I want to test your intelligence in mathematics?

Question

3^n +3^n +3^n
hint:note that the answer is not 3^3n since the symbol is not multiplication but addition

without using a calculator,evaluate
(10+20+30+............+100) / (20+40+60+.............+400)

Answer 1

3^n +3^n +3^n = 3^n(1+1+1) =3*3^n = 3^(n+1)

(10+20+30+............+100) / (20+40+60+.............+400)
The sum of the numerator = 10/2(20+100) = 600
The sum of the denominator = 20/2(20 +400) = 4200
so quotient = 600/4200 = 1/7

Answer 2

3^n + 3^n + 3^n = 3 * 3^n = 3^(n+1)

(10 + 20 + ..100) = 10*(1..10)
(20 + 40 + 60 + ...400) = 20*(1..10) + (200 +20*(1..10))

Divide everything by 10. 1..10 = 55 (10*11/2)

55/(2*55 + 200 + 2*55) = 55/(110+200+110) = 55/420 = 11/84

I suspect you copied the question in here wrong.

Had you asked (10 + 20 + ...100)/(20 + 40 + 60 + ...200) then the answer would by inspection be 1/2.

Answer 3

3^n +3^n +3^n = 3(3^n) = 3^(n+1)

(10+20+30+............+100) / (20+40+60+.............+400)
= 10(1+2+3+...+10) / {20(1+2+3+...+20)}
= 55 / {2*210} = 55/420 = 11/84

Answer 4

This is a pretty lame intelligence test and by what right do you test us anyhow?
At any rate, the first expression is 3(3^n) which is 3^(n+1)
The second question is a little more interesting. To do it without a calculator, you;d either have to be very patient and accurate to do it by hand (not a math problem, only an arithmetic problem) or you'd have to be one of those rare savant folks who can do extensive mental arithmetic. (I could do this when I was a kid, but outgrew it) Or you'd use the formula for sum of an arithmetic series, twice, and simplify the quotient. This might marginaly qualify for a question on a test of intelligence in mathematics, but a single question is hardly a test...
Ok, let's do it that way...
The sum of the natural numbers 1 thru n is n(n+1)/2
So your expression simplifies to (10(sum of the natural numbers 1 thru 10))/(20(sum of the natural numbers 1 thru 20)) =
1/2(sum of the natural numbers 1 thru 10)/(sum of the natural numbers 1 thru 20) =
(1x10x11/2)/(2x20x21/2)= 55/(2x210) which reduces to 11/84
And I did this without a calculator!
But you'll probalbly never see this because you're probalby the one who gave me a thumbs down for saying that this is a lame "test of intelligence."

Answer 5

3^n + 3^n + 3^n = 3*3^n = 3^(n + 1)

(10 + 20 + ... + 100) / (20 + 40 + ... + 400) ?

did you mean: (10 + 20 + ... + 100) / (20 + 40 + ... + 200) ?

Answer 6

(1) 3^(n+1)

(2) (110 * 5) / (420 * 10) = 11 / 84.

Answer 7

800

1600

Answer 8

3^(n+1)

55/420

Answer 9

5*110/10*420=110/2*420=55/420=11/84

3*3^n=3^(n+1)

Answer 10

=3(3^n)=3^(3+n)=27 *3^n___second one=11/21