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01 May 2011, 13:48
1
7
00:00

Difficulty:

55% (hard)

Question Stats:

65% (02:01) correct 35% (01:59) wrong based on 222 sessions

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During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of$25.00 Did the store sell more sweaters than shirts during the sale?

1) The average of the prices of all of the shirts and sweaters that the store sold during the sale was $21.00 2) The total of the prices of all of the shirts and sweaters that the store sold during the sale was$420.00
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28 Mar 2012, 09:04
1
4
dchow23 wrote:
from statement 2,

shirts x
sweaters y

15x +20y = 420

Can we say that since 60 is a common multiple between the 15 and 20, there will be more than one answer that can satisfy the equation?
If there is a common multiple for

Not sure that I understand your question correctly but generally for such kind of question it's always better to check whether an equation whose solution must be integers only has one or more set of variables satisfying it.

For more on this type of questions check:
eunice-sold-several-cakes-if-each-cake-sold-for-either-109602.html
martha-bought-several-pencils-if-each-pencil-was-either-a-100204.html
a-rental-car-agency-purchases-fleet-vehicles-in-two-sizes-a-105682.html
joe-bought-only-twenty-cent-stamps-and-thirty-cent-stamps-106212.html
a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html
joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html

As for the question.

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 --> since the average sale price of$21 is closer to $25 than to$15 then store sold more sweaters than shirts (sweaters have more weight in the weighted average and thus pulled it closer to $21). Sufficient. (2) The total of the prices of all the shirts and sweaters that the store sold during the sale was$420 --> 15x + 25y =420 --> 3x+5y=84. If x=8 and y=12 then x<y but if x=13 and y=5 then x>y. Not sufficient.

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##### General Discussion
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Re: During a sale, a clothing store sold each shirt at a price of $15 and [#permalink] ### Show Tags 01 May 2011, 15:52 WE can do this without even framing eqn. Stat 1 says that avg of all shirts and sweaters = 21.00$ means its closer to the price of sweaters ($25) vis-a-vis that of shirts ($20) hence more of sweaters must have been sold.

hence statement 1 alone is sufficient to answer the question

stat 2 says that 15 shirts + 25 sweaters = 420 hence cannot be solved.

thus Ans - A
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20 Jul 2017, 12:07
1
agdimple333 wrote:
During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of$25.00 Did the store sell more sweaters than shirts during the sale?

1) The average of the prices of all of the shirts and sweaters that the store sold during the sale was $21.00 2) The total of the prices of all of the shirts and sweaters that the store sold during the sale was$420.00

Cost of Shirts = $15 Let shirts be x. Cost of Sweaters =$25
Let sweaters be y.
Is y>x?

1) $$\frac{15x + 25y}{x+y}$$ = 21
=> 15x + 25y = 21x + 21y
=> $$\frac{x}{y}$$ = $$\frac{2}{3}$$
This basically means for every 2 shirts sold, 3 sweaters are sold.
y > x. Sufficient.

2) 15x + 25y = 420
3x + 5y = 84
x = 8, y =12 => y > x
x = 18, y = 4 => x > y
Insufficient.

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Re: During a sale, a clothing store sold each shirt at a price of $15 and [#permalink] ### Show Tags 16 Jun 2018, 10:16 agdimple333 wrote: During a sale, a clothing store sold each shirt at a price of$15 and each sweater at a price of $25.00 Did the store sell more sweaters than shirts during the sale? 1) The average of the prices of all of the shirts and sweaters that the store sold during the sale was$21.00
2) The total of the prices of all of the shirts and sweaters that the store sold during the sale was $420.00 The average of the prices of all of the shirts and sweaters that the store sold during the sale was$21.00.

Since the average price of $21 is closer to$25 than it is to $15, there must be more sweaters sold than shirts. Statement one alone is sufficient. Statement Two Alone: The total of the prices of all of the shirts and sweaters that the store sold during the sale was$420.00.

It’s possible that 12 sweaters and 8 shirts are sold since 12 x 25 + 8 x 15 = 300 + 120 = $420. It’s also possible that 6 sweaters and 18 shirts are sold since 6 x 25 + 18 x 15 = 150 + 270 =$420. In the former example, more sweaters were sold; however, in the latter example, more shirts were sold. Statement two alone is not sufficient.

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Re: During a sale, a clothing store sold each shirt at a price  [#permalink]

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22 Feb 2019, 08:31
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Re: During a sale, a clothing store sold each shirt at a price   [#permalink] 22 Feb 2019, 08:31
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