Cybermusings wrote:6 countries in a certain region send a total of 75 representatives to the international congress and no two nations send the same number of representatives. Of the 6 nations, if Country A sent the second highest number of representatives did it send atleast 10 representatives.

1) One country sent 41 representatives

2) A sent less than 12 Representatives

OA after some replies

I am conjuring up...

A + B + C + D + E + F = 75 & A ≠ B ≠ C ≠ D ≠ E ≠ F. Also, A stands second in descending order. Is A ≥ 10?

(1) When one country, let's say it's B, sent 41 representatives, then A + C + D + E + F = 75 - 41 = 34. Here, keeping all constraints to mind, A could share less than, more than, or even equal to 10 representatives to become the second highest, because the sum of the remaining four distinct numbers could be more than, less than, or even equal to 24. Insufficient
(2) If A sent less than 12 representatives and is the second highest, then the topper must have sent 12 or more representatives. Very indecisive about A, because it could still be less than, more than, or even equal to 10 representatives to become the second highest. Insufficient

When taken together...

We have, A + C + D + E + F = 34 and A < 12, hence C + D + E + F > 22. The minimum contribution of C, D, E, and F could be 23, hence A cannot exceed 11, and [spoiler]that's all I could conclude about A.

E

Received a pm for this[/spoiler]

Total no. of countries = 6
Total no. of reps = 75
Country A : SECOND HIGHEST number of reps. Did it send ATLEAST 10 reps?

1) One country sent 41 reps. Now, this leaves 34 reps for the rest of the countries. Thus obviously this is the country with the highest number of reps.

Let us say country A sent 9 reps, this leaves 25 reps for the rest of the 4 countries. Their values cannot be more that 8+7+6+5 = 26. Since we only need them to account for 25, this will work. Any increase in the number of reps country A accounts for would only reduce the required number of reps from the rest of the 4, and thus would be allowable, to a minimum of 1+2+3+4 = 10 reps. Thus actually this is only telling us that the number of reps country A sent cannot be more than than 24, or less than 9. But it need not be ATLEAST 10.

INSUFFICIENT.

2) A sent less than 12 reps.

Let's see if A could have sent 9. The max value of the 4 countries after A is 8+7+6+5 = 26. This leaves 40 as the highest value of the country on top.

A = 11 also works fine, since highest one could have been 39 and the ones below A could have been the same 8,7,6,5.

INSUFFICIENT


Both 1 and 2

First one is 41. A is less than 12. Could A have sent 9? Yes we proved that in statement 1. And ofcourse it could send 10 too.

INSUFFICIENT.

Pick E.