Question

question 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?

Answer 1

(1) One of the six countries sent 41 representatives to the congress --> obviously x6=41x6=41 --> x1+x2+x3+x4+A=34x1+x2+x3+x4+A=34.

Given: x1<x2<x3<x4<A<x6x1<x2<x3<x4<A<x6 and x1+x2+x3+x4+A+x6=75x1+x2+x3+x4+A+x6=75. Q: is A≥10A≥10

Can A≥10A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11 --> sum=34sum=34 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9 --> sum=34sum=34 (answer to the question NO).

(2) Country A sent fewer than 12 representatives to the congress --> A<12A<12.

The same breakdown works here as well:

Can 12>A≥1012>A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11, x6=41x6=41 --> sum=75sum=75 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9, x6=41x6=41 --> sum=75sum=75 (answer to the question NO).

(1)+(2) The given examples fit in both statements and A in one is more than 10 and in another less than 10. Not sufficient.