Author Topic: Logical mathematical reasoning/Razonamiento lógico matemático. x4  (Read 2981 times)

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Offline AdrenalineXV

Pedro boasts that it is still young. If divides his age by 2,3,4,5 or 6 the remainder is 1. What is the age of Pedro?   Regards
A) 41
(B) 51
(C) 61
(D) 71


Pedro presume que es todavía joven. Si se divide su edad 2,3,4,5 o 6 el resto es 1. ¿Cuál es la edad de Pedro?   Saludos cordiales.
A) 41
(B) 51
(C) 61
(D) 71


Offline [MAF]mooman

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Re: Logical mathematical reasoning/Razonamiento lógico matemático. x4
« Reply #1 on: April 06, 2015, 12:35:45 am »
I don't know if there's some smart way to calculate it but the answer is 61.
will read and answer your forum PMs when I'm less busy!

Offline AdrenalineXV

Re: Logical mathematical reasoning/Razonamiento lógico matemático. x4
« Reply #2 on: April 06, 2015, 12:43:01 am »
I don't know if there's some smart way to calculate it but the answer is 61.
mooman, explain your answer, please.

Offline [MAF]Agus

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Re: Logical mathematical reasoning/Razonamiento lógico matemático. x4
« Reply #3 on: April 06, 2015, 03:00:02 am »
X = [least common multiple (mínimo común múltiplo en español) of 2, 3, 4, 5 and 6] +1

Prime factorization
2 = 2
3 = 3
4 = 2^2
5 = 5
6 = 3 x 2

LCM (MCM) = 5 x 3 x 2^2 = 60

X = 60 + 1
X = 61

Offline AdrenalineXV

Re: Logical mathematical reasoning/Razonamiento lógico matemático. x4
« Reply #4 on: April 06, 2015, 03:28:19 am »
X = [least common multiple (mínimo común múltiplo en español) of 2, 3, 4, 5 and 6] +1

Prime factorization
2 = 2
3 = 3
4 = 2^2
5 = 5
6 = 3 x 2

LCM (MCM) = 5 x 3 x 2^2 = 60

X = 60 + 1
X = 61

It can also be done by 60/2, 60/3, 60/4, 60/5, 60/6 plus 1 I think
Although I do not understand what you mean with the LCM explanation. Regards

Offline [MAF]Agus

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Re: Logical mathematical reasoning/Razonamiento lógico matemático. x4
« Reply #5 on: April 06, 2015, 03:49:34 am »
Not really, using 60 from the start would just be the demonstration, but if you had no options and couldn't be able to make trial and error the way I did it gives you the right number. Adding the numbers you said gives you more than 60.

http://es.wikipedia.org/wiki/M%C3%ADnimo_com%C3%BAn_m%C3%BAltiplo


Offline AdrenalineXV

Re: Logical mathematical reasoning/Razonamiento lógico matemático. x4
« Reply #6 on: April 06, 2015, 04:59:27 am »
Not really, using 60 from the start would just be the demonstration, but if you had no options and couldn't be able to make trial and error the way I did it gives you the right number. Adding the numbers you said gives you more than 60.

http://es.wikipedia.org/wiki/M%C3%ADnimo_com%C3%BAn_m%C3%BAltiplo

So if it says: Pedro boasts that it is still young. If divides his age by 12, 15, 20, or 30 the remainder is 11. What is the age of Pedro?

X=LCM of [12, 15, 20, 30] + 11
12 = 2 ^ 2 * 3
15 = 3 * 5
20 = 2 ^ 2 *5
30 = 2*2*5

We take the factors with the biggest exponent, so: 2 ^ 2 * 3 * 5 = 60 -> 60 + 11 = 71.

Why do we take the LCM and not the GCD? Because of the reminder, Wikipedia says: http://en.wikipedia.org/wiki/Greatest_common_divisor

Thank you  Agus, I have got some other doubts to solve.
Regards.

Offline [MAF]Agus

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Re: Logical mathematical reasoning/Razonamiento lógico matemático. x4
« Reply #7 on: April 06, 2015, 03:37:40 pm »
Exactly, in your case it'd be 71.

And I'm not sure how to explain the reason why you use LCM instead of GCD :L

In this case it also has a bit of common sense, because if you had used GCD in the original problem, his age would be 2 because the GCD of those numbers is 1, and it already says that his age can be divided by 2, 3, 4, 5 and 6, and have a reminder of 1, so it wouldn't make sense

Offline nero

Re: Logical mathematical reasoning/Razonamiento lógico matemático. x4
« Reply #8 on: April 06, 2015, 06:16:01 pm »
Stop doing this kids homework guys...  :police: