantity B($155)

So, Answer will be A.
Hope it helps!

Watch the following video to Learn the Basics of Statistics