BTGModeratorVI wrote: ↑

Thu Jul 23, 2020 6:35 am

A certain ski shop sold 125 pairs of skis and 100 pairs of ski boots for a total of $75,000. What was the average (arithmetic mean) selling price of a pair of the ski boots?

(1) The average selling price of a pair of skis was $300.
(2) The selling price of a pair of ski boots varied from $150 to $900.

Answer: A
Source: GMAT prep

Given: A certain ski shop sold 125 pairs of skis and 100 pairs of ski boots for a total of $75,000.
Let K = the COMBINED selling price of all 125 pairs of skis
Let B = the COMBINED selling price of all 100 pairs of ski boots
We can write: K + B = 75,000

Also, since B = the COMBINED price of all 100 pairs of ski boots, the average price per pair of boots = B/100

Target question: What is the value of B/100?

Statement 1: The average selling price of a pair of skis was $300
The ski shop sold a total of 125 pairs of skis, for a combined price of K dollars.
So we can write: K/125 = 300
Multiply both sides of the equation by 125 to get: K = 37,500
Since we already know that K + B = 75,000, we can substitute to get 37,500 + B = 75,000, which means B = 37,500, which means B/100 = 37,500/100 = 375
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The selling price of a pair of ski boots varied from $150 to $900.
This is clearly not enough information to answer the target question with certainty
Statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent