aman88 wrote:In a group of people, 3/5 have brown hair and 3/4 of the people with brown hair also have brown eyes, while only one quarter of the people who don't have brown hair have brown eyes. What is the ratio of the number of people with both brown hair and brown eyes to the number with neither?
A. 1/2
B. 9/8
C. 3/2
D. 5/2
E. 9/2
OA C
This is an EITHER/OR group problem.
Everyone EITHER has brown hair OR does not.
Everyone EITHER has brown eyes OR does not.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.
Let BH = brown hair, NBH = no brown hair, BE = brown eyes, NBE = no brown eyes.
Let the total = the LCM of the two denominators in the problem = 5*4 = 20.
______________BH_____NBH_______Total
BE:
NBE:
total:___________________________20
Now let's use the information in the problem to complete the grid step by step.
As soon as we know 2 entries in a row or a column, we can calculate the remaining entry in that row or column.
3/5 have brown hair.
3/4 of the people with brown hair also have brown eyes.:
______________BH_____NBH_______Total
BE:____________9
NBE:___________3
total:_________12_______8_________20
One quarter of the people who don't have brown hair have brown eyes:
_______________BH______NBH_______Total
BE:_____________9________2_________11
NBE:___________3_________6_________9
total:__________12________8_________20
With the grid complete, we can answer the question stem:
(Brown hair and brown eyes) / Neither = 9/6 = 3/2.
The correct answer is
C.
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