pre-gmat wrote:Yes sorry, 32 is the correct answer.
I got this question from Testmagic, but the explanation was not that clear and I wanted to see if the formula works.
Here's another one if you wanna try.
In a class of 217 students, the number of students who passed in English only is 43, in Math only is 47, in commerce only is 56. The number who passed in English and Maths is 14, Maths and Commerce is 26 and English and Commerce is 21 and the number who passed in all the subjects is 6. Find the number of students who failed in all the subjects.
The formula doesn't apply because we don't have the right information.
True # of objects =
(total # in group 1) + (total # in group 2) + (total # in group 3) + (total # in none of the groups) - (# in only groups 1&2) - (# in only groups 1&3) - (# in only groups 2&3) - 2(# in all 3 groups)
We haven't actually been given the
total # in group 1, we're given the number who are
only in group 1 - same for groups 2 and 3. Further, we're not given
# in only groups 1&2, we're given the total # in groups 1&2 (same for groups 1&3 and groups 2&3).
With this information, we could answer very quickly with a Venn diagram. The only extra counting is among those who have passed either 2 or 3 courses.
To calculate:
217 = 43 + 47 + 56 + (14-6) + (26 - 6) + (21 - 6) + 6 + none
(we subtract 6 from each of the "double passes" because we already count those 6 people in the "triple pass" group.)
217 = 43 + 47 + 56 + 8 + 20 + 15 + 6 + none
217 = 195 + none
22 = none
Moral of the story: read the information in the question carefully to see if it matches up with the formula that you're using!
