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An automobile dealership sells only sedans and coupes. It sells each i

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An automobile dealership sells only sedans and coupes. It sells each i  [#permalink]

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New post 24 Feb 2017, 23:22
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Question Stats:

65% (02:17) correct 35% (02:25) wrong based on 48 sessions

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An automobile dealership sells only sedans and coupes. It sells each in only two colors: red and blue. Last year, the dealership sold 9,000 vehicles, half of which were red. How many coupes did the dealership sell last year?

(1) The dealership sold three times as many blue coupes as red sedans last year.
(2) The dealership sold half as many blue sedans as blue coupes last year.

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Re: An automobile dealership sells only sedans and coupes. It sells each i  [#permalink]

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New post 21 Feb 2019, 11:10
Official Explanation


Create a table to solve this proportions question. It should look something like this:

Attachment:
1.jpg
1.jpg [ 31.04 KiB | Viewed 178 times ]


The question stem tells us how many cars were sold last year. Because it tells us that half the cars sold were red, it also tells us the number of blue cars sold last year.
Statement (1) tells us: “The dealership sold three times as many blue coupes as red sedans last year.” Enter this information into the table in algebraic terms:

Attachment:
2.jpg
2.jpg [ 29.29 KiB | Viewed 178 times ]


Because two unknowns—red coupes and blue sedans—remain, Statement (1) does not provide enough information to solve the problem. The correct answer is BCE.
Use the same procedure to test Statement (2): “The dealership sold half as many blue sedans as blue coupes last year”:

Attachment:
3.jpg
3.jpg [ 27.03 KiB | Viewed 178 times ]


Again, two unknowns remain. This time, though, we have all the information we need to write a solvable equation. We know that 2x + x = 4,500. Therefore x equals 1,500. We now know the following:

Attachment:
4.jpg
4.jpg [ 30.12 KiB | Viewed 178 times ]


Unfortunately, this still isn’t enough information to answer the question. The answer is (C) or (E). Combine the information from the two statements. Statement (2) tells us that the dealership sold 3,000 blue coupes; combined with Statement (1), this tells us that the dealership sold 1,000 red sedans. We can now subtract 1,000 from 4,500 to determine that the dealership sold 3,500 red coupes. Therefore, it sold 6,500 coupes last year. The correct answer is (C).

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Re: An automobile dealership sells only sedans and coupes. It sells each i  [#permalink]

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New post 25 Feb 2017, 03:55
Total cars - 9000; red cars- 4500; blue cars- 4500;

(1) Blue coupes = 3*red sedans
Not enough information; hence, Insufficient.

(2) blue coupes = 2*blue sedans;
Total blue cars - 4500; hence, blue coupes = 3000;
But it doesn't give any information about red sedans; hence, Insufficient.

(1) & (2) together,
Blue coupes = 3000 = 3* red sedans;
Therefore, red sedans = 1000;
Now total red cars 4500; hence, red coupes = 4500 - 1000 = 3500;
So, total coupes sold = 3000 + 3500 = 6500; Sufficient.

Answer C.
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Re: An automobile dealership sells only sedans and coupes. It sells each i   [#permalink] 25 Feb 2017, 03:55
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