Problem Solving

BTGmoderatorDC wrote:Each of the 200 students in a class enrolled in at least one of the three subjects: Physics, Chemistry and Mathematics. If 30 participated in, Physics, 150 participated in Chemistry and 100 participated in Mathematics and if "x" participated in all the three activities, then what could be the maximum value of x?

A. 10
B. 20
C. 30
D. 40
E. 50

OA C

Source: e-GMAT

Say,

the number of participants in Physics = P = 30;
the number of participants in Chemistry = C = 150;
the number of participants in Mathematics = M = 100;

the number of participants in Physics as well as Chemistry = PC;
the number of participants in Physics as well as Mathematics = PM;
the number of participants in Mathematics as well as Chemistry = MC;

the number of participants in all the three subjects = x; we have to maximize x

Thus, we have

200 = P + C + M - PC - PM - MC + x

200 = 30 + 150 + 100 - (PC + PM + MC) + x

-80 = - (PC + PM + MC) + x

We do not know the value of (PC + PM + MC); thus, we cannot get the value of x; however, we can get its maximum value. Since x is the number of participants in all the three subjects and the number of participants in Physics = 30 ( least among Physics, Chemistry, and Mathematics), the value of x ≤ 30. Thus, the maximum value of x = 30.

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote:Each of the 200 students in a class enrolled in at least one of the three subjects: Physics, Chemistry and Mathematics. If 30 participated in, Physics, 150 participated in Chemistry and 100 participated in Mathematics and if "x" participated in all the three activities, then what could be the maximum value of x?

A. 10
B. 20
C. 30
D. 40
E. 50

OA C

Source: e-GMAT

Since x is the number of students who enrolled in all the three courses, the maximum value of x can't exceed the number of students in the least enrolled course, which is Physics. Therefore, the maximum value of x is 30.

Answer: C