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At an international conference, “Red” world countries and “Blue” world

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At an international conference, “Red” world countries and “Blue” world  [#permalink]

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New post 11 Feb 2020, 03:05
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Question Stats:

89% (01:48) correct 11% (02:29) wrong based on 57 sessions

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At an international conference, “Red” world countries and “Blue” world countries are the only participants. The ratio of “Red” world participants to “Blue” world participants is 5:4. If one-third of “Red” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed?

(A) 13/36
(B) 13/27
(C) 14/27
(D) 23/36
(E) 23/37

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Re: At an international conference, “Red” world countries and “Blue” world  [#permalink]

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New post 11 Feb 2020, 05:08
let total = 27
so Red = 5/9 * 27 ; 15
and Blue = 4/9 * 27; 12
Red LH = 15 *1/3 ; 5 and RH ; 10
Blue LH = 2/3 *12 ; 8 and Rh ; 4
total LH of participants ; 13/27
IMO B


Bunuel wrote:
At an international conference, “Red” world countries and “Blue” world countries are the only participants. The ratio of “Red” world participants to “Blue” world participants is 5:4. If one-third of “Red” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed?

(A) 13/36
(B) 13/27
(C) 14/27
(D) 23/36
(E) 23/37
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Re: At an international conference, “Red” world countries and “Blue” world  [#permalink]

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New post 17 Feb 2020, 03:29
Bunuel wrote:
At an international conference, “Red” world countries and “Blue” world countries are the only participants. The ratio of “Red” world participants to “Blue” world participants is 5:4. If one-third of “Red” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed?

(A) 13/36
(B) 13/27
(C) 14/27
(D) 23/36
(E) 23/37


If there are 27 total participants, then the number of “Red” world participants is 15, and the number of “Blue” world participants is 12.

Thus, 1/3 x 15 = 5 “Red” world participants are left-handed and 2/3 x 12 = 8 “Blue” world participants are left-handed.

So, (5 + 8)/27 = 13/27 of the participants are left-handed.

Answer: B
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Re: At an international conference, “Red” world countries and “Blue” world   [#permalink] 17 Feb 2020, 03:29
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