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averages

by smohsin » Mon Oct 27, 2008 6:56 am
In a certain clothing store, the store sold each shirt for $15 and each sweater for $25. Did the store sell more sweaters than shirts?

1) The avg (arithmatic mean) of the prices off all of the shirts and sweaters that the store sold was $21.

2) the total prices of all shirts and sweaters that the store sold was $420


Please explain the answer.
going big!
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Source: — Data Sufficiency |
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by uttara » Mon Oct 27, 2008 7:24 am
answer is (a) - option 1 is enough.

if equal no of shirts n sweaters were sold, the avg price will be $20.

Assume the store sold n shirts and n sweaters
$avg price = (15n +25 n)/2n
= 40n/2n
= 20

As the given avg price is greater than $20, the store sold more of the higher priced item ie sweaters.

-----

Option B -
is not sufficient as it means
420=15h+25w
which has multiple solutions.
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by rohangupta83 » Tue Oct 28, 2008 4:46 am
Let the number of shirts sold = x

sweaters sold = y

therefore,

average = (15x + 25y)/(x+y) = 21

or 15x + 25y = 21x + 21y

or 6x = 4y

3x = 2y

So, more sweaters were sold than shirts

we can check this by plugging in for x

lets say x = 2
therefore, y from the above equation is 3

IMO A

statement 2 is insuficient

uttara wrote:
-----

Option B -
is not sufficient as it means
420=15h+25w
which has multiple solutions.
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by callmemo » Sat Nov 01, 2008 5:35 am
IMO D.

I can think of only one solution for the eq, 420=15h+25w

15 x 8 + 25 x 12 = 420
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by cramya » Sat Nov 01, 2008 5:59 am
Smohsin,
The question is "Did the store sell more sweaters than shirts" We can tell this if we can find the ratio of shirts to sweaters which we can from statement I

If the question had asked how many sweaters then we need both stataments to find x or y.


I think the key is to recognioze whast being asked and the reason whcy I am saying this is because I have made mistakes in DS porblems by overlooking whats asked.

Hope this helps.
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by cramya » Sat Nov 01, 2008 6:02 am
Smohsin,
The question is "Did the store sell more sweaters than shirts" We can tell this if we can find the ratio of shirts to sweaters which we can from statement I

If the question had asked how many sweaters then we need both stataments to find x or y.


I think the key is to recognioze whast being asked and the reason whcy I am saying this is because I have made mistakes in DS porblems by overlooking whats asked.

Hope this helps.
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by stop@800 » Sat Nov 01, 2008 2:58 pm
callmemo wrote:IMO D.

I can think of only one solution for the eq, 420=15h+25w

15 x 8 + 25 x 12 = 420
15*3 + 25*15
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by callmemo » Mon Nov 03, 2008 6:14 pm
ah! thanks. Is there an easy way to enumerate all combinations? OR is it simply by trail and error?
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