Number Sense Marathon #6

[asquaredplusb]

(*) (363 x 59)^2 / (31 x 119)

7/12 - 27/49

124 x 142

555 x 6/37

[darksaber21]

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or


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[darksaber21]

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Use the double "loif" technique:

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Thus, the answer is 17608.

[darksaber21]

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Read or for more information.

[darksaber21]

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[MacNS]

1) 1^2 + 2^2 + 3^2 + 4^2 + ... 8^2 + 9^2 =
2) 563(base 8) / 7(base 8) (Is there a shorter way than converting to base 10 first and then reconverting back to base 8?)
3) 314.2 * (pi)^3 =

[darksaber21]

[redhawk2015]

What are the tricks for:

Dividing big numbers by nine?
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Adding series of squares?
Ex. [unparseable or potentially dangerous latex formula]

Adding series of Fibonacci squares?
Ex. [unparseable or potentially dangerous latex formula]

[sxk1693]

[asquaredplusb]

What is the general trick for problems like:

(x-5)/(x+4) + (x+4)/(x-5) is written as the mixed number A + B/C. B = ?

[101dalmatians]

[asquaredplusb]

7/11 - 69/111

Is there a general trick?

[qwerty123]

[101dalmatians]

READ PREVIOUS POSTS!!!!! +n/-n trick POST IS IMPORTANT!!!!!!!

[sxk1693]

[BlasianAsian]

A last minute question before districts...

I've always seen these, but never managed to figure out how to do them.

73) Find X, 0 (LESSTHANOREQUALTO) X (LESSTHAN) 7, if [(5!)(3!)]/(4!) (WIERDEQUALSIGN) x (mod 7).

Answer: 2

Many thanks.

[101dalmatians]

[101dalmatians]

[BlasianAsian]

Well, +9 points for me, even if the solution was pretty simple.

Thanks!

[asquaredplusb]

* 235689 / 111 = ___

1.5 x 1.6 x 2.4 = ___ (fraction)

7^8 / 9 has a remainder of ___

110 x 11/27 = ___ (mixed number)

[Fredfredburger]

[darksaber21]

[101dalmatians]

@asquaredplusb: If you read that +n/-n trick page, then you can like get so many more qs right on the NS test. Im not kidding. I didnt no that and I took so long on the third col. After learning that, it took me like 5 secs to do it getting me further on the test...

[BlasianAsian]

These might have been answered before, but I can't seem to find them with the search function. Oh well, here goes.

What is the sum of a right triangle's perimeter given one leg? I tried memorizing all the primary triplets below 100, but they STILL pop up a couple like "the smaller leg of a right triangle with integral sides is 23''". 23?! DX

Also, how do you find the sum of a fibonacci sequence? Now, before you start jumping me, I mean when they give you like the first 5 terms of a fibo sequence that doesn't start with 1 or 2, and they make you find the sum of the first ten. I know how to do it (go up 2 and subtract second number), but finding that 12th element in the sequence is quite the hassal. Anyone happen to know?

Thanks!

[rcoker7]

Usually, in the right triangle problems like that, you have to assume the sides are of the form y, x, x+1. It turns out that x+(x+1)=y^2 in this case, so the sum when y=23 is 23+529=552.

For the fibbonacci sequence, you don't need to go all the way to the 12th element. If the first element is a and the second is b, then the sums of the first 8,9,10, 11, and 12 are given by
first 8: 11(5th term)-a
first 9: 11(6th term)+a-b
first 10: 11(7th term)
first 11: 11(8th term)+a
first 12: 11(9th term)+a+b