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Rose grows two kinds of orchid plants, Phalaenopsises and

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Rose grows two kinds of orchid plants, Phalaenopsises and

by BTGmoderatorLU » Thu May 30, 2019 2:53 am

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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 Phalaenopsises that have yellow flowers.

The OA is C
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by Ian Stewart » Fri May 31, 2019 6:16 am

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Statement 1 only guarantees we have at least 14 of the P flowers, and Statement 2 only guarantees we have an even number of the G flowers (since we must be able to multiply that number by 1.5 = 3/2 and get a whole number answer). But there remain many possible numbers of P flowers using either Statement alone.

Using both Statements, we have 14 white P flowers. So we have 40 flowers left, which are either yellow P flowers or G flowers. If we have 50% more of the G flowers, or 3/2 times as many G flowers, then yellow P flowers and G flowers are in a 2 to 3 ratio. So 2/5 of the 40 flowers are yellow P flowers, or 16 of them, so we have 14 +16 = 30 of the P flowers in total, and the answer is C.
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