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
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rishianand7
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Hi rishianand7
This is a quirky DS question and I imagine that MANY Test Takers would get it wrong. If you pay attention to the numbers and take good notes, then you'll be able to get it correct.
We're told that a car dealership sells only Sedans and SUVS and that it sold 1/6 of its Sedans on Tuesday (notice THAT weird fraction!). No new vehicles were added that day. The question asks IF the dealership has MORE THAN 100 vehicles at the beginning of the day.
Fact 1 tells us that the dealership sold Sedans and SUVs in a ratio of 8 to 9. This means that the total number of Sedans sold was a multiple of 8 and the total number of SUVs sold is an equivalent multiple of 9
IF....
8 Sedans were sold, and that represents 1/6 of Sedans on the lot, then there were 48 Sedans at the start of the day
So 9 SUVs were sold, but that doesn't tell us how many SUVs there were in total....
If total SUVs = 9, then 48 + 9 = 57 and the answer to the question is NO
If total SUVs = 100, then 48 + 100 = 148 and the answer to the question is YES
Fact 1 is INSUFFICIENT
Fact 2 tells us that Sedans sold on Tuesday = 85% of Sedans sold on Wednesday. **NOTE: Most Test Takers will blow this off because it doesn't mention the SUVs, but think about what 85% MEANS!!!**
85% = 17/20, which means that the LEAST number of Sedans that were sold on Wednesday is 17
With 17 Sedans sold, and that represents 1/6 of Sedans on the lot, then there were 102 Sedans at the start of the day.
THE NUMBER OF SUVs IS IRRELEVENT because we already have over 100 vehicles. The answer to the question is ALWAYS YES!!!
Fact 2 is SUFFICIENT
Final Answer:B
GMAT assassins aren't born, they're made,
Rich
This is a quirky DS question and I imagine that MANY Test Takers would get it wrong. If you pay attention to the numbers and take good notes, then you'll be able to get it correct.
We're told that a car dealership sells only Sedans and SUVS and that it sold 1/6 of its Sedans on Tuesday (notice THAT weird fraction!). No new vehicles were added that day. The question asks IF the dealership has MORE THAN 100 vehicles at the beginning of the day.
Fact 1 tells us that the dealership sold Sedans and SUVs in a ratio of 8 to 9. This means that the total number of Sedans sold was a multiple of 8 and the total number of SUVs sold is an equivalent multiple of 9
IF....
8 Sedans were sold, and that represents 1/6 of Sedans on the lot, then there were 48 Sedans at the start of the day
So 9 SUVs were sold, but that doesn't tell us how many SUVs there were in total....
If total SUVs = 9, then 48 + 9 = 57 and the answer to the question is NO
If total SUVs = 100, then 48 + 100 = 148 and the answer to the question is YES
Fact 1 is INSUFFICIENT
Fact 2 tells us that Sedans sold on Tuesday = 85% of Sedans sold on Wednesday. **NOTE: Most Test Takers will blow this off because it doesn't mention the SUVs, but think about what 85% MEANS!!!**
85% = 17/20, which means that the LEAST number of Sedans that were sold on Wednesday is 17
With 17 Sedans sold, and that represents 1/6 of Sedans on the lot, then there were 102 Sedans at the start of the day.
THE NUMBER OF SUVs IS IRRELEVENT because we already have over 100 vehicles. The answer to the question is ALWAYS YES!!!
Fact 2 is SUFFICIENT
Final Answer:B
GMAT assassins aren't born, they're made,
Rich
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Statement 1: By the end of the day, the dealership had sold 8/9 as many sedans as SUVs.varun289 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.
Plug in the MINIMUM value for the number of SUVs sold.
Let SUVs sold = 9.
In this case, sedans sold = (8/9)8 = 8.
Since 1/6 of the TOTAL number of sedans were sold, we get:
8 = (1/6)(total sedans)
Total sedans = 48.
Here, the MINIMUM number of vehicles at the beginning of Tuesday = (SUVs sold) + (total sedans) = 9+48 = 57, which is LESS than 100.
But the total number of SUVs at the beginning of Tuesday could be ANY VALUE.
If at the start of Tuesday there were 1000 SUVs -- of which 9 were sold -- then the total number of vehicles at the beginning of Tuesday = (total SUVs) + (total sedans) = 1000 + 48 = 1048, which is GREATER than 100.
INSUFFICIENT.
Statement 2: The dealership sold 85% as many sedans on Tuesday as it did on Wednesday.
Since 85/100 = 17/20, we get:
(sedans sold on Tuesday) = (17/20)(sedans sold on Wednesday).
Plug in the MINIMUM value for the number of sedans sold on Wednesday.
Let sedans sold on Wednesday = 20.
In this case, sedans sold on Tuesday = (17/20)20 = 17.
Since 1/6 of the TOTAL number of sedans were sold, we get:
17 = (1/6)(total sedans)
Total sedans = 102.
Thus, the total number of vehicles at the beginning of Tuesday was greater than 100.
SUFFICIENT.
The correct answer is B.
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As a tutor, I don't simply teach you how I would approach problems.
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Java_85
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I solve this question using the LCM technique, since the total number of cars should be an integer, therefore, multiplying the total number of cars and given fractions should result in an integer.
(1) we have two fractions here 1/6 and 8/9 for sedans==> the LCM for 6 and 9 is 18 ==> we should have at least 18 sedans and 18 SUV's which there is no guarantee to have more than 100 vehicles in total.
(2) we have 1/6 and 85/100 ==> LCM of 100 and 6 is 300 and it does guarantee having more than 100 vehicles.
(1) we have two fractions here 1/6 and 8/9 for sedans==> the LCM for 6 and 9 is 18 ==> we should have at least 18 sedans and 18 SUV's which there is no guarantee to have more than 100 vehicles in total.
(2) we have 1/6 and 85/100 ==> LCM of 100 and 6 is 300 and it does guarantee having more than 100 vehicles.
