Hi KamalJ,
This is a difficult question that will unlikely affect your overall score if you do encounter it, but here is the way to do it.
Basically, you're looking at an overlapping sets question. I needed to visualize it, so I drew a Venn diagram (attached) and labelled each segment with a letter:
- X: Sweaty Palms ONLY
Y: Vomitting ONLY
Z: Dizziness ONLY
a: Sweaty Palms AND Vomiting
b: Sweaty Palms AND Dizziness
c: Vomiting AND Dizziness
d: Sweaty Palms AND Vomiting AND Dizziness (All three)
Zero students experienced no symptoms
In this case, it becomes apparent that we want the value of (X+Y+Z).
I then used the fact that all the students experienced at least one symptom (provided in the question) to create a series of equations:
Since 40% of students did experience sweaty palms, 60% of students did not experience sweaty palms, so we can add up all the terms that do not contain Sweaty Palms and they should equal 60%:
Y+Z+c=60
Since 30% of students did experience vomiting, 70% of students DID NOT experience sweaty palms, so we can add up all the terms that do not contain Vomiting and they should equal 70%:
X+Z+b=70
Since 75% of students did experience dizziness, 25% of students did not experience sweaty palms, so we can add up all the terms that do not contain Dizziness and they should equal 25%:
X+Y+a=25
Now, add them all together:
Y+Z+c+X+Z+b+X+Y+a = 60 + 70 + 25
2(X+Y+Z) + (a+b+c) = 155
Notice that a+b+c includes all the people who experienced exactly two symptoms. According to the question, that value is equal to 35%. So we now have:
2(X+Y+Z) + 35 = 155
2(X+Y+Z) = 120
(X+Y+Z) = 60%
60% of 300 is 180, which is answer choice D.
This question will definitely take a bit of time. An alternative approach if your running low on time and want to eliminate some wrong choices would be to calculate the percentages represented in the answer choices:
A) 105/300 = 7/20 = 35 %
B) 125/300 = 5/12 = not a clean percentage (instantly makes me skeptical given the information in the question all involves clean percentages and I know that for set questions, I will typically only be adding/subtracting terms)
C) 130/300 = 13/30 = not a clean percentage
D) 180/300 = 3/5 = 60%
E) 195/300 = 13/20 = 65%
So having eliminated B and C, I would have A,D,and E to choose from. I would likely eliminate A because it seems low given the numbers. Also, something I learned from an Empower course with Rich suggests that A and E would be incorrect. Thus, in a pinch I would still narrow it down to D.
Best,
-OWN
$$$$
