swerve wrote:Rose grows two kinds of orchid plants, Phalaenopsises and Gongoras. Each of the orchids has either yellow or white flowers (but not both). If Rose grows a total of 54 orchid 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 the Phalaenopsises that have yellow flowers.

The OA is C.

Please, can anyone explain this DS question? I'm not sure why C is the correct answer. I need help. Thanks.

Say the number of white Phalaenopsises = Pw, the number of yellow Phalaenopsises = Py, the number of white Gongoras = Gw, and the number of yellow Gongoras = Gy

=> Pw + Py + Gw + Gy = 54.

We have to get the value of Pw + Py

Let's take each statement one by one.

(1) Rose grows 14 Phalaenopsises that have white flowers.

=> Pw = 14, but we do not know Py. Insufficient.

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

Gw + Gy = 150% of Py = 1.5Py

Can't get the value of Pw + Py. Insufficient.

(1) and (2) together

We know that Pw + Py + Gw + Gy = 54

Thus, 14 + Py + 1.5Py = 54

=> 2.5Py = 40 => Py = 40/2.5 = 16

=> Pw + Py = 14 + 16 = 30. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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