AdrenalineX Forums
General => Off-Topic => Topic started by: AdrenalineXV on April 06, 2015, 12:19:02 am
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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
(http://www.ultraimg.com/images/XC6zB.gif)
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I don't know if there's some smart way to calculate it but the answer is 61.
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I don't know if there's some smart way to calculate it but the answer is 61.
mooman, explain your answer, please.
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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
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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
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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
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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 (http://en.wikipedia.org/wiki/Greatest_common_divisor)
Thank you Agus, I have got some other doubts to solve.
Regards.
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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
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Stop doing this kids homework guys... :police: