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Bunuel
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A store sold 6 bicycles with an average sale price of $1,000. What was 06 Oct 2015, 05:59
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E
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69% (02:06) correct 31% (02:01) wrong based on 424 sessions

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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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E
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A store sold 6 bicycles with an average sale price of $1,000. What was 06 Oct 2015, 07:18
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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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A store sold 6 bicycles with an average sale price of $1,000. What was 06 Oct 2015, 07:27
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Bunuel
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.
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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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A store sold 6 bicycles with an average sale price of $1,000. What was 06 Oct 2015, 08:18
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Bunuel
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.
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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: https://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

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A store sold 6 bicycles with an average sale price of $1,000. What was 03 Mar 2016, 08:05
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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

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P
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A store sold 6 bicycles with an average sale price of $1,000. What was 03 Mar 2016, 23:02
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prakharkaushik
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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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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A store sold 6 bicycles with an average sale price of $1,000. What was 05 Sep 2020, 13:01
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Bunuel
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.
Show more
Solution:

We know the total amount of money the 6 bicycles sold for is $6000. We need to determine the most expensive bicycle.

Statement One Alone:

The median price was $1,000.

This is not sufficient. It’s possible that each bicycle sold for $1000. In this case, the most expensive bicycle is still $1000. It’s also possible that two sold for $500 each, two sold for $1000 each and two sold for $1500. In this case, the most expensive bicycle is $1500.

Statement Two Alone:

The range of prices was $600.

This is not sufficient. It’s possible that three sold for $700 each and the other three sold for $1300. In this case, the most expensive bicycle is $1300. It’s also possible that two sold for $600 each and the other four sold for $1200 each. In this case, the most expensive bicycle is $1200.

Statements One and Two Together:

The two statements together are not sufficient, either. It’s possible that three bicycles sold for $700 each and the other three sold for $1300. In this case, the most expensive bicycle is $1300. It’s also possible that two sold for $800 each, three sold for $1000 each, and the last one sold for $1400. In this case, the most expensive bicycle is $1400.

Answer: E
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A store sold 6 bicycles with an average sale price of $1,000. What was 03 Jun 2022, 12:50
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Bunuel
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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Statements combined:

Prompt --> sum of the 6 prices = 6000
S1 --> sum of the two middle prices = 2000, implying that the sum of the remaining four prices = 4000
S2 --> greatest price - smallest price = 600

Given that the prices DO NOT HAVE TO BE INTEGERS, there are virtually an infinite number of ways for the remaining four prices to sum to 4000 such that the greatest and smallest have a difference of 600.
Since the greatest price can assume almost an infinite number of values, the two statements combined are INSUFFICIENT.

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A store sold 6 bicycles with an average sale price of $1,000. What was 03 Feb 2023, 20:13
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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.

Stem: Sum of sales price of 6 bicycles = 6*1000 = 6000

(1) The median price was $1,000.
No of terms is = 6 ,so median is 3rd+4th term/2 = 1000, this implies there are 2 other terms greater than median and 2 terms less than or equal to median. Not sufficient.

(2) The range of prices was $600.
Clearly Not sufficient, min could be 600 max could be 1200, min could be 500 max could be 1100.Not sufficient.

Combining, median = 1000, so 3rd + 4th term = 2000 , and range = 600, 2 cases possible.
Case 1: 700+700+1000+1000+1300+1300
Case 2: 600+1000+1000+1000+1200+1200
E
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A store sold 6 bicycles with an average sale price of $1,000. What was 28 Aug 2025, 02:25
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Given that the prices DO NOT HAVE TO BE INTEGERS, there are virtually an infinite number of ways, yeah
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