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Source: — Problem Solving |
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by sixpointer » Sat Oct 23, 2010 10:38 am
using 1st statement 15x+25y/x+y=21

3x-2y ( Not possible)

Using 2nd statement= 15x+25y=420 (Many x and y values will be there)

using both => 3x-2y=0
3x+5y=84

Y= 12

x=8


So, we can conclude number of sweater >shirt

Ans 3
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by sixpointer » Sat Oct 23, 2010 10:48 am
Sorry wrong post.
Last edited by sixpointer on Sat Oct 23, 2010 11:14 am, edited 2 times in total.
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by saurabhmahajan » Sat Oct 23, 2010 10:49 am
But the OA is A
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by sixpointer » Sat Oct 23, 2010 11:13 am
okay ! I made a mistake

We should get a unique solution that means sufficient enough to get the answer as yes or no (Yes is equivalent to No)

3X=2Y

X will always be less than Y

So, we are getting the unique solution

Ans will be A


P.S: - First time Iam solving this question and I thought we need to find the exact answer but No , we need to find whether the condition is sufficient to give us unique solution.
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by GMATGuruNY » Sun Oct 24, 2010 3:08 am
During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of $25. Did the store sell more sweaters than shirts during the sale?

(1) The average (arithmetic mean) of the prices of all the shirts and sweaters that the store sold during the sale was $21.

(2) The total of the prices of all the shirts and sweaters that the store sold during the sale was $420
Statement 1:
Just use common sense. If the store sold an equal number of shirts and sweaters, the average would be (15+25)/2 = 20. Since the average was greater than 20, the store must have sold a greater number of the more expensive item (the sweaters). Sufficient.

Statement 2:
Let x= shirts, y = sweaters.
15x + 25y = 420.
5(3x + 5y) = 420.
3x + 5y = 84.
x=3, y=15 works, because 3*3 + 5*15 = 84. In this case, x<y.
x=28, y=0 works, because 3*28 + 5*0 = 84. In this case, x>y.
Insufficient.

The correct answer is A.
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by Rezinka » Mon Oct 25, 2010 11:08 pm
Alternate solution :
We can also get the answer by simply analyzing the question.

Statement 1 :
The average price of all shirts and sweaters is 21.
21 is closer to 25 as compared to 15, so there are more sweaters.... SUFFICIENT

Statement 2 :
Total price for all shirts and sweaters is 420$. No information about number of shirts and sweaters.. NOT SUFFICIENT
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