Question 1140169: If there are five people in a room. 3 of them are studying math. 4 people are studying
science. How many people are studying both math and science, if one person is
studying neither math nor science?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! This is a Venn diagram with 2 intersecting
circles. There is 1 person outside of both circles
( math and science circles ), so 
are in the circles. Label as follows:
X = only studies math
Y = studies both
Z = only studies science
(1) X + Y + Z = 4
(2) X + Y = 3 ( given )
(3) Y + Z = 4 ( given )
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From (1) and (3), X must be zero
So, from(2), Y = 3 , and plug this into (3)
Z = 1
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So, 3 people are studying both.
Get another opinion if needed
Answer by ikleyn(52879)  (Show Source):
You can put this solution on YOUR website! .
From these 5 people, separate the one who studying neither Math nor Science.
You will get then 4 persons, each of which is studying some of the two subjects.
But you are given that four of the persons are studying Math - hence, these 4 are studying Math.
Further, that three, who studying Science, are among that four. Hence, 3 persons are studying both subjects.
ANSWER. 3 persons are studying both subjects.
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