GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Sep 2018, 17:39

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Oct 2013
Posts: 173
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)
If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of  [#permalink]

### Show Tags

Updated on: 29 Dec 2013, 04:16
11
00:00

Difficulty:

65% (hard)

Question Stats:

58% (01:36) correct 42% (01:22) wrong based on 352 sessions

### HideShow timer Statistics

If $$a=\frac{13!^1^6-13!^8}{13!^8+13!^4}$$ what is the unit digit of $$\frac{a}{13!^4}$$?

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

_________________

learn the rules of the game, then play better than anyone else.

Originally posted by gmat6nplus1 on 29 Dec 2013, 04:09.
Last edited by Bunuel on 29 Dec 2013, 04:16, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 04 Oct 2013
Posts: 173
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)

### Show Tags

29 Dec 2013, 04:10
4
5
$$\frac{(13!^1^6-13!^8)}{(13!^8+13!^4)}=\frac{(13!^8-13!^4)(13!^8+13!^4)}{(13!^8+13!^4)}$$. 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.
_________________

learn the rules of the game, then play better than anyone else.

##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 49271
Re: If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of  [#permalink]

### Show Tags

29 Dec 2013, 04:18
1
1
gmat6nplus1 wrote:
If $$a=\frac{13!^1^6-13!^8}{13!^8+13!^4}$$ what is the unit digit of $$\frac{a}{13!^4}$$?

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

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.
_________________
Manager
Joined: 26 Nov 2014
Posts: 95
Re: If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of  [#permalink]

### Show Tags

01 Aug 2015, 12:55
1
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)
Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 390
Re: If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of  [#permalink]

### Show Tags

17 Nov 2016, 15:08
1
Tricky little bugger.

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

1. Factor the equation & simplify
[(13!^8)(13!^8 -1)]/[(13!^4)(13!^4 +1)] --> [(13!^4)(13!^8 -1)]/[(13!^4 +1)]

2. We know a is going to be divided by 13!^4, so let's apply that to (1) as well
{[(13!^4)(13!^8 -1)]/[(13!^4 +1)]}/(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.
Director
Joined: 13 Mar 2017
Posts: 619
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of  [#permalink]

### Show Tags

23 Jun 2017, 00:03
gmat6nplus1 wrote:
If $$a=\frac{13!^1^6-13!^8}{13!^8+13!^4}$$ what is the unit digit of $$\frac{a}{13!^4}$$?

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

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

_________________

CAT 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Manager
Status: Target 760
Joined: 20 Aug 2014
Posts: 58
Location: India
Concentration: Strategy, Economics
GMAT 1: 670 Q50 V30
GPA: 3.25
WE: Corporate Finance (Investment Banking)
Re: If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of  [#permalink]

### Show Tags

26 Dec 2017, 12:02
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.
Re: If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of &nbs [#permalink] 26 Dec 2017, 12:02
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.