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Sedans and SUVs

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Sedans and SUVs

by pareekbharat86 » Sun Nov 24, 2013 1:37 am
A car dealership carries only sedans and SUVs, and on Tuesday it sold 1/6 of the sedans that it had in stock at the beginning of the day. If no new inventory arrived at any point on Tuesday, and the only change in inventory was that some vehicles were sold, did the dealership have more than 100 vehicles in inventory at the beginning of the day Tuesday?

(1) By the end of the day, the dealership had sold 8/9 as many sedans as SUVs.

(2) The dealership sold 85% as many sedans on Tuesday as it did on Wednesday.

OA is B.

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by Uva@90 » Sun Nov 24, 2013 1:46 am
Here you can see Experts reply,
https://www.beatthegmat.com/a-car-dealer ... 14127.html

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by [email protected] » Sun Nov 24, 2013 5:44 pm
Hi Bharat,

This DS question has some interesting "clues" built into it that will affect what the correct answer is.

We're told that there are Sedans and SUVs and that 1/6 of the Sedans were sold. This means that the TOTAL number of Sedans MUST BE a multiple of 6 (6, 12, 18, etc.). The number of SUVs can be any positive integer.

We're asked "did the dealership have more than 100 vehicles at the BEGINNING of the day?" This is a YES/NO question.

Fact 1: The dealership sold 8/9 as many Sedans as SUVs.

Let's TEST Values:
If 8 Sedans were sold and 9 SUVs were sold, then the dealership started with:

48 Sedans (since 1/6 were sold)
At least 9 SUVs, but we don't know how many

If it's 9, then 48 + 9 = 57 and the answer is NO
If it's 100, then 48 + 100 = 149 and the answer is YES.
Fact 1 is INSUFFICIENT

Fact 2: The dealership sold 85% as many Sedans on Tuesday as it did on Wednesday.

This is an INTERESTING piece of information that most people would mishandle.

85% = 17/20

So, we know that the number of Sedans is a MULTIPLE OF 6 AND a MULTIPLE OF 17.
The smallest possible number of Sedans would be 6 x 17 = 102

At that point, the number of SUVs is irrelevant.
102 + any positive integer > 100, so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer: B

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