Out of 100 dragons, every 6th dragon has glowing eyes, every 4th dragon shall...

[RLaicher]

Can someone help with this problem? The only way I figured it out was by doing a chart. Is there a "mathematical" way to solve this? Thank you!

Out of 100 dragons, every 6th dragon has glowing eyes, every 4th dragon shall breathe fire, every 3rd dragon shall billow clouds of smoke and every 8th dragon shall have a tail with spikes. How many dragons will have one characteristic, two characteristics, three characteristics, four characteristics?

 

[stapel]

Out of 100 dragons, every 6th dragon has glowing eyes, every 4th dragon shall breathe fire, every 3rd dragon shall billow clouds of smoke and every 8th dragon shall have a tail with spikes. How many dragons will have one characteristic, two characteristics, three characteristics, four characteristics?

Is there a "mathematical" way to solve this?

What topics have you recently covered in class? Does "Least Common Multiple" ring any bells?

 

[CALCULUS' GOD]

LCM based question

According to Question,
numbering of drangons :-
1. with glowing Eyes(G.E.)= 6th , 12th , 18th .......96. ( since,greatest multiple of 6 before 100 is 96).
2.Similarly, who can breathe fire(B.F.)= 4th , 8th, 12th...........100th.
3.Who shall clouds of smoke (C.S.)= 3rd, 6th ,................,99th.
4.Spikey Tail(S.T.)= 8th ,16th,................,96th.

Now,
the dragons having all four characteristics will be numbered after each interval of (24 i.e. L.C.M of 3,4,6,8) = 24th , 48th , 72nd and 96th =4 dragons (Ans.)
Now,
only two characteristics in the dragon can be:-
GE,CS = no. of dragons having these two only=numbers common to only 6 and 3 = 6,18,...........,90 =6*1 , 6*3 , .....6*15= 8 dragons
similarly,
ST,BF=8th,16th, 32nd,40th,...........80,88th.=8 dragons.
There is no other pair having only two characteristics common.
Therefore no. of dragons having two characteristics common =8+8=16 dragons
Now
No. of dragons having three characteristics common can be found similarly............:razz:

 

[John Harris]

The question's ambiguous, it depends on what "How many dragons will have one characteristic, two characteristics, three characteristics, four characteristics" means.

Is it at least one, two, three, four, or is it only one, two, three, four. The answers differ for one, two and three.

 

[trubuddy]

What I Believe

Can someone help with this problem? The only way I figured it out was by doing a chart. Is there a "mathematical" way to solve this? Thank you!

Out of 100 dragons, every 6th dragon has glowing eyes, every 4th dragon shall breathe fire, every 3rd dragon shall billow clouds of smoke and every 8th dragon shall have a tail with spikes. How many dragons will have one characteristic, two characteristics, three characteristics, four characteristics?

Bold = Same Dragon Number
Here are our variables:
G(glowing eyes)
F(fire)
S(smoke)
T(tail with spikes)

G= 6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96

F= 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,74,80,84,88,92,96,100

S= 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,71,74,77,80,83,86,89,92,95,98

T= 8,16,24,32,40,48,56,64,72,80,88,96

Multiples of eight are always multiples of four.
Multiples of six are always multiples of three.