Question

A group of 75 math students were asked whether they like algebra and whether they like geometry. A total of 45 students like algebra, 53 like geometry, and 6 do not like algebra or geometry.
What are the correct values of a, b, c, d, and e?


a = 16, b = 29, c = 22, d = 30, e = 24

a = 29, b = 16, c = 30, d = 22, e = 24

a = 16, b = 29, c = 24, d = 22, e = 30

a = 29, b = 16, c = 24, d = 30, e = 22

Answer 1

It is very easy to find the values for a, b, c, d and e. All you have to do is use the Algebra vs. Geometry table to use the given values to find the rest. Please see attachment to see the table. For example if we want to find e we simply subtract 53 from 75. This way e = 22, then use this to find the next value which will be b.

The answer is:

a = 29, b = 16, c = 24, d = 30 and e = 22

I hope this helps, Regards.

Answer 2

Let x be the number of students that like both algebra and geometry. Then:

1. 45-x is the number of students that like only algebra;

2. 53-x is the number of students that like only geometry.

You know that 6 students do not like any subject at all and there are 75 students in total. If you add the number of students that like both subjects, the number of students that like only one subject and the number of students that do not like any subject, you get 75. Therefore,

x+45-x+53-x+6=75.

Solve this equation:

104-x=75,

x=104-75,

x=29.

You get that:

1. 29 students like both subjects;
2. 45-29=16 students like only algebra;
3. 53-29=24 students like only geometry;
4. 24+6=30 students do not like algebra;
5. 16+6=22 students do not like geometry.

The correct choice is D.