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PS-Tester--how to solve it?

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Director
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PS-Tester--how to solve it? [#permalink]

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New post 20 Feb 2009, 23:25
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A tester can pass a certain test only when all the three examiners pass him or her. A
total of 30 testers took the test. If examiner A passed 20 testers, B passed 17 testers,
and C passed 15 testers, at least how many testers passed the test?
A. 0
B. 2
C. 3
D. 5
E. 8
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Kudos [?]: 747 [0], given: 17

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Re: PS-Tester--how to solve it? [#permalink]

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New post 21 Feb 2009, 01:35
Hi nitya34,


Let testers be T1, T2, T3,......T15,......T29, T30

Now since we have to find out the minimum no. of testers who passed the test, we can assume that

1.) Examiner C passed first 15 testers i.e., T1, T2, T3,......T14, T15

2.) Now since Examiner B passed 17 testers, there have to be at least 2 testers who were passed by both examiner C & B.

Let Examiner B passed T14, T15, T16, T17,......,T29, T30

3.) Now here's the trap: Don't assume that since examiner B & C already got 2 testers in common, and as we know that examiner A passed 20 testers, we can conclude that at least 2 testers passed the test.

Though we can have the following scenario,
Total no. of testers passed by examiner A (20) ---> T11, T12, T13, T14, T15, T16, T17,......,T29, T30
Total no. of testers passed by examiner B (17) ---> T14, T15, T16, T17,......,T29, T30
Total no. of testers passed by examiner C (15) ---> T1, T2, T3,....T14, T15
where there are 2 common testers,


but we can also have the following scenario,
Total no. of testers passed by examiner A (20) ---> T1,T2,T3,.....,T8,T9,T10,T20,T21,T22,......,T28,T29,T30
Total no. of testers passed by examiner B (17) ---> T14, T15, T16, T17,......,T29, T30
Total no. of testers passed by examiner C (15) ---> T1, T2, T3,....T14, T15
where there are NO common testers.


So, my choice is 0 testers passed.

Hope that helps.


Regards,
Technext
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VP
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Re: PS-Tester--how to solve it? [#permalink]

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New post 21 Feb 2009, 08:41
Technext is right and I fell for the common 2 trap.

0 seems to be the right answer.

Kudos [?]: 437 [0], given: 1

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Location: New York
Re: PS-Tester--how to solve it? [#permalink]

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New post 21 Feb 2009, 11:30
nitya34 wrote:
A tester can pass a certain test only when all the three examiners pass him or her. A
total of 30 testers took the test. If examiner A passed 20 testers, B passed 17 testers,
and C passed 15 testers, at least how many testers passed the test?
A. 0
B. 2
C. 3
D. 5
E. 8



Least No. of Testers passed by both A and B = 20+17-30 = 7

Least No.of testers passed by (A and B) and C = 15+7 -30 < 0
So Answer should be A (0)
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Kudos [?]: 1060 [0], given: 5

Re: PS-Tester--how to solve it?   [#permalink] 21 Feb 2009, 11:30
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