The Cyclepaths Bicycle Factory has 300 bicycles in stock.

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The Cyclepaths Bicycle Factory has 300 bicycles in stock. The bicycles are either blue or red, and they come in two sizes: large and small. If 175 bicycles are blue, and 140 are large, how many are both blue and large?

1) There are 90 small red bicycles.
2) There are twice as many small blue bicycles as there are large red bicycles.

The OA is D

Source: Magoosh
Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Aug 06, 2019 4:00 am

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swerve wrote:The Cyclepaths Bicycle Factory has 300 bicycles in stock. The bicycles are either blue or red, and they come in two sizes: large and small. If 175 bicycles are blue, and 140 are large, how many are both blue and large?

1) There are 90 small red bicycles.
2) There are twice as many small blue bicycles as there are large red bicycles.

The OA is D

Source: Magoosh
See the following self-explanatory image.

Image

The correct answer: D

Hope this helps!

-Jay
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by deloitte247 » Thu Aug 08, 2019 7:53 am

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Question => how many bicycles are both blue and large?
Given that large bicycles = 140
blue bicycles = 175
small bicycles = 300 - 140 = 160
red bicycles = 300 - 175 =125
Let small blue bicycles = x
small red bicycles = 160 - x
large blue bicycles = 175 - x
large red bicycles = 140 - ( 175 - x ) = x - 35
Statement 1 => there are 90 small red bicycles
90 = 160 - x
x = 70
for blue and large or large blue bicycles = 175 - x
where x = 70
175 - 70 = 105 ; statement 1 is SUFFICIENT
Statement 2 => there as twice as many blue bicycles as there are large red bicycles
x = 2 ( x - 35 ) = 2x - 70
x = 70
for large blue bicycles = 175 - x where x = 70
175 - 70 = 105 ; statement 2 is SUFFICIENT
Each statement alone is SUFFICIENT
Answer = option D