If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of

Question

If  a=\frac{13!^{16}-13!^8}{13!^8+13!^4}  what is the unit digit of  \frac{a}{13!^4} ?

A. 0 
B. 1
C. 9
D. 4
E. 6

gmat6nplus1 · Accepted Answer

\frac{(13!^1^6-13!^8)}{(13!^8+13!^4)}=\frac{(13!^8-13!^4)(13!^8+13!^4)}{(13!^8+13!^4)} . Cancel out the denominator of our fraction.

Now.  \frac{a}{13!^4}=13!^4-1 . Unit digit of  13!^4  will always be 0.  13!^4  will always be greater than 1 and will have a unit digit of 0 let's assume it's 10. Now 10-1=9 which is our unit digit.

shashankism · Answer

a= \frac{13!^1^6-13!^8}{13!^8+13!^4}  
 =\frac{13!^8(13!^8-1)}{(13!^4(13!^4+1)}  
 =\frac{13!^4(13!^4+1)(13!^4-1)}{(13!^4+1)}  
 =13!^4(13!^4-1)  
So,  \frac{a}{13!^4} = (13!^4-1)

13!^4  has unit's digit 0 
so  (13!^4-1)  has unit's digit = 10-1 =9

Answer C

Bunuel · Answer

Similar questions to practice: if-12-16-12-8-12-16-12-4-a-what-is-the-unit-s-digit-86818.html baker-s-dozen-128782-40.html#p1057520 Hope this helps.

shyind · Answer

After simplification, we have (13!)^4 - 1 = a/(13!)^4,

considering 13*12*11*10... 1, which has multiplier of 10, so the unit digit must end with 0 and if we subtract 1, the end digit will be 9.

Ans C)

law258 · Answer

Tricky little bugger.

Don't be fooled into thinking you need to multiply out the factorial. Nope.

1. Factor the equation & simplify 
 /  -->  /

2. We know a is going to be divided by 13!^4, so let's apply that to (1) as well
{ / }/(13!^4)

We're left with 13!^4 -1 --> We know 13! will leave us with units digit of 0 (won't change if it's raised to a power). We need to subtract the 1 off a multiple of 10 and we will arrive at our answer.

10-1 =  9

C.

NikGujju · Answer

In this problem... break the eqn into two solutions and you cancel the denominator.

13! is having 10 and hence, if 1 is subtracted from 13! we should be having 9 as a unit's digit.

felipehendrix · Answer

a=\frac{(13!^1^6- 13!^8)}{(13!^8+13!^4)}

As the numerator is a difference of squares we can re wite this as

a=\frac{(13!^8+13!^4)(13!^8-13!^4)}{(13!^8+13!^4)}

Then  \frac{a}{13!^4}  =  \frac{13!^4(13!^4-1)}{(13!^4)}

we know that 13! is 13*12*11*10*9... As it has a 10 in it, it will always end up with a unit digit of 0, even if we power it to 4. So, if we substract 1 to it we will get a unit digit of 9.

RastogiSarthak99 · Answer

Great question. I eventually arrived at this:

13!^4 - 1 which gives us 9 as the units digit considering 13!^4 ends with 0 due to 10 in the mix.

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If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of

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If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of

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