For the math nerds (again)

[Sarcasm]

Got a totally BS question for you guys to try. Don't be surprised if you don't get the answer at all, but I'm curious to know if anyone manages to figure it out. I'll post the full solutions to this later.

[Drown]

Who cares about math, seriously?

[Matsy]

Maths....not even gonaa

 

[felixbearpig]

my guess is 16

[Youbetternot]

Maths....not even gonaa

 

 

No No No. This

[ilikemacandpc]

a & e are relatively prime and form parts of a geometric sequence? how?

Edit: I'm an idiot. See my solution below. 

 

I support mathematics. You need it to create all of this beautiful technology this forum loves. 

 

Edit: Got it. 36

 

Solution: 

 

If you look at the sequence of a,b,c,d,e, it is geometric as stated in the question. Thus, one must multiply by a common ration to get consecutive terms.  

 

If the ratio between the terms was an integer, the gcd ( a,e) cannot equal 1. They would be multiples of each other. 

 

Thus, the ratio must be a non-integer. 

 

Also, it must be less than 2.65, as (100/2)^1/4 ~ 2.65. 

 

Thus, I guessed the ratio would be in the form of (x/2), where x is some integer. 

 

Rewrite the sequence as a, ar, ar^2, ar^3, ar^4, you realize that the last term will be in the form of a*((x^4)/16))

 

a must be divisible by 16, and x should not be so large as for e to be greater than 100. Set a = 16.

 

I guess x=3 for the ratio to be 3/2.  Multiply by the common ratio twice. c=36. Ta-da. 

 

And, a and e share no common factors. Boom. 

 

The terms: 

a=16

b=24

c=36

d=54

e=81

 

edit 2: I did this myself. So no accusations of looking it up are allowed. 

 

edit 3: edited some things. 

[b1khoa]

what is gcd stand for?

[Sarcasm]

a & e are relatively prime and form parts of a geometric sequence? how?

It means the ratio isn't an integer. It's still possible.

[megadarkwood]

92

[Camul]

I have no idea how to even approach that question. 

[Canoas]

hmm.. ok.

 

either a or e is a prime number

e can't be a prime number because it's a geometric sequence

a x^4 < 100

 

a can be 2, 3, 5 and x must be 2, or e will be higher than 100

therefore c can be 8, 12 or 20

[Sarcasm]

hmm.. ok.

 

either a or e is a prime number

e can't be a prime number because it's a geometric sequence

a x^4 < 100

 

a can be 2, 3, 5 and x must be 2, or e will be higher than 100

therefore c can be 8, 12 or 20

Well I'll spoil the ending for you, e is the prime, not a. Just because it's a prime number doesn't mean it can't me made by multiplying a number by a ratio.

[AMICLG]

The answer is clearly "42".

[Canoas]

Well I'll spoil the ending for you, e is the prime, not a. Just because it's a prime number doesn't mean it can't me made by multiplying a number by a ratio.

hmm.. ok. I guess that works as well, so you can go backwards.

instead of it being

2 4 8 16 32 it is

32 16 8 4 2

but it's still irrelevant, because C is in the middle which means you can change "a b c d e" with "e d c a e" and the answer is the same.

 

c = 8, 12, 20

[Spannerhands]

The answer is clearly "42".

I was thinking the same thing lol...

[juretrn]

What does the notation gcd(a,e) mean?

And I thought I saw a lot of math while studying electrical engineering. 

[Sarcasm]

hmm.. ok. I guess that works as well, so you can go backwards.

instead of it being

2 4 8 16 32 it is

32 16 8 4 2

but it's still irrelevant, because C is in the middle which means you can change "a b c d e" with "e d c a e" and the answer is the same.

 

c = 8, 12, 20

None of those values are equal to C.

[Sarcasm]

What does the notation gcd(a,e) mean?

Greatest common divisor of the values (a,e)

[ilikemacandpc]

math is awesome. bring on the hate. 

[ilikemacandpc]

hmm.. ok.

 

either a or e is a prime number

e can't be a prime number because it's a geometric sequence

a x^4 < 100

 

a can be 2, 3, 5 and x must be 2, or e will be higher than 100

therefore c can be 8, 12 or 20

 

Yeah... no... It just means that a and e are relatively prime. If x is 2, then condition ii in the problem isn't satisfied. 

[Canoas]

None of those values are equal to C.

sorry, I don't why I decided that it has to start with 2. 2 is still divisible by 2 so the gcd with a multiple of 2 can never be 1.

 

1 2 4 8 16

1 3 9 27 81

and the opposite, since you just start at the top and divide instead of multiply

 

So 4 and 9

[Canoas]

Yeah... no... It just means that a and e are relatively prime. If x is 2, then condition ii in the problem isn't satisfied. 

Yeah, sorry, my bad. For some reason in my head 2 not being divisible by 2 made sense. I guess it's time to go to sleep.

[Sarcasm]

sorry, I don't why I decided that it has to start with 2. 2 is still divisible by 2 so the gcd with a multiple of 2 can never be 1.

 

1 2 4 8 16

1 3 9 27 81

and the opposite, since you just start at the top and divide instead of multiply

 

So 4 and 9

It never said it started at 2. It says the first number has to be equal to OR GREATER THAN 2.

[Canoas]

It never said it started at 2. It says the first number has to be equal to OR GREATER THAN 2.

Damn I'm stupid, now I forgot the first property

 

Wait..

they're all integers

between 2 and 100

E can't be divisible by A

a x^4 = e

 

I assumed that x was an integer, but it can't be, it's just not possible since e can't be divisible by a.

So I have to find an x that makes a even and e odd, or vice versa. 

a x^4 = e

x^4 = e/a

picking the easiest r to work with, since it can't be an integer, I'll go with 1.5 because I know even number times 1.5 can be both odd and even

 

a 1.5^4 = e

e/a = 1.5^4

a = 16

c = 36

e = 81

 

 

I'm sure there's a better way to this because I just picked 1.5 out of the blue, though it is the number that makes the most sense, so maybe there are other solutions. I'd need a relation between a, e and x that could find me all the possible solutions for x, but I'm sure this one is right.

[Sarcasm]

-snip-

Congratz. you managed to do it. I've seen one way to solve it in class that is pretty hard to explain, but here's the official solution