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25 Apr 2024, 01:30
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71% (01:58) correct
29%
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A certain automobile dealer has 80 luxury cars in its inventory. Of these cars, 60 have leather seats, 50 have a moon roof, and 40 are equipped with a navigation system. There are 5 cars in the dealer's inventory that have none of these features. How many cars have exactly two of the three features?
(1) Ten cars have leather seats and a moon roof but no navigation system.
(2) The dealer has 25 cars with all three of these features.
(1) Ten cars have leather seats and a moon roof but no navigation system.
(2) The dealer has 25 cars with all three of these features.
25 Apr 2024, 05:00
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We are told that the number of luxury cars is 80. From these 80, in total, 60 have leather seats; 50 have moon roofs; 40 have a navigation system and that 5 have none of these. The values of each of the features encompasses not only include the cars with just the feature, but also cars with an additional of the three features and cars with all three features. This is why adding them will create a double count of the cars with two features and a triple count of cars which have all three features. To rectify this one needs to subtract all the cars with two of the features once and subtract twice the amount of cars with all three.
Let the cars with two features = \(x\) and the cars with three features = \(y\)
Creating an equation would look like this: Total Luxury Cars = (Sum of cars with features) - (Cars with two features) - 2(Cars with three features) + (cars with no features)
\(80 = (60+50+40) - x - 2y + 5\)
\(80 = 155 - x - 2y\)
\(75 = x + 2y\)
(1) Ten cars have leather seats and a moon roof but no navigation system.
Does not offer information which can be used to solve for \(x\).
INSUFFICIENT
(2) The dealer has 25 cars with all three of these features.
This statement gives the value of \(y\). Plugging that into the equation above: \(75 = x + 2(25)\)
\(x = 25\)
SUFFICIENT
ANSWER B
Let the cars with two features = \(x\) and the cars with three features = \(y\)
Creating an equation would look like this: Total Luxury Cars = (Sum of cars with features) - (Cars with two features) - 2(Cars with three features) + (cars with no features)
\(80 = (60+50+40) - x - 2y + 5\)
\(80 = 155 - x - 2y\)
\(75 = x + 2y\)
(1) Ten cars have leather seats and a moon roof but no navigation system.
Does not offer information which can be used to solve for \(x\).
INSUFFICIENT
(2) The dealer has 25 cars with all three of these features.
This statement gives the value of \(y\). Plugging that into the equation above: \(75 = x + 2(25)\)
\(x = 25\)
SUFFICIENT
ANSWER B
25 Apr 2024, 05:55
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Bunuel
The answer could also be found logically. Remember, we are not to find the exact value but an answer to whether we can find the value.
There are 80 cars, out of which we have 75 with at least one feature.
Total number of cars with features = 60+50+40 = 150, meaning there are cars with multiple features, and we have to account for these 75 extra cars.
These could be accounted by exactly two features or by all three features in a car. We are to find number of cars with exactly two features.
1) Ten cars have leather seats and a moon roof but no navigation system.
This just gives one part of three different possibilities under exactly two.
(2) The dealer has 25 cars with all three of these features.
Knowing how many have all three, we can find exactly two too.
Sufficient
B
