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A flower arrangement consists of 30 roses, each of which is

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A flower arrangement consists of 30 roses, each of which is [#permalink] New post 13 May 2007, 02:18
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A flower arrangement consists of 30 roses, each of which is either white or red. If a rose is to be selected at random from the flower arrangement, the probability that the rose selected will be white is twice the probability that it will be red. How many white roses are in the flower arrangement?
A. 5
B. 10
C. 15
D. 20
E. 25

If the product of the 3 digits of the positive integer k is 14, what is the value of k?
(1) k is an odd integer
(2) k <700> i know its a pretty easy answer but just want to make sure how you solve for each condition
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 [#permalink] New post 13 May 2007, 03:55
Q1. 20/30 is 2 times more than 10/30. Hence, 20 white roses are in the flower arrangement. Answer is D.

Q2. Didn't get the second statement. Elaborate pls.
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Re: A flower arrangement consists of 30 roses, each of which is [#permalink] New post 26 Mar 2013, 06:45
Probability of red: Pr = X
Probability of white: Pw = 2X
Total Roses: 30

1/x + 1/2x = 1/30, x=1/20

Hence, 20 roses are white, 10 are red.

Hope its clear.
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Re: A flower arrangement consists of 30 roses, each of which is [#permalink] New post 26 Mar 2013, 08:17
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Jamesk486 wrote:
A flower arrangement consists of 30 roses, each of which is either white or red. If a rose is to be selected at random from the flower arrangement, the probability that the rose selected will be white is twice the probability that it will be red. How many white roses are in the flower arrangement?
A. 5
B. 10
C. 15
D. 20
E. 25

If the product of the 3 digits of the positive integer k is 14, what is the value of k?
(1) k is an odd integer
(2) k <700> i know its a pretty easy answer but just want to make sure how you solve for each condition


Hi James486,

The roses is rather straight forward in that there must be twice as many white roses as red roses. This is a simple probability without any outside factors. There must be 10 red and 20 white roses as elaborated upon above. You can also set it up as two algebraic formulas:

W+R = 30
W = 2R.
Substituting we find 3R = 30, R=10, W=20. Answer choice D.


The second question is interesting as well. I read statement 2 as K < 700. The rest is just a comment about the facility of the question.

If the product of the digits of k = 14, then we need to look at the prime factors of 14, which are simply 2 and 7. Thus, the three digits must be 2, 7 and 1 in some order. Simple permutation yields possible options of: {127, 172, 217, 271, 712 and 721}. No other combination of digits will yield a product of 14 and be 3 digits.

Statement 1 is insufficient since it eliminates 2 answer choices (evens) but leaves 127, 217, 271 and 721.
Statement 2 is insufficient since it eliminates 2 answer choices (>700) but leaves 127, 172, 217 and 271.
Combining them we can eliminate 3 answer choices (evens or >700) but still have 127, 217 and 271 that satisfy these conditions.

Answer is therefore E in this data sufficiency question. It could have been C had statement 2 been k>700 instead of <... but as written we cannot differentiate between 3 valid options.

Hope this helps!
-Ron
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Re: A flower arrangement consists of 30 roses, each of which is   [#permalink] 26 Mar 2013, 08:17
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A flower arrangement consists of 30 roses, each of which is

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