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Alice sells apples. She sold at least 10 lb every day last w

by Max@Math Revolution » Tue Apr 24, 2018 11:27 pm

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[GMAT math practice question]

Alice sells apples. She sold at least 10 lb every day last week. If the total weight of apples sold last week was 140, what is the largest possible range of the weights of apples sold on each day last week?

A. 40
B. 50
C. 60
D. 70
E. 80
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by GMATGuruNY » Wed Apr 25, 2018 2:26 am
Max@Math Revolution wrote:[GMAT math practice question]

Alice sells apples. She sold at least 10 lb every day last week. If the total weight of apples sold last week was 140, what is the largest possible range of the weights of apples sold on each day last week?

A. 40
B. 50
C. 60
D. 70
E. 80
Since at least 10 apples are sold every day, the least number of apples sold on a single day = 10.
The maximize the range, we must maximize the GREATEST number of apples sold on a single day.
To maximize the greatest number of apples sold on a single day, we must MINIMIZE the number of apples sold on each of the other 6 days.
Since at least 10 apples are sold every day, the least possible number of apples sold on each of the other 6 days = 10, for a total of 60 apples sold on the 6 days with the lowest sales.
Since the total number of apples sold on all 7 days = 140, the greatest possible option for the day with the highest sales = 140-60 = 80 apples.
The following range is yielded:
(highest possible sale day) - (lowest possible sale day) = 80-10 = 70.

The correct answer is D.
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by swerve » Wed Apr 25, 2018 10:02 am
We have to find the largest range. So we have to increase the gap between the largest and smallest.

Smallest is given as 10.

How do we make one of them largest possible- by taking all remaining to be 10...

So 10*6 = 60

7th day, 140 - 60 = 80...

Range 80 - 10 = 70. Option D.

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by Scott@TargetTestPrep » Thu Apr 26, 2018 3:00 pm
Max@Math Revolution wrote:[GMAT math practice question]

Alice sells apples. She sold at least 10 lb every day last week. If the total weight of apples sold last week was 140, what is the largest possible range of the weights of apples sold on each day last week?

A. 40
B. 50
C. 60
D. 70
E. 80
We want to maximize the range of the 7 days' sales. Therefore, we will minimize the values of the first 6 days, and that will make the value on the 7th day a maximum value, and then the range of the set will be maximized. We can let the number of pounds of apple she sold on each of the first 6 days be exactly 10. Thus, the maximum number of pounds of she sold on the last day is 140 - (6 x 10) = 140 - 60 = 80. Therefore, the largest possible range is:

80 - 10 = 70

Answer: D

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EDIT

by Max@Math Revolution » Fri Apr 27, 2018 12:03 am
=>

Since the minimum weight of apples sold is 10, the greatest range occurs for the greatest maximum. The greatest maximum occurs when all but one of the weights sold is 10 lb.
If the weights are 10, 10, 10, 10, 10, 10, max, then we must have max + 10 + 10 + 10 + 10 + 10 + 10 = max + 60 = 140.
Thus, max = 80.
The range is max - min = 80 - 10 = 70.
Therefore, the answer is D.
Answer : D
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