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# Last year 4/5 of the applicants for a job on a police force passed the

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Math Expert
Joined: 02 Sep 2009
Posts: 56357
Last year 4/5 of the applicants for a job on a police force passed the  [#permalink]

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16 Dec 2014, 05:47
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:02) correct 29% (02:24) wrong based on 207 sessions

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Tough and Tricky questions: Overlapping Sets.

Last year 4/5 of the applicants for a job on a police force passed the physical examination. If 3/4 of the applicants who passed the physical examination also passed the written examination, how many of the applicants passed both examinations ?

(1) The number of applicants who did not pass either examination was equal to the number who passed the written examination only.
(2) There was a total of 100 applicants.

Kudos for a correct solution.

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Re: Last year 4/5 of the applicants for a job on a police force passed the  [#permalink]

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16 Dec 2014, 09:39
1. the number of applicants unknown.Insufficient

2, No. of applicants given . Sufficient

Ans B
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Re: Last year 4/5 of the applicants for a job on a police force passed the  [#permalink]

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16 Dec 2014, 12:05
1
Bunuel wrote:

Tough and Tricky questions: Overlapping Sets.

Last year 4/5 of the applicants for a job on a police force passed the physical examination. If 3/4 of the applicants who passed the physical examination also passed the written examination, how many of the applicants passed both examinations ?

(1) The number of applicants who did not pass either examination was equal to the number who passed the written examination only.
(2) There was a total of 100 applicants.

Kudos for a correct solution.

Total # of applicants: A
# of applicants passed Physical exam: P = 4/5 * A
# of applicants who passed the physical exam and written exam:X = 3/4P
= 3/4 (4/5* A)
= 3/5 * A

Statement 1: We can find the ratio but cannot find the # of applicants - Not Sufficient
Statement 2: By substituting 100 in the above equation we can get the answer - Sufficient

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Re: Last year 4/5 of the applicants for a job on a police force passed the  [#permalink]

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23 Dec 2014, 06:57
Bunuel wrote:

Tough and Tricky questions: Overlapping Sets.

Last year 4/5 of the applicants for a job on a police force passed the physical examination. If 3/4 of the applicants who passed the physical examination also passed the written examination, how many of the applicants passed both examinations ?

(1) The number of applicants who did not pass either examination was equal to the number who passed the written examination only.
(2) There was a total of 100 applicants.

Kudos for a correct solution.

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Re: Last year 4/5 of the applicants for a job on a police force passed the  [#permalink]

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23 Dec 2014, 07:03
took me 16 seconds to find the answer, hope it is a sign that i'm good at DS :D
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Re: Last year 4/5 of the applicants for a job on a police force passed the  [#permalink]

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23 Dec 2014, 08:56
60 passed both. DS:- B
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Joined: 11 Jan 2016
Posts: 4
Re: Last year 4/5 of the applicants for a job on a police force passed the  [#permalink]

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01 Mar 2017, 03:56
Bunuel wrote:
Bunuel wrote:

Tough and Tricky questions: Overlapping Sets.

Last year 4/5 of the applicants for a job on a police force passed the physical examination. If 3/4 of the applicants who passed the physical examination also passed the written examination, how many of the applicants passed both examinations ?

(1) The number of applicants who did not pass either examination was equal to the number who passed the written examination only.
(2) There was a total of 100 applicants.

Kudos for a correct solution.

Hi Bunuel, i am in difficulty with this kine of problems. When should i assume that Neither is = 0?
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Last year 4/5 of the applicants for a job on a police force passed the  [#permalink]

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08 Mar 2017, 21:58
1
ion wrote:
Bunuel wrote:
Bunuel wrote:

Tough and Tricky questions: Overlapping Sets.

Last year 4/5 of the applicants for a job on a police force passed the physical examination. If 3/4 of the applicants who passed the physical examination also passed the written examination, how many of the applicants passed both examinations ?

(1) The number of applicants who did not pass either examination was equal to the number who passed the written examination only.
(2) There was a total of 100 applicants.

Kudos for a correct solution.

Hi Bunuel, i am in difficulty with this kine of problems. When should i assume that Neither is = 0?

in this question it was simply asked about the no. of applicants who passed both the examinations that is equal to 60.
so no need to find neither and you can't assume neither equal to zero until or unless it is not specified in the question stem.

hope it helps
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Re: Last year 4/5 of the applicants for a job on a police force passed the  [#permalink]

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09 Mar 2018, 04:23
how many of the applicants passed both examinations ?

Whenever you face a .... both questions, remember to use the Venn Diagram:

Physical + Written - Both +Neither = Total .... which is actually the: N(A) + N(B) -N(A intersect B) +Neither = All

So ... 4/5 of All = physical examination.
And ... here is the trick! 3/4 of the applicants who passed the physical examination, also passed the written examination! This is equal to the BOTH . So if we have the total number of applicants, we also know the number of physical and consequently we do know the number of BOTH which is equal to 3/4 of the applicants who passed the physical examination. Hence (2) statement is sufficient and (1) is not sufficient. Thus it is B.
Re: Last year 4/5 of the applicants for a job on a police force passed the   [#permalink] 09 Mar 2018, 04:23
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