2 practice questions off the AMC!! (1 Viewer)

[lookoutastroboy]

HEY GUYS,

i need help solving these two problems and if you could supply ur answers and solutions to each one, that'd be greatly appreciated.

9. What is the maximum size of a subset,​

P, of {1, 2, 3, . . . , 50} with the property that no pair of distinct elements of P​

has a sum divisible by 7?
(A) 21 (B) 22 (C) 23 (D) 24 (E) 25
​

10.​

How many three-digit numbers from 100 to 999 inclusive
have one digit which is the average of the other two?​

(A) 121 (B) 117 (C) 112 (D) 115 (E) 105

Thanks in advance, lookoutastroboy
(P.S. if you could tell me the specific mathematical methods to approach each question, that'd also be another great help!!! )
(Side note: I've also posted the 2 same questions above in the Maths Extension 1 forums)

 

[Affinity]

9. C group the numbers according to remainders
10. A , use case bashing

 

[lookoutastroboy]

9. C group the numbers according to remainders
10. A , use case bashing

hey affinity, thanks for your input to the question,
could you please explain what case bashing is?

 

[Affinity]

The most primitive way of doing things.. list all the possibilities methodically

 

[nerdsforever]

The most primitive way of doing things.. list all the possibilities methodically

lol good point