Practicegmat wrote:
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.
Official solution from Veritas Prep.
The question doesn't put any restriction on the number of SUVs not sold, so you can make this number as big as you want to prove the answer "yes".
Statement 2, however, is sufficient. While it may not look so at first, it combines with the given information to guarantee that the dealership had a minimum of 102 sedans. Knowing that:
-The number of sedans sold was 17/20 (85%) of the number sold on another day tells us that the number of sedans sold must be a multiple of 17.
-The number of sedans in stock is equal to 6(the number sold) tells us that the number of sedans in stock must be 17 x a multiple of 6. The lowest such number is 102, guaranteeing that at least 102 vehicles were in stock at the beginning of the day.
Strategically, this problem is a good opportunity to "Leverage Assets" and ask "Why Are You Here?". The fact that statement 2 talks about Wednesday when everything else in the problem talks only about Tuesday might seem like a total throwaway, but remember: the GMAT rarely, if ever, completely throws away a DS statement. If a statement seems irrelevant upon first glance, it's a good opportunity for you to ask why it's there:
-Could it be a clue that helps you better understand the other statement? -Could it be a trap, a piece of information that you thought you might need but you actually don't? -Could it be, as it is in this case, a cleverly-worded piece of information that you can make useful by Leveraging Assets - manipulating algebra, applying a number property or divisibility rule, etc.?
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