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M27-03

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16 Sep 2014, 01:26
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Difficulty:

95% (hard)

Question Stats:

46% (01:19) correct 54% (01:35) wrong based on 292 sessions

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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.

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16 Sep 2014, 01:26
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.

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16 Oct 2014, 15:39
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.

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.
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17 Oct 2014, 00:51
earnit wrote:
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.

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.

We cannot assume that there are no patients with some other phobias in the hospital. Moreover, (1) says: 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. The patients who have neither arachnophobia nor acrophobia, are those who have some other phobias. So, we are in fact directly told that there are patients with some other phobias in the hospital.
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10 Jan 2015, 06:54
I think this question is good and helpful.
Very Good Question
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31 May 2015, 14:30
Bunuel wrote:
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.

What confuses me about this question is that the math is simple where the x's just cancel out making the total non acro # = total arachno #. Made me think I did it wrong so I picked C - both are required. But I guess logically, if the patient #'s are the same between both arachno and acro and neither arachno and acro, then the math works out.
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12 Jul 2015, 13:44
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.

Bunuel Sir, Could please explain in more detail that how we got Number of patients who have acrophobia as 58-45=13.

From the given and statement i) I could only conclude that people having Arachnophobia is 45 and people not having Arachnophobia is 13.

And I assumed people having both phobias to be x and people having none to be x.
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13 Jul 2015, 01:29
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anurag356 wrote:
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.

Bunuel Sir, Could please explain in more detail that how we got Number of patients who have acrophobia as 58-45=13.

From the given and statement i) I could only conclude that people having Arachnophobia is 45 and people not having Arachnophobia is 13.

And I assumed people having both phobias to be x and people having none to be x.

It's all in the matrix:

The number of patients of Vertigo Hospital who have both arachnophobia and acrophobia (X) is the same as the number of patients who have neither arachnophobia nor acrophobia (X).

The number of patients with arachnophobia but no acrophobia is 45 - x.
The number of people without acrophobia is (45 - x) + x = 45.
Acrophobia = Total - No Acrophobia = 58 - 45 = 13.
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13 Jul 2015, 16:59
Bunuel wrote:
anurag356 wrote:
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.

Bunuel Sir, Could please explain in more detail that how we got Number of patients who have acrophobia as 58-45=13.

From the given and statement i) I could only conclude that people having Arachnophobia is 45 and people not having Arachnophobia is 13.

And I assumed people having both phobias to be x and people having none to be x.

It's all in the matrix:

The number of patients of Vertigo Hospital who have both arachnophobia and acrophobia (X) is the same as the number of patients who have neither arachnophobia nor acrophobia (X).

The number of patients with arachnophobia but no acrophobia is 45 - x.
The number of people without acrophobia is (45 - x) + x = 45.
Acrophobia = Total - No Acrophobia = 58 - 45 = 13.

Thanks, I now understood where I was wrong, to be honest with you I actually couldn't figure out how 45-x+x=45 and therefore i couldn't understand the 58-13=45 part.

But now as you stressed on the fact that its in the matrix, thanks to u on more careful observation I figured out the issue. People having Arachnophobia and Acrophobia is assumed x , we have people having Arachnophobia is 45 therefore people with Arachnophobia but no Acrophobia is 45-x. 45-x+x=45. Now as People having none is also x , therefore again we have the same equation for People having No Acrophobia but Arachnophobia + none of phobias =45-x+x =45. Hence 58-45=13

Thanks ))
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13 Sep 2015, 21:38
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I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Problem with this answer is that it has taken a assumption that all patients have either arachophobia or acrophobia. No patient is having neither is these two diseases. Therefore, I think question stem must change in order to accommodate this assumption , so that option A is correct
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14 Sep 2015, 00:23
prateekjainstar90 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Problem with this answer is that it has taken a assumption that all patients have either arachophobia or acrophobia. No patient is having neither is these two diseases. Therefore, I think question stem must change in order to accommodate this assumption , so that option A is correct

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04 Oct 2015, 12:05
I think this is a poor-quality question. guyes u need to reconfigure your overlappins problems. they are misleading. i ve noted in my posts somewhere that you are inconsistent in logic: in overlapping sets you leave the room for assumptions, in other type of questions you dont.
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04 Oct 2015, 21:26
I think this is a poor-quality question. guyes u need to reconfigure your overlappins problems. they are misleading. i ve noted in my posts somewhere that you are inconsistent in logic: in overlapping sets you leave the room for assumptions, in other type of questions you dont.

Please elaborate what you mean. Thank you.
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27 Dec 2015, 16:28
I understand the (45 -x) + x part, but how do you know this equation equals 45?
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27 Dec 2015, 20:54
dau245 wrote:
I understand the (45 -x) + x part, but how do you know this equation equals 45?

(45 -x) + x = 45 - x + x = 45.
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10 Sep 2016, 15:56
One can use the venn diagram where the value of x will vary from 0 to 13 giving the count of the patient having acrophobia always to be 13.
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24 Oct 2016, 13:42
why is b insufficient ? 58-32 should give us the number of patients having acrophobia......
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17 Nov 2016, 12:28
Option B should be sufficient too. 45 - x = 32 leading to x = 13 which in turn the number of people with ACR and not ARA = 0. In conclusion the total number of people with ACR is equal to 13. The same number obtained with option A. Thus Option D should be correct. Plz Correct me if I am wrong.
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17 Nov 2016, 23:18
Diranims wrote:
Option B should be sufficient too. 45 - x = 32 leading to x = 13 which in turn the number of people with ACR and not ARA = 0. In conclusion the total number of people with ACR is equal to 13. The same number obtained with option A. Thus Option D should be correct. Plz Correct me if I am wrong.

Yes, that's wrong. We cannot deduce the red portion for the second statement.
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08 Jan 2017, 02:02
Hi Bunuel,
I am getting confused while trying to understand how the count for total acrophobia which as per your solution is equal to 58-45=13? I think the following should be the correct case:- Total number of patients - No Arachnophobia = Acrophobia+ Neither of the two.
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