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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
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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21 Feb 2009, 01:35
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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
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
