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At a certain auto dealership, 500 cars were sold last week. [#permalink]

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27 Jul 2016, 05:04

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At a certain auto dealership, 500 cars were sold last week. If a different number of cars were sold on each of the seven days, did the dealership sell at least 50 cars on Friday of that week?

(1) On Monday, the dealership sold 75 cars, which was the third-highest number of cars sold on any day that week.

(2) On Saturday, the dealership sold 77 cars, which was the highest number of cars sold on any day that week.

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Re: At a certain auto dealership, 500 cars were sold last week. [#permalink]

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27 Jul 2016, 05:49

Nevernevergiveup wrote:

At a certain auto dealership, 500 cars were sold last week. If a different number of cars were sold on each of the seven days, did the dealership sell at least 50 cars on Friday of that week?

(1) On Monday, the dealership sold 75 cars, which was the third-highest number of cars sold on any day that week.

(2) On Saturday, the dealership sold 77 cars, which was the highest number of cars sold on any day that week.

Statement 1 : (1) On Monday, the dealership sold 75 cars, which was the third-highest number of cars sold on any day that week.

It means we could have 0 cars on a single day and around 100+ cars on some other day. Hence, we are not sure if Friday would have at least 50 cars or not. Insufficient.

Statement 2 : (2) On Saturday, the dealership sold 77 cars, which was the highest number of cars sold on any day that week.

If 77 is the highest number of cars, then we could have 6 days with 77 cars and the left 38 cars on some other day. Again no information for Friday. Insufficient.

Combining, Highest is 77 and 3rd highest is 75=> 2nd highest is 76.

Still, apart from these, we could have other days containing 75 cars except one(which could be Friday). or we could have Friday containing 50+ cars.

Re: At a certain auto dealership, 500 cars were sold last week. [#permalink]

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27 Jul 2016, 06:04

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Number of cars sold in the week = 500

St1: 3rd highest = 75 --> Since there is no upper limit there is a possibility that the number of cars sold on a given day is less than 50 and that day may or may not be Friday. Not Sufficient

St2: Highest = 77 --> Upper limit = 77 In order to reduce the value of the lowest assume the other 5 values to be 76, 75, 74, 73, 72 77 + 76 + 75 + 74 + 73 + 72 = 447. The least value on any given day is 500 - 447 = 53 --> Number of cars sold on Friday > 52 Sufficient

Re: At a certain auto dealership, 500 cars were sold last week. [#permalink]

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27 Jul 2016, 06:55

Vyshak wrote:

Number of cars sold in the week = 500

St1: 3rd highest = 75 --> Since there is no upper limit there is a possibility that the number of cars sold on a given day is less than 50 and that day may or may not be Friday. Not Sufficient

St2: Highest = 77 --> Upper limit = 77 In order to reduce the value of the lowest assume the other 5 values to be 76, 75, 74, 73, 72 77 + 76 + 75 + 74 + 73 + 72 = 447. The least value on any given day is 500 - 447 = 53 --> Number of cars sold on Friday > 52 Sufficient

Answer: B

why did you assume the other days would have 74,73 and 72?

We can have something like 77 + 76 + 75 + 75 + 75 + 75 = 453. Hence, Friday could have 47 cars sold as well.

Please correct me if I am missing anything.
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Re: At a certain auto dealership, 500 cars were sold last week. [#permalink]

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27 Jul 2016, 08:29

Nevernevergiveup wrote:

At a certain auto dealership, 500 cars were sold last week. If a different number of cars were sold on each of the seven days, did the dealership sell at least 50 cars on Friday of that week?

For these types of questions, the statement: a different number of cars were sold on each of the seven days is very important.

(1) On Monday, the dealership sold 75 cars, which was the third-highest number of cars sold on any day that week.

The majority of cars could be sold on the top 3 days, leaving Friday with 0 cars sold. Alternately, Friday could have sold more than 50 if it were the 4th highest.

Insufficient

(2) On Saturday, the dealership sold 77 cars, which was the highest number of cars sold on any day that week.

We want Friday to be at the lowest possible, so have all other days at the maximum possible. To obtain the maximum sales: Take the sum of the 6 consecutive integers counting down from 77: \(77 + 76 + \ldots +72 = 6 \times \frac{1}{2} \times (77 + 72) = 447\)

Therefore the minimum number of cars sold on Friday is 53

Re: At a certain auto dealership, 500 cars were sold last week. [#permalink]

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28 Jul 2016, 04:48

At a certain auto dealership, 500 cars were sold last week. If a different number of cars were sold on each of the seven days, did the dealership sell at least 50 cars on Friday of that week?

(1) On Monday, the dealership sold 75 cars, which was the third-highest number of cars sold on any day that week.

(2) On Saturday, the dealership sold 77 cars, which was the highest number of cars sold on any day that week.

A) M = 75, from the other 5 days let 2nd highest be 76 and highest be 77

take the 6 days other than fri as (in increasing order) : 72, 73, 74, 75, 76, 77 Total is less than 250, hence Fri can be more than 50, but need not be. If the max number of car sold exceeds say its 100, and the rest remain the same, Fri will be less than 50 ----> not sufficient

B) as proved above, if highest is 77 then least is more than 50. -----> sufficient (B)
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Re: At a certain auto dealership, 500 cars were sold last week. [#permalink]

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