Six countries in a certain region sent a total of 75

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AAPL: Moderator; Posts: 2685; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Wed Nov 21, 2018 5:21 am

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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 greatest number of representatives, 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.

OA E.

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Source: Beat The GMAT — Data Sufficiency | Wed Nov 21, 2018 5:21 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Nov 21, 2018 9:30 am

AAPL wrote:GMAT Prep

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 greatest number of representatives, 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.

Let the 6 countries be A, B, C, D, E and F.

The question stem asks whether Aâ‰¥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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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Wed Nov 21, 2018 10:44 pm

AAPL wrote:GMAT Prep

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 greatest number of representatives, 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.

OA E.

Given:

> Total number of reps from 6 countries = 75;
> Country A sent the second greatest number of reps

Question: Did Country A send at least 10 reps?

Let's take each statement one by one.

(1) One of the six countries sent 41 representatives to the Congress.

Since 41 > 75/2, the country, which sent 41 reps, must be the country that sent the greatest number of reps.

Case 1: Say Country A sent 10 reps, thus, the remaining 4 countries, together would have sent 75 - 41 - 10 = 24 reps. This is possible, for example, the four countries sent 9, 8, 6 and 1 reps, respectively. The answer is Yes.

Case 2: Say Country A sent 9 reps, thus, the remaining 4 countries, together would have sent 75 - 41 - 9 = 25 reps. This is possible, for example, the four countries sent 8, 7, 6 and 4 reps, respectively. The answer is No.

No unique answer. Insufficient.

(2) Country A sent fewer than 12 representatives to the Congress.

Both the cases discussed above are applicable here too. So, even combining the two statements will not suffice. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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