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DS HELP nutcrackers

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by manihar.sidharth » Thu Aug 02, 2012 7:54 am
At a holiday store, the average price of the German nutcrackers is $225, and the average price of all nutcrackers is $205. What is the average price of the non-German nutcrackers?

(1) The combined price of all the nutcrackers in the store is $2,050.

(2) Sixty percent of the nutcrackers in the store are German.
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Aug 02, 2012 9:22 am
manihar.sidharth wrote:At a holiday store, the average price of the German nutcrackers is $225, and the average price of all nutcrackers is $205. What is the average price of the non-German nutcrackers?

(1) The combined price of all the nutcrackers in the store is $2,050.

(2) Sixty percent of the nutcrackers in the store are German.
Statement 1: The combined price of all the nutcrackers in the store is $2,050.
Thus, the total number of nutcrackers = sum/average = 2050/205 = 10.

Case 1:
It's possible that the number of German nutcrackers = 2, with a total cost of 2*225 = 450.
Here, there are 8 non-German nutcrackers, with an average cost of (2050-450)/8 = 200.

Case 2:
It's possible that the number of German nutcrackers = 6, with a total cost of 6*225 = 1350.
In this case, there are 4 non-German nutcrackers, with an average cost of (2050-1350)/4 = 175.

Since the average cost of the non-German nutcrackers can be different values, iNSUFFICIENT.

Statement 2: Sixty percent of the nutcrackers in the store are German.
This is the ratio used in Case 2 above:
Of every 10 nutcrackers (with a total cost of 2050), 6 are German (with a total cost of 1350), with the result that the average cost of the 4 non-German nutcrackers = 175.
SUFFICIENT.

The correct answer is B.
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by niketdoshi123 » Thu Aug 02, 2012 9:24 am
manihar.sidharth wrote:At a holiday store, the average price of the German nutcrackers is $225, and the average price of all nutcrackers is $205. What is the average price of the non-German nutcrackers?

(1) The combined price of all the nutcrackers in the store is $2,050.

(2) Sixty percent of the nutcrackers in the store are German.
Solving the question stem first

Let the # of German nutcrackers = x
and the # of non-German nutcrackers = y

Total # of nutcrackers = x+y

Avg. price of German nutcrackers = $225
Total price of German nutcrackers = $225x

Avg. price of non-German nutcrackers = "?"
Total price of non-German nutcrackers = ?*y

Avg price of all nutcrackers = $205
Total price of all nutcrackers = $205(x+y)

Total price of all nutcrackers = Total price of German nutcrackers + Total price of non-German nutcrackers
=> 205x + 205y = 225x + ?*y
=> 205y - ?*y = 20x
=> (205 - ?)y = 20x
=> 205 - ? = 20x/y
=> ? = 205 - 20x/y
Hence if we know the value of x/y we can find the value of "?"

So, rephrasing the question stem

What is the value of x/y ?

Statement 1:
2050 = 205(x+y)
=> x+y = 10
But we need to find the value of x/y . Hence insufficient

Statement 2:

60(x+y)/100 = x
=> 60x + 60y = 100x
=> 40x = 60y
=> x/y = 6/4

From this statement we can get a unique value of x/y. Hence sufficient

The correct answer is B
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