Joanna worked 5 shifts at a used car lot last week. Joanna earns $200

Question

Joanna worked 5 shifts at a used car lot last week. Joanna earns $200 for any shift she sells 4 or fewer cars and $300 for any shift she sells 5 or more cars. How much did Joanna earn last week working at the used car lot?

(1) Joanna sold an average (arithmetic mean) and median of 4 cars per shift last week.
(2) Joanna sold 3 or fewer cars during 2 of her shifts.

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PyjamaScientist · Answer

1)  From this statement, in five shifts, Joanna could sell cars as either of the following while maintaining  mean = median = 4 :
3 3 4 5 5
4 4 4 4 4
3 4 4 4 5 etc..
Each combination would give different pay for Joanna. Insufficient.

2)  From this statement, Joanna sold 3 or fewer cars in 2 shifts. So, she got paid $200 for those two shifts. But what about the other 3 shifts? No information is provided. Insufficient.

1) + 2)  together restrict the positions for no. of cars sold in statement 1. And thus only combination 3 3 4 5 5 would hold true.

Thus, both together are sufficient. Option  (C) .

arvind910619 · Answer

Imo E

This is a very tricky question

Statement 1 clearly insufficient as we do not have any information regarding individual cars sold in each shift

It could be 4, 4, 4, 4, 4 or 1, 3, 4, 5, 7

Statement B is also insufficient as we do not have nay information regarding cars sold in rest of the shifts

Together we have

Mean = Median = 4
For 2 shifts cars sold are 3 or fewer

1 , 3, 4 , 5,7 or 3, 3, 4, 5, 5 or 3, 3, 4, 4, 6

Clearly insufficient

bovannu01 · Answer

I'm confused by this question.

I thought if the average equals to the median, than it means that the list is made of consecutive numbers. When the avergae is 4, that means that the middle number is 4, the 2 numbers to the left must be smaller than 4, and the 2 numbers on the right must be larger than 4. This results in 2 possible sets (2,3,4,5,6) or (0,2,4,6,8). Either way, we know for sure how many shifts are less than 4 cars, and how many shifts are more than 4 cars. With this information, we can determine how much money she'll make. Therefore, answer 1 is sufficient.

Please clarify if my thinking is correct.

Bunuel · Answer

If you've read the solutions above, you'd easily spot the flaw in your reasoning. If a set is evenly spaced, its average and median are equal, but the converse is not always true. In other words, the average and median can be equal, but the set might not be evenly spaced. For example, consider the following set: {1, 3, 4, 5, 7}. In this set, both the mean and median are equal to 4, but the set is not evenly spaced.

Joanna worked 5 shifts at a used car lot last week. Joanna earns $200 for any shift she sells 4 or fewer cars and $300 for any shift she sells 5 or more cars. How much did Joanna earn last week working at the used car lot?

To answer the question, we need to know how many shifts Joanna sold 4 or fewer cars and how many shifts she sold 5 or more cars.

(1) Joanna sold an average (arithmetic mean) and median of 4 cars per shift last week.

The average of 4 implies that the total number of cars sold is 4*5 = 20.
The median of 4 implies that the middle number is 4.

So, we have the following list {a, b, 4, c, d}, where a ≤ b ≤ 4 ≤ c ≤ d and a + b + c + d = 16. We can construct many lists with these constraints:
{0, 0, 4, 8, 8}
{0, 1, 4, 4, 11}
{4, 4, 4, 4, 4}
etc.

Not sufficient.

(2) Joanna sold 3 or fewer cars during 2 of her shifts.

The information above is clearly insufficient.

(1)+(2) We can still construct different lists giving different answers. For example, consider {0, 0, 4, 4, 12} and {0, 0, 4, 8, 8}. Not sufficient.

Answer: E.

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Joanna worked 5 shifts at a used car lot last week. Joanna earns $200

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Joanna worked 5 shifts at a used car lot last week. Joanna earns $200

Prep Toolkit

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