Gold Coins

[Aman verma]

Q: Ethan had some gold coins with him . He distributed all the gold coins to 20 boys who approached him one after another. The nth boy who approached him got n! gold coins from him . Find the unit's digit of the number of gold coins Ethan initially had.

a)0

b)1

c)2

d)3

e)4

[liferocks]

From 5!,unit digit of the gold coins received will be 0
So the unit's digit of the number of gold coins Ethan initially had digit is,unit's digit of
1!+2!+3!+4!=1+2+6+24 i.e 3

Ans option D

[gmatmachoman]

@LR, seems i should be a nocturnal bird to post one answer ahead of u!!

Its a good question...dealing with factorials..after a long time i saw this one over here.

Unit digits of the Sum of (1!+2!+3!......+19!+20!) needs to be figured out.

unit digits of 1!+2!+3!+4! end with 3 and the remaining numbers will have 0 as its unit digits.

Pick D

[Gmat Bond]

What's the OA ?

[Aman verma]

OAD.

[Thouraya]

I understood the solution (though it took me a while to get it :$), but how is the 5! edge supposed to occur to me? I mean now I understood this, but if in the exam, I get a number other than 20, then how am I supposed to approach this problem (thought process)?THANK YOU!

[kevincanspain]

I understood the solution (though it took me a while to get it :$), but how is the 5! edge supposed to occur to me? I mean now I understood this, but if in the exam, I get a number other than 20, then how am I supposed to approach this problem (thought process)?THANK YOU!

You look for a pattern: for any integer value of n > 4 n! is a multiple of 10

[Testluv]

I understood the solution (though it took me a while to get it :$), but how is the 5! edge supposed to occur to me? I mean now I understood this, but if in the exam, I get a number other than 20, then how am I supposed to approach this problem (thought process)?THANK YOU!

This question is testing your translation skills and your number property skills.

The nth boy receives n! coins, which just means (translates to) the 1st boy receives 1! coins, the 2nd boy receives 2! coins, etc.

Because the question asks about units digits begin figuring out the units digits of 1!, 2!, etc, and add them up as you figure them out. Because there are 20 boys, we need to figure out the units digit of (1! + 2! +....20!) as gmatmachoman points out.

After accounting for the units digits of 1!, 2!, 3!, 4!, when you get to 5!, notice that the units digit is 0 because you are multiplying by (among other numbers) 2*5 or 10.

At this point, you can notice that you will always be multipying by (among other numbers) 2*5, and so the units digit of 6!, 7!, etc will also just be 0. But even if you didn't, it is not necessarily fatal by any means, because you are more likely to see that at 6!, and then even more likely at 7!, etc. Or, at that point, even if you didn't see why the units digit was 0, you could also just trust in GMAT's pattern-based tendencies.