Bunuel wrote:
Official Solution: Tricky question.
(1) The number of patients of Vertigo Hospital who have both arachnophobia and acrophobia is the same as the number of patients who have neither arachnophobia nor acrophobia. Use double-set matrix:
As you can see, # of patients who have acrophobia is \(58-45=13\). Sufficient.
(2) 32 patients of Vertigo Hospital have arachnophobia but not acrophobia. Clearly insufficient.
Answer: A
I have a query with regard to understanding the underlying assumption involved here:
Are we assuming that the hospital could have patients with diseases other than arachnophobia and acrophobia ? And if NO, then why is statement 2 insufficient?
As per Statement 2: 32 patients of Vertigo Hospital have arachnophobia but not acrophobia, implies that the no. of people with both arachnophobia and acrophobia should be 13, satisfying the given no. of 45 and hence the no. of people acrophobia should amount to 13 and hence the ans is 23.
I cannot draw the venn diagram, but assuming the intersection part as x and only acro as y:
32+x+y = 58
32+x = 45 given
Hence y = 58-45 = 13
Reqyired answer: 13+x = 13+13 = 26.
Yes it defies the logic that both statments always give the same answer but what am i missing here.