2010 Questions

[thatoneguy]

The sum of the positive integral divisors of 16 is?

The LCM of 72 and 96 is?

101101/14443 is?

How many integers less than 20 are relatively prime o 20?

11^5/15 has a remainder of?

How many ways can 5 people be seated 3 at a time in a row of 3 chairs?

1(1!) + 2(2!) + 3(3!)...+ 6(6!)= ?

If log base 16 of (4x) = 3/4 then x=?

480 miles/hour =__________feet/second?

F(x)= log(3x-2) has an asymptote at x=

160 acres is equivalent to ____miles?

The 6th hexagonal number is?

333*23.8*(5/14) approx.

The units digit of 8^8 is?

[nsguy1350]

For every prime to an exponent in the prime factorization, [unparseable or potentially dangerous latex formula] use the formula [unparseable or potentially dangerous latex formula], then multiply the results.

[unparseable or potentially dangerous latex formula], so [unparseable or potentially dangerous latex formula] You can see that 1 + 2 + 4 + 8 + 16 = 31.
Two tricks: Using the formula on [unparseable or potentially dangerous latex formula] yields p+1, and using the formula on [unparseable or potentially dangerous latex formula] = [unparseable or potentially dangerous latex formula].

LCM = Least Common Multiple. You can either recognize it, or use some type on method.
With experience, you can see that this is 72 x 4 or 96 x 3 = 288. Find something that divides both of the numbers, with the remaining factors relatively prime, and then multiply by the other factor. You can see that 24 goes into both, with 72 having 3 left over, while 96 have 4, and since 3 and 4 are relatively prime, multiply one by the other's remainder (96 x 3, 72 x 4).
101101/14443 = 7. That's like the 111/37 = 3, or the 1001/143 = 7 trick. Just know it.

Find the prime factorization, then take each base and take away the reciprocal times the number from it (hopefully my example clears it up.)
[unparseable or potentially dangerous latex formula]. Take away 1/2 and 1/5.
[unparseable or potentially dangerous latex formula]
Final answer = 8.

You mod the base by the number you are dividing by (mod meaning take the remainder of, like 7 mod 3 = 1, 8 mod 6 = 2, 123134 mod 5 = 4), leaving you with [unparseable or potentially dangerous latex formula], which is easier to handle. You could further reduce this in several ways, one of which is expanding [unparseable or potentially dangerous latex formula] to [unparseable or potentially dangerous latex formula]. You can mod that expression by 15, giving you [unparseable or potentially dangerous latex formula]

I believe this is [unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula].
7! - 1 = 5039.

If you know that [unparseable or potentially dangerous latex formula], you know that n = 8 (because 16^(3/4) = 8). Set 4x = 8, then solve for x = 2.

15mph = 22ft/s
480/15 = 32.
22ft/s x 32 = 704ft/s

Since log(0) in any base does not exist, set 3x-2 = 0, solve for x = 2/3.

1 mile = 640 acres, so 160 acres = .25 miles.

The formula for hexagonal numbers is [unparseable or potentially dangerous latex formula], so letting n = 6, you get 66.

I would treat 333 as 1000/3, then treat 23.8 as 24, then cancel out the 3 in 24 and the 3 in 1000/3 to produce 8000 x 5/14.
This becomes 40000/14, and I know that 42000/14 = 3000, so 40000/14 is a bit less (actually 2 6/7 x 1000), giving me approximately 2850.

You can mod the exponent by 4 to achieve an equivalent answer (notice how 3^0, 3^4, 2^5, 2^1, 7^2,7^6, etc. have the same units digits. All, besides 1,5,0,and 6, cycle in fours, while the 0,1,5,6 cycle in 1s.), giving you 8^0 = 1, so your units digit is 1.

Hopefully all of the above is correct!