NuMbEr SeNsE QuEsTiOnS

[smeag]

21^3

If 5^-1 + x^-1 = 4^-1, then x =

7 (5/6) X 5 (5/6) =

Find the smallest integral value for k if k>0 and 442k1 is divisible by 11. k =

approximate: 721 x 4 1/11 / 9

55 x 7272

If A is 12% more than B and B is 13% more than C, then A is ____________% more than C

2^2 - 3^2 + 4^2 - 5^2 + ...-9^2

(123)base5 + (321)base5 / 6 has a remainder of

csc[Sin^-1(.4)]

If log2 = .3 and log3 = .5, then log72 =

[michel470]

#1. 21^3
Memorize your cubes up to 25, 30 if you're feeling prestigious

#2. If 5^-1 + x^-1 = 4^-1, then x =
Rewrite the problem as 1/5 + 1/x = 1/4, solve for x and take its reciprocal

#3. 7 (5/6) X 5 (5/6) =
Multiply the fractions(25/36, write it down) add the whole numbers(7+5=12) and multiply that sum by the fraction(12*(5/6)=10), that is your "carry". Multiply the whole numbers(7*5=35) and add your "carry"(35+10=45) Write it down. Answer: 45 25/36

#4. Find the smallest integral value for k if k>0 and 442k1 is divisible by 11. k =
To find the remainder when dividing by eleven, add every other number starting from the back(1+2+4=7), and every other number starting from the second to last(k+4). For the number to be divisible by eleven, these two sums must be equal: 7=k+4, so k=3.

#5. approximate: 721 x 4 1/11 / 9
Guesstimations are fun, figure them out yourself :)

#6. 55 x 7272= 5(11) * 72(101)= (5*72)(101*11)=(360)(1111)=399960

#7. If A is 12% more than B and B is 13% more than C, then A is ____________% more than C
"more" means the number itself and some...A=1.12B, B=1.13C A=(1.12*1.13)C(Use over a hundred's trick) =1.5625, since it asks for % more, remove the one so it becomes .5625, and convert into a percent= 56.25%

#8. 2^2 - 3^2 + 4^2 - 5^2 + ...-9^2
(n+1)th triangular number for alternating squares(the answer is either negative or positive depending on the sign of the last number, in this case, negative)...in this case, -1^2 is missing, so you must subtract a -1 from the answer, making it -44

#9. (123)base5 + (321)base5 / 6 has a remainder of
Use eleven's trick(for remainders, see #4) on each term. 123mod11=2 + 321mod11=2...2+2=4 and that's your answer. Applicable when the base is one less than the number you're dividing by

#10. csc[Sin^-1(.4)]
csc=1/sin so...take the reciprocal of .4

#11. If log2 = .3 and log3 = .5, then log72
Multiplying logs is equivalent to adding whatever they are equal to so...log72= 2log3 * 3log2 --> which is equivalent to 2(.5) + 3(.3) = 1.9

Let me know if there's any explanation I can make clearer