Gmat_mission wrote:What fraction of the students in a class have blue eyes?
(1) 10% of the girls have blue eyes.
(2) 20% of the boys have blue eyes.
[spoiler]OA=E[/spoiler].
Experts, using both statements together is not sufficient? Is not the answer 30%? <i class="em em-confused"></i>
30% can never be an incorrect answer. See how.
Case 1: Say the number of girls = the number of boys = x
Thus, the total number of students = x + x = 2x
Thus, the number of girls = 10% of x = 0.1 x and the number of boys = 20% of x = 0.2 x
The total number of students with blue eyes = 0.1x + 0.2x = 0.3x
The fraction of the students in the class that have blue eyes = 0.3x/2x = 3/20.
Case 2: Say the number of girls = x and the number of boys = 2x
Thus, the total number of students = x + 2x = 3x
Thus, the number of girls = 10% of x = 0.1 x and the number of boys = 20% of 2x = 0.4 x
The total number of students with blue eyes = 0.1x + 0.4x = 0.5x
The fraction of the students in the class that have blue eyes = 0.5x/3x = 1/6
No unique answer. Insufficient.
The correct answer:
E
Hope this helps!
-Jay
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