Six countries in a certain region sent a total of 75 representatives to a conference, and no two countries sent the same number of representatives. Of the six countries, if country A sent the second highest number of reps, did country A send at least 10 reps?
i) One of the six countries sent 41 reps.
ii) Country A sent fewer than 12 reps.
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Let the 6 countries be A, B, C, D, E and F.Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if country A sent the second highest number of representative, did country A send at least 10 representatives?
1. One of the six countries sent 41 representatives to the congress.
2. Country A sent fewer than 12 representatives to the congress.
The question stem asks whether A≥10.
Plug in A=10 (which satisfies statement 2 and is at least 10) and A=9 (which also satisfies statement 2 but is NOT at least 10).
To save time, let F=41, which satisfies statement 1.
Case 1: Total = 75, F=41, A=10.
Remaining representatives for B, C, D and E = 75-41-10 = 24.
The following combination works for B, C, D and E:
B=9
C=8
D=6
E=1.
Thus, it's possible that A=10.
Case 2: Total = 75, F=41, A=9.
Remaining representatives for B, C, D and E = 75-41-9 = 25.
The following combination works for B, C, D and E:
B=8
C=7
D=6
E=4.
Thus, it's possible that A<10.
Since it's possible that A=10 or that A<10, the two statements combined are INSUFFICIENT.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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