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A store sold 6 bicycles with an average sale price of $1,000. What was

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A store sold 6 bicycles with an average sale price of $1,000. What was [#permalink]

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New post 06 Oct 2015, 04:59
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A store sold 6 bicycles with an average sale price of $1,000. What was the price of the most expensive bicycle?

(1) The median price was $1,000.
(2) The range of prices was $600.


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[Reveal] Spoiler: OA

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Re: A store sold 6 bicycles with an average sale price of $1,000. What was [#permalink]

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New post 06 Oct 2015, 06:18
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Total cost of 6 bicycles = 6x1000= 6000 $
B1+B2+B3+B4+B5+B6=6000

1. Median price was 1000 $
B3+B4=2000
B1+B2+B5+B6=4000
Not sufficient

2. Range of prices was 600 $
Difference between B1 and B6 is 600 , but the most expensive still can take any different values.
Suppose B1= 900 and B6 =1500
B1+B6=2100
B2+B3+B4+B5=3900

Or B1= 800 and B6= 1400
B1+B6=2200
B2+B3+B4+B5=3900

Combining 1 and 2,
B3+B4=2000
=>B1+B2+B5+B6=4000
If ,B1=B2 =700 , then B5=B6=1300

If , B1=B2 = 800 , then B5=1000 and B6=1400


Still ,Not sufficient .
hence E. :?
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Re: A store sold 6 bicycles with an average sale price of $1,000. What was [#permalink]

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New post 06 Oct 2015, 06:27
Bunuel wrote:
A store sold 6 bicycles with an average sale price of $1,000. What was the price of the most expensive bicycle?

(1) The median price was $1,000.
(2) The range of prices was $600.


Kudos for a correct solution.


Let, a, b, c, d, e, f refer to prices of 6 bicycles in ascending (increasing) order of their prices

Given: a + b+ c + d + e + f = 100*6 = 6000

Question: f = ?

Statement 1: The median price was $1,000.
i.e. (c+d)/2 = 1000
i.e. c+d = 2000
but it doesn't give us any information to conclude about f. hence
NOT SUFFICIENT

Statement 2: The range of prices was $600.
i.e. f - a = 600
but it doesn't give us any information about a to conclude about f. hence
NOT SUFFICIENT

Combining the two statements
a + b+ c + d + e + f = 6000
Since, c+d = 2000
therefore, a + b+ e + f = 4000
Since, f - a = 600
therefore, (f-600) + b+ e + f = 4000
i.e. b + e + 2f = 4600
Since we still lack information about b and e therefore
NOT SUFFICIENT

Answer: option E
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Re: A store sold 6 bicycles with an average sale price of $1,000. What was [#permalink]

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New post 06 Oct 2015, 07:18
Bunuel wrote:
A store sold 6 bicycles with an average sale price of $1,000. What was the price of the most expensive bicycle?

(1) The median price was $1,000.
(2) The range of prices was $600.


Kudos for a correct solution.


Target question: What was the price of the most expensive bicycle?

Given: The store sold 6 bicycles with an average sale price of $1,000.
This means the SUM of the 6 bikes = $6000 (since $6000/6 bikes = $1000 average)

Statement 1: The median price was $1,000.
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several scenarios that satisfy statement 1. Here are two:
Case a: the prices are {1000, 1000, 1000, 1000, 1000, 1000} in which case the most expensive bike is $1000
Case b: the prices are {900, 1000, 1000, 1000, 1000, 1100} in which case the most expensive bike is $1100
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: The range of prices was $600
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several scenarios that satisfy statement 2. Here are two:
Case a: the prices are {700, 1000, 1000, 1000, 1000, 1300} in which case the most expensive bike is $1300
Case b: the prices are {600, 1000, 1000, 1000, 1200, 1200} in which case the most expensive bike is $1200
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are STILL several scenarios that satisfy BOTH statements. Here are two:
Case a: the prices are {700, 1000, 1000, 1000, 1000, 1300} in which case the most expensive bike is $1300
Case b: the prices are {600, 1000, 1000, 1000, 1200, 1200} in which case the most expensive bike is $1200

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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Re: A store sold 6 bicycles with an average sale price of $1,000. What was [#permalink]

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New post 03 Mar 2016, 07:05
Hi,

The statement in Q and statement 1 tell that mean=median. Thus the set of 6 prices should be equally space and hence an AP. So by using statement 1 and 2,we can get the highest price.

Can someone please clarify the discrepancy here

Regards
P

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Re: A store sold 6 bicycles with an average sale price of $1,000. What was [#permalink]

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New post 03 Mar 2016, 22:02
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prakharkaushik wrote:
Hi,

The statement in Q and statement 1 tell that mean=median. Thus the set of 6 prices should be equally space and hence an AP. So by using statement 1 and 2,we can get the highest price.

Can someone please clarify the discrepancy here

Regards
P


Your premise is incorrect. Mean = Median does not tell you that the set is equally spaced.

e.g.

1, 2, 4, 5, 7, 7, 9

Median = 5
Mean = 5

The reverse is true - An equally spaced set does have mean = median.
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Re: A store sold 6 bicycles with an average sale price of $1,000. What was [#permalink]

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Re: A store sold 6 bicycles with an average sale price of $1,000. What was   [#permalink] 15 Sep 2017, 19:30
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