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both math and science

by sanju09 » Tue Feb 24, 2009 4:28 am
In a class of 50 students, 10 did not opt for math. 15 did not opt of science and 2 did not opt for either. How many students of the class opted for both math and science?

A. 37

B. 25

C. 23

D. 27

E. 48
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by bluementor » Tue Feb 24, 2009 5:27 am
10 did not opt for math includes those who opted for science only AND those who opted for neither

10 = Science_only + Neither

15 did not opt for science includes those who opted for math only AND those who opted for neither

15 = Math_only + Neither

Total = Math_only + Science_only + Both + Neither
50 = (Math_only + Neither) + (Science_only + Neither) - Neither + Both
50 = 15 + 10 - 2 + Both
Both = 50 - 23 = 27.

Choose D.

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by DanaJ » Tue Feb 24, 2009 5:29 am
You've got:
M - students that opted for math only
S - students that opted for science only
N - students that did not opt for anything
B - students that opted for both.


You are told that:
M + S + N + B = 50
S + N = 10
M + N = 15
N = 2

Use N = 2 and you get S = 8, M = 13.

B = 50 - 8 - 13 - 2 = 27.


I say D.
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Re: both math and science

by sureshbala » Tue Feb 24, 2009 5:34 am
sanju09 wrote:In a class of 50 students, 10 did not opt for math. 15 did not opt of science and 2 did not opt for either. How many students of the class opted for both math and science?

A. 37

B. 25

C. 23

D. 27

E. 48
Given that 2 opt did not opt for either. Hence we have 48 students who opt of at least of the two subjects.

Given 10 do not opt for math...implies 40 opted for math
15 did not opt for science....implies 35 opted for science.

So when we add this we get 40+35 = 75. But we have only 48 students who opted for at least one, so the extra 27 are the people who opted for both
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by ven4gmat » Tue Feb 24, 2009 5:40 am
Yes...my answer is also 27...Dear sanju, can you please post the OA for your questions?
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by sanju09 » Tue Feb 24, 2009 5:50 am
ven4gmat wrote:Yes...my answer is also 27...Dear sanju, can you please post the OA for your questions?
Dear ven4gmat, I will be forced to post OA in case I see 5 persons coming up with five different views or anything like that :)
The mind is everything. What you think you become. -Lord Buddha



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