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Rose grows two kinds of orchid plants, Phalaenopsises and

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by AAPL » Thu Oct 25, 2018 10:49 am

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Economist GMAT

Rose grows two kinds of orchid, Phalaenopsises and Gongoras. Each of the orchids has either yellow or white flowers (but not both). If Rose grows a total of 54 orchids plants, then how many of them are Phalaenopsises?

1. Rose grows 14 Phalaenopsises that have white flowers.
2. Among the orchids that Rose grows, the total number of Gongoras is 50% greater than the number of Phalaenopsises that have yellow flowers.

OA C.
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Source: — Data Sufficiency |
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by deloitte247 » Fri Oct 26, 2018 2:46 pm
$$Yellow\ Phalaenopsises=P_y$$
$$white\ Phalaenopsises=P_w$$
$$white\ Gongoras=G_w$$
For the two orchid plants we have four different varieties of flowers.
Total orchid plants=54
$$P_y+P_w+G_y+G_w=54$$
How many of them are phalaenopsises? $$Find\ P_y+P_w$$

Statement1 : Ross grows 14 Phalaenopsises that have white colour
$$P_w=14$$
$$P_y+14+G_y+G_w=54$$
$$P_y+G_y+G_w=54-14$$ ; statement 1 is INSUFFICIENT

Statement 2: Total number of Gongoras is 50% greater than the number of yellow Phalaenopsises.
$$G_y+G_w=\ 150\%\ of\ P_y$$
$$\ P_y+P_w+\left(\frac{3}{2}\left(P\right)_y\right)=54$$
Statement 2 is INSUFFICIENT

combining statement 1 and 2 together
P $$P_y+P_w+G_y+G_w=5$$
$$from\ statement\ 1,\ P_w=14\ \ \ from\ statement\ 2;\ \ G_w+G_y=\frac{3}{2}\left(P_y\right)$$
$$P_y+14+\left(\frac{3}{2}P_{y_{ }}\right)=54-14=40$$
$$P_y=\frac{40\cdot2}{4}=20$$ $$Total\ number\ of\ phalaenopsises=P_y+P_w=20+14=34\ $$
$$Two\ statements\ together\ are\ SUFFICIENT;\ option\ C$$
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by Jay@ManhattanReview » Fri Oct 26, 2018 6:07 pm
AAPL wrote:Economist GMAT

Rose grows two kinds of orchid, Phalaenopsises and Gongoras. Each of the orchids has either yellow or white flowers (but not both). If Rose grows a total of 54 orchids plants, then how many of them are Phalaenopsises?

1. Rose grows 14 Phalaenopsises that have white flowers.
2. Among the orchids that Rose grows, the total number of Gongoras is 50% greater than the number of Phalaenopsises that have yellow flowers.

OA C.
Pl. refer to this image.

Image

The correct answer: C

Hope this helps!

-Jay
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