What fraction of the students in a class have blue eyes?

This topic has expert replies
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Mon Mar 12, 2018 3:46 am
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
_________________
Manhattan Review GMAT Prep

Locations: New York | Vienna | Kuala Lumpur | Sydney | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.