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# When 100 mice were injected with a certain chemical, some de

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Manager
Joined: 08 Dec 2012
Posts: 61
Location: United Kingdom
WE: Engineering (Consulting)
When 100 mice were injected with a certain chemical, some de  [#permalink]

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Updated on: 16 Aug 2013, 14:18
3
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:23) correct 40% (01:18) wrong based on 181 sessions

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When 100 mice were injected with a certain chemical, some developed inflammation at the site of the injection and some developed the condition of nausea. How many of the mice developed inflammation but not nausea?

(1) 88 mice developed neither inflammation nor nausea.

(2) 2 mice developed nausea.

Not sure about the OA though, what about the option of 12 mice having inflammation with 2 having nausea as well? Would we have to assume there is no overlap when it is not explicitly stated?

Originally posted by nave on 11 Aug 2013, 11:03.
Last edited by nave on 16 Aug 2013, 14:18, edited 1 time in total.
Manager
Joined: 27 Feb 2012
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Re: When 100 mice were injected with a certain chemical, some de  [#permalink]

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11 Aug 2013, 11:51
nave81 wrote:
When 100 mice were injected with a certain chemical, some developed inflammation at the site of the injection and some developed the condition of nausea. How many of the mice developed inflammation but not nausea?

(1) 88 mice developed neither inflammation nor nausea.

(2) 2 mice developed nausea.

Should be C.
On Combining we wil have I not N.
Two by two matrix will get you there.
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Re: When 100 mice were injected with a certain chemical, some de  [#permalink]

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14 Apr 2015, 11:32
Assume :
Only Inflammation = I
Only Nausea = N
Both = B
None = 88
Total=100
1)
I+N+B=100-88=12................. Insufficient

2)
N+B=2 ........................ Insufficient

Combining 1 & 2 , I=10

nave wrote:
When 100 mice were injected with a certain chemical, some developed inflammation at the site of the injection and some developed the condition of nausea. How many of the mice developed inflammation but not nausea?

(1) 88 mice developed neither inflammation nor nausea.

(2) 2 mice developed nausea.

Not sure about the OA though, what about the option of 12 mice having inflammation with 2 having nausea as well? Would we have to assume there is no overlap when it is not explicitly stated?

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Joined: 17 May 2015
Posts: 14
Re: When 100 mice were injected with a certain chemical, some de  [#permalink]

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13 Jul 2015, 16:17
Hi all,

I'm getting E on this one. How do we know there is no overlap? Thanks!
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When 100 mice were injected with a certain chemical, some de  [#permalink]

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13 Jul 2015, 16:38
4
warnimont wrote:
Hi all,

I'm getting E on this one. How do we know there is no overlap? Thanks!

Even without the information about the overlap, we can calculate how many mice had inflammation with no nausea. Refer to the following solution.

The easiest way to solve this is by 2X2 matrix method (Attached Figure 1):

Figure 1 shows the given information. X= number of mice with inflammation but not nausea.

Per statement 1 (figure 2), We get x+y+88=100 but no other information and we have 2 variables with 1 equation ----> not sufficient.

Per statement 2 (figure 3), We get total nausea cases = 2 ----> Total 'not nausea' cases = 100-2 = 98, but without any other information, we wont be able to calculate x. Thus this statement is still insufficient.

Combining, we see x+88 = 98 ----> x =10. Thus combined , both statements are sufficient. Thus C is the correct answer.

I have also attached venn diagram approach for the same question (with a= inflammation only, b = inflammation and nausea, c =nausea only, d = neither inflammation nor nausea)

Hope this helps. Sometimes, DS questions give you values of lets say b+c instead of just b. But for us getting b+c is lot more beneficial to get the value of 'a'. Thus although it would look like it is not sufficient but on a deeper analysis of the question, it will become quite evident that you actually have all the information to answer the questions.
Attachments

Venn Diagram Approach.jpg [ 78.33 KiB | Viewed 1486 times ]

2X2 Matrix Approach.jpg [ 77.49 KiB | Viewed 1486 times ]

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Re: When 100 mice were injected with a certain chemical, some de  [#permalink]

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13 Jul 2015, 19:07
I see it now. Crystal clear. Thank you very much!
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Joined: 21 Mar 2014
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Re: When 100 mice were injected with a certain chemical, some de  [#permalink]

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07 Sep 2015, 14:48
can some one please explain this with a matrix table
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Re: When 100 mice were injected with a certain chemical, some de  [#permalink]

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07 Sep 2015, 14:54
saroshgilani wrote:
can some one please explain this with a matrix table

Refer to when-100-mice-were-injected-with-a-certain-chemical-some-de-157723.html#p1548774 , refer to 2nd attached figure that solves it by the matrix method.
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Re: When 100 mice were injected with a certain chemical, some de  [#permalink]

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26 Nov 2019, 23:50
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Re: When 100 mice were injected with a certain chemical, some de   [#permalink] 26 Nov 2019, 23:50
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