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by akashrg » Sat Jun 14, 2008 10:10 am
Coach Jackson will choose at least two players for his team from those who tryout on Saturday. How many players will Coach Jackson choose?

(1) Coach Jackson could choose exactly 20 different teams.

(2) At least two players at the tryout will not be chosen.

A Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

B Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D EACH statement ALONE is sufficient.

E Statements (1) and (2) TOGETHER are NOT sufficient.



OA is C
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Source: — Data Sufficiency |
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by anshul265 » Sat Jun 14, 2008 11:21 am
i) It is not possible to determine the number of players he chose by knowing how many ways he can. There can be a number of situations/conditions with different possible answers. INSUFFICIENT.

ii) 2 will not be selected. We don't know the total number of players so can't determine the number of players chosen. INSUFFICIENT.

Together, we know atleast 2 will be picked and 2 will be left. So there are atleast 4 players who are trying out. Condition 1 says, the total number of ways he can choose is 20.

Let the total number of players trying out be n. So n>=4.

The total number of ways should be nC2+nC3+...+nC(n-2) = 20.
The combinations start at 2 as minimum 2 will be selected and end at n-2 as exactly 2 will be left.

Now we can put the values and see.
For n=4, it will be 4C2=6. (It is not 20 so case not possible)
Next, for n=5, 5C2+5C3=10+10=20. So we have found n which is 5. Now we know that the number of players chosen is 3.

Hence answer is C.
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