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During a sale, a clothing store sold each shirt at a price of $15 and

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During a sale, a clothing store sold each shirt at a price of $15 and [#permalink]

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New post 01 May 2011, 13:48
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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
[Reveal] Spoiler: OA

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Re: During a sale, a clothing store sold each shirt at a price of $15 and [#permalink]

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New post 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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Re: During a sale, a clothing store sold each shirt at a price of $15 and [#permalink]

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New post 01 May 2011, 22:45
15 sh + 25 sw = 21(sh+sw)
4sw = 6sh
2sw = 3sh Sufficient.

15 sh + 25 sw = 420
3sh + 5sw = 84

5 * 16 = 80 (max sw = 16)
Hence by trial method sw = 15, sh = 3

3* 28 = 84 (max sh = 28)
hence by trial method 3*sh = 54 gives sw = 6
meaning sh = 18,sw = 6. Hence not sufficient.

Thus A.
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Re: During a sale, a clothing store sold each shirt at a price of $15 and [#permalink]

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New post 12 Apr 2017, 14:17
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


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.

Answer: A.
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During a sale, a clothing store sold each shirt at a price of $15 and [#permalink]

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New post 20 Jul 2017, 12:07
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.

A is the answer.
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During a sale, a clothing store sold each shirt at a price of $15 and   [#permalink] 20 Jul 2017, 12:07
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