The University of Dunning gives students the flexibility to
specialize in one or two areas out of four – Commerce,
Humanities, Medicine and Science. It is known that in a
batch of 300, 50 specialize in only Commerce and half of
those who specialize in Commerce specialize in
Humanities also. No one who specializes in Medicine
specializes in Humanities where as everyone who
specializes in Science also opts for a specialization in
Commerce.
1. What is the maximum number of students who
specialize in only Humanities, if it is known that every
area has at least ten students specializing in it?
(A) 185 (B) 200 (C) 170 (D) 180
2. By how much is the maximum number of students
who can specialize in Commerce more/less than the
maximum number of students who can specialize in
Medicine?
(A) 50 more (B) 50 less
(C) 100 more (D) 100 less
3. The ratio of the number of students who opted for
both Commerce and Science or both Commerce
and Medicine, to the number of students who opted
for both Commerce and Humanities can be _____.

4. The number of students specializing in exactly one
area among Commerce, Humanities, Science or
Medicine is _____.
(A) 300 (B) at least 75
(C) at least 100 (D) at least 50
5. The maximum number of students who specialize in
Science is _____.
(A) 100 (B) 105 (C) 95 (D) 125