arithmetic mean

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divya23: Master | Next Rank: 500 Posts; Posts: 113; Joined: Mon Apr 26, 2010 8:58 amFollowed by: 14 members; Thanked: 2 times

by divya23 » Mon Jun 13, 2011 10:13 pm

during sale each shirt sold at 15 and sweatr for 25 ,did the store sell more sweater than shirts
a.mean of all prices of shirt and sweater is = 21
b.total price of all the shirt and sweater sold = 420

[spoiler]ans = a[/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Mon Jun 13, 2011 10:13 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jun 14, 2011 1:27 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

This is a weighted average question. Almost no math is needed.

Statement 1: Average of all sales = $21.
Since the average (21) is closer to the price of a sweater (25) than to the price of a shirt (15), the store sold more sweaters than shirts.
Sufficient.

Statement 2: Total of all sales = $420.
No way to determine whether the store sold more sweaters than shirts.

The correct answer is A.

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Thu Jun 16, 2011 9:15 pm

a using weighted average since 21 is closer to 25 hence it is sufficient.

allegation formula confirms this = (25-21)/(21-15) = 4/6 = 2/3 = sw/shirts.

b 3 shirts + 5 sweaters = 84

shirts = 84/3 = 28 possible with sweaters = 0
or sweaters = 15 giving 15*5 = 75

75 + 9 = 84 meaning sweaters = 3 sweaters. not sufficient.

Thus A it is.

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