abhirup1711 wrote:3/20 members of a social club are retirees who are bridge players, 7/20 members are retirees, and one half of the members are bridge players. If 120 of the members are neither retirees nor bridge players,what is the total number of members in the social club?
240
300
360
400
480
Please help
This is an EITHER/OR problem.
Every member EITHER plays bridge OR doesn't.
Every member EITHER is a retiree or OR isn't.
Since the fractions in the problem are 3/20 and 7/20, let the total number of members = 20x.
To organize the data, draw a GROUP GRID:
In the grid above, B = bridge, NB = no bridge, R = retiree, NR = not a retiree.
3/20 members are retirees who are bridge players:
RB = (3/20)20x = 3x.
7/20 of the members are retirees:
R = (7/20)20x = 7x.
One half of the members are bridge players:
B = (1/2)(20x) = 10x.
Enter these values into the grid:
Complete the grid:
The grid indicates that the number of members who are neither retirees nor bridge players is equal to 6x.
Since 120 members are neither retirees nor bridge players, we get:
6x = 120
x = 20.
Thus:
Total members = 20x = 20*20 = 400.
The correct answer is
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