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16 Sep 2014, 01:26
Kudos
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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.
(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.
16 Sep 2014, 01:26
Kudos
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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:
• "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
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:
• "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
02 Dec 2024, 09:19
Kudos
Bookmarks
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.
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.
