Gmat_mission wrote:On a hot summer day, a coffee and tea shop sold a container of coffee beans at $15 and a container of tea bags at $25. Did the shop sell more containers of coffee beans than containers of tea bags that day?
(1) The average (arithmetic mean) of all containers of coffee beans and tea bags sold that day was $21.
(2) The aggregate sales of the two items that day was $420.
[spoiler]OA=A[/spoiler].
Can any expert clarify this DS question for me? I don´t know how to solve it. <i class="em em-disappointed"></i>
Note that average of two items always lies between their values. Thus, the average (arithmetic mean) of all containers of coffee beans and tea bags sold that day would lie between $15 and $25.
If the number of containers of coffee beans and the number of containers of tea bags were equal, then the average (arithmetic mean) of all containers of coffee beans and tea bags sold that day would be (15 + 25)/2 = $20.
If the number of containers of coffee beans ($15) is
more than the number of containers of tea bags ($25), then the average (arithmetic mean) of all containers would lie between $15 and $20; however, if the number of containers of coffee beans ($15) is
less than the number of containers of tea bags ($25), then the average (arithmetic mean) of all containers would lie between $20 and $25.
Let's take each statement one by one.
(1) The average (arithmetic mean) of all containers of coffee beans and tea bags sold that day was $21.
We see that the statement gives that the average (arithmetic mean) of all containers of coffee beans and tea bags sold that day was $21 (between $20 and $25), the number of containers of coffee beans ($15) is less (NOT MORE) than the number of containers of tea bags ($25). The answer is No. Sufficient.
(2) The aggregate sales of the two items that day was $420.
With the given data of sales, we cannot find out the proportion of sales of the number of containers of coffee beans and the number of containers of tea bags
Say the number of containers of coffee beans = x, the number of containers of tea bags = y, where x and y are positive integers
Thus, 15x + 25y = 420
=> 3x + 5y = 84
=> x = (84 - 5y)/3 = 28 - 5y/3
Since x is a positive integer, y must be a multiple of 3.
Case 1: Say y = 3, then x = 28 - 5 = 23. We see that x > y.
Case 2: Say y = 15, then x = 28 - 25 = 3. We see that x < y.
No unique answer. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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