M27-03

Question

Of the 58 patients of Vertigo Hospital, 45 have arachnophobia. How many of the patients have acrophobia?

(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.
 
(2) 32 patients of Vertigo Hospital have arachnophobia but not acrophobia.

Bunuel · Accepted Answer

Official Solution:

Of the 58 patients of Vertigo Hospital, 45 have arachnophobia. How many of the patients have acrophobia? 
 
This is one of the trickiest questions in our question pool, and it is crucial to approach it with great care and attention to detail when reading the solution.
 
(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:
 
 https://gmatclub.com/gmat-practice-tests/resources/import/img/M27-03.png 
 
• "Both" and "Neither" are both equal to  x ;
 
• Green box  = 45 - x ;
 
• Blue box  = (45 - x) + x = 45 ;
 
• Yellow box  = 58 - 45 = 13 .
 
As you can see, the number of patients who have acrophobia is 13. Sufficient.
 
(2) 32 patients of Vertigo Hospital have arachnophobia but not acrophobia. Clearly insufficient.

Answer: A

earnit · Answer

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.

Bunuel · Answer

We cannot assume that there are no patients with some other phobias in the hospital. Moreover, (1) states that the number of patients at Vertigo Hospital who have both arachnophobia and acrophobia is equal to  the number of patients who have neither arachnophobia nor acrophobia . The patients who have neither arachnophobia nor acrophobia are those who have some other phobias. Therefore, we are directly told that there are patients with some other phobias in the hospital.

Mahmud6 · Answer

I think this question is  good  and  helpful .
Very Good Question

Gladiator59 · Answer

I think this is a  high-quality  question and I agree with explanation. One of the trickiest!

joe123x · Answer

I love this question, really high quality. 
reminder to keep an eye for little tricks.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

xxdw0007 · Answer

I think this is a  high-quality  question and I agree with explanation.

cosmiclatte · Answer

My approach was similar but slightly different than the official solution to arrive at the correct answer:

I used the equation T = A + B - Both + Neither.

I substituted the known values for 58 = 45 + B - Both + Neither.

Looking at Statement 1, since Both and Neither are the same values, they will always cancel each other out, leaving the equation as 
58 = 45 + B
B = 13

Admittedly, I figured that was too simple (because I know the GMAT likes to be tricky) and ultimately did the Venn Diagram to double-check. Besides swapping the location of the labels, it was the same as the official solution.

M27-03

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards