BTGModeratorVI wrote: ↑Wed Oct 07, 2020 7:14 am
A certain toy store sold 20 toys yesterday, each of which was either a $40 toy or a $20 toy. How many $20 toys did the toy store sell?
1) The average price of the toys sold yesterday was $35.
(2) The total price of the 20 toys sold yesterday was between $650 and $750.
Answer:
A
Source: GMAT hacks
Given: A certain toy store sold 20 toys yesterday, each of which was either a $40 toy or a $20 toy.
Let C = NUMBER of $20 toys sold (C for cheap)
Let E = NUMBER of $40 toys sold (E for expensive)
Since 20 toys were sold, we can write:
C + E = 20
Target question: How many $20 toys did the toy store sell?
In other words, our goal is to
determine the value of C
Statement 1: The average price of the toys sold yesterday was $35
In other words, (total revenue from the toys)/20 = $35
How do we determine total revenue?
Well, revenue from the $20 toys = 20C, and revenue from the $40 toys = 40E
So, we can write: (20C + 40E)/20 = 35
Multiply both sides by 20 to get:
20C + 40E = 700
We now have a system of two equations:
C + E = 20
20C + 40E = 70
Since we COULD solve this system for C, we COULD determine the number of $20 toys sold.
Since we COULD answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The total price of the 20 toys sold yesterday was between $650 and $750
This statement does not feel sufficient, so let's test some values.
Case a: the store sold 5 $20 toys and 15 $40 toys. This yields a total revenue of $700. In this case,
the store sold 5 $20 toys
Case b: the store sold 6 $20 toys and 14 $40 toys. This yields a total revenue of $680. In this case,
the store sold 6 $20 toys
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
