pinklemonade

2 gallons per 70 minutes = 2/70

reduces down to 1/35

35 miles per gallon

Thank you so much! I get it now. 

I am taking it too! I know there are some very helpful prep classes over on AoPS online. They cover all the topics, and I personally took one just last weekend. I also reccommend going through the problems from past years within the designated time period. 

Best of luck to you!

there's introduction to number theory by aops! i heard it's really helpful :)

thank you!

happyredpanda! :)

you should round to the nearest one for all of the decimals, then multiply them. the estimate should be within the same zone as the real answer. see ElectricPavlov's example for more info. 

let's make a key:

Julio's age = x

Julio's father's age = 4x

the sum of their ages is no less than 55, so it's equal or more than 55. we have this inequality:

4x+x > 55

5x>55

x>11

so the youngest Julio can be is 11 years old. 

:)

there are plenty! as long as it's not an imaginary number such as i (i^2=-1). it's not real!

some examples are 1.71, 1.711, 1.74528, and 1.73

:)

first 20 digits: 73897156067403508131

last 20: 33408341373887572343

please correct me if i'm wrong :)

It has to start on 5 and then go to 0, or else not all of the numbers will go in the knight move pattern. 

We have 5034927618 and 5038167294, plus their opposites (the same number backwards). So only 4 numbers can be formed. 

Please correct me if I am wrong! 

31.54 should be correct... 

first, let's change everything to a common denominator so it's easier to add:

3/14=6/28

1/7=4/28

1/28=1/28

3/28=3/28

so we have 6/28+4/28+1/28+3/28=14/28=1/2

so the other 1/2 is used for toilet flushing!