Question

Of 28 students taking at least one subject, the number taking Math and English but not History equals the number taking Math but not History or English. No student takes English only or History only, and six students take Math and History but not English. The number taking English and History but not Math is 5 times the number taking all three subjects. If the number taking all three subjects is even and non-zero, the number taking English and Math but not History is

Answer 1

The answer is 5 students taking English and Math but not History

Explanation:

The total students are 28 which are divided into 5 possible groups with no students taking either English only or History only:

1. Taking Math only
2. Taking English and Math but not History
3. Taking Math and History but not English
4. Taking English and History but not Math
5. Taking triple subjects

The number of students in group 3 is 6. Hence, the total number in group 1, 2, 4 and 5 is: 28 - 6 = 22

Also, the number of students in group 4 is five times the number in group 5, therefore: group 2 + group 5 = 6 times group 5

Additionally, the number of students in group 1 equals that in group 2.

Hence, the equation is: 6 x group 5 + 2 x group 2 = 22 => group 2 = 11 - 3 x group 5 => group 2 = 5 because group 5 is an even number and non-zero, it must be 2.