It is currently 17 Oct 2017, 10:33

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the units digit of 6^15 - 7^4 - 9^3?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 11 Feb 2011
Posts: 129

Kudos [?]: 248 [2], given: 21

What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

23 Jul 2011, 01:56
2
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

62% (00:45) correct 38% (00:48) wrong based on 357 sessions

### HideShow timer Statistics

What is the units digit of 6^15 - 7^4 - 9^3?

A) 8
B) 7
C) 6
D) 5
E) 4
[Reveal] Spoiler: OA

_________________

target:-810 out of 800!

Kudos [?]: 248 [2], given: 21

SVP
Joined: 16 Nov 2010
Posts: 1599

Kudos [?]: 592 [1], given: 36

Location: United States (IN)
Concentration: Strategy, Technology

### Show Tags

23 Jul 2011, 02:02
1
KUDOS
The unit's digit of 6^15 = 6
The unit's digit of 7^4 = 1
The unit's digit of 9^3 = 9

So the The unit's digit of product = 6 - 1 - 9

.........6
........10
-------------
6

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 592 [1], given: 36

Manager
Joined: 11 Feb 2011
Posts: 129

Kudos [?]: 248 [0], given: 21

### Show Tags

23 Jul 2011, 02:50
@Subhash : Can you pls brief a bit .
_________________

target:-810 out of 800!

Kudos [?]: 248 [0], given: 21

SVP
Joined: 16 Nov 2010
Posts: 1599

Kudos [?]: 592 [0], given: 36

Location: United States (IN)
Concentration: Strategy, Technology

### Show Tags

23 Jul 2011, 02:56
AnkitK wrote:
@Subhash : Can you pls brief a bit .

What I've done here is - take the unit's digit of all the individual numbers into consideration because the unit's digit of the sum of the digits will be decided ultimately by the unit's digit of all the individual numbers.

Thereafter, if you see the expression, I've grouped together positive and negative numbers.

6^15 is a very big number and much > 7^4 + 9^3.

So you need to visualize it as (xxxx6 - 10), and 6 can borrow 1 easily from left side because it's very big number.

HTH.

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 592 [0], given: 36

Senior Manager
Joined: 03 Mar 2010
Posts: 422

Kudos [?]: 360 [0], given: 22

Schools: Simon '16 (M)

### Show Tags

23 Jul 2011, 05:42
As subhashgosh did, let me just add visual to it.
Interesting to see that 6^15 is large number something like XXXXXXXX6
7^4 = 2401
9^3 = 729
Now subtract
XXXXXXXX6
- 2401
--------------------------
xxxxxxxxxx5

xxxxxxxxxx5
- 729
--------------------------
xxxxxxxxxxx6

Unit digit = 6

OA C.
_________________

My dad once said to me: Son, nothing succeeds like success.

Kudos [?]: 360 [0], given: 22

Senior Manager
Joined: 11 Apr 2011
Posts: 264

Kudos [?]: 658 [0], given: 13

### Show Tags

23 Jul 2011, 14:14
1
This post was
BOOKMARKED

6^15 will always result in a unit digit of 6.

unit digit of 7^4 = 7*7 = 49. 7*9 = 63. 7*3=21---> Unit digit of 21 = 1.

Unit digit of 9^3 = 9*9 = 81. 9*1 = 9 --->unit digit of 9 is 9.

6-1 = 5. 5 - 9 = 4----> THIS IS WRONG. because remember, when subtracting a bigger number from a smaller number, you add 10 to the smaller number.

In this case, you add 10 to 5, which gives us 15. 15 - 9 = 6.
_________________

Powerscore CR Bible Full Chapter Notes | Easily Extend Vocabulary List with Google Dictionary

Please kudo me if you found my post useful. Thanks!!!

Kudos [?]: 658 [0], given: 13

Moderator
Joined: 01 Sep 2010
Posts: 3355

Kudos [?]: 9041 [0], given: 1152

What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

19 May 2012, 18:04
1
This post was
BOOKMARKED
What is the units digit of 6^15 - 7^4 - 9^3?

A. 8
B. 7
C. 6
D. 5
E. 4
_________________

Last edited by carcass on 20 May 2012, 07:53, edited 1 time in total.

Kudos [?]: 9041 [0], given: 1152

Intern
Joined: 28 Feb 2012
Posts: 26

Kudos [?]: 46 [0], given: 1

Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

19 May 2012, 19:36

Unit digit of 6^15 is 6.
Unit digit of 7^4 is 1.
Unit digit of 9^3 is 9.

Now question is xxx6 - xx1- xx9 = 16 - 10 = 6

Kudos [?]: 46 [0], given: 1

Senior Manager
Joined: 30 Jun 2011
Posts: 267

Kudos [?]: 88 [0], given: 20

Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

20 May 2012, 00:15
yes it is C, same method - cyclic unit digits

Kudos [?]: 88 [0], given: 20

Moderator
Joined: 01 Sep 2010
Posts: 3355

Kudos [?]: 9041 [0], given: 1152

Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

20 May 2012, 07:55
Yup

OA is C

Even though the tricky part is if you assume that 6-1 is -4 so you take the positive value of 4 and then pick E
_________________

Kudos [?]: 9041 [0], given: 1152

Intern
Joined: 16 Apr 2012
Posts: 4

Kudos [?]: [0], given: 1

GMAT Date: 06-01-2012
Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

21 May 2012, 18:04
Where am I going wrong...I don't understand the step of 16-10.

I went with 6-1-9, which arrived at (-4), so picked E because closest thing to the answer. I know, dumb reason but still, 16-10? what am I missing?

Kudos [?]: [0], given: 1

Current Student
Joined: 21 May 2012
Posts: 97

Kudos [?]: 42 [0], given: 0

Location: United States (CA)
Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

21 May 2012, 18:37
mantazuma wrote:
Where am I going wrong...I don't understand the step of 16-10.

I went with 6-1-9, which arrived at (-4), so picked E because closest thing to the answer. I know, dumb reason but still, 16-10? what am I missing?

Think about it like you're using elementary subtraction and subtracting these.

xxxxxxxx6
xxxxxxxx1
- xxxxxxxx9
__________

After subtracting the first 2 numbers, subtract again:
xxxxxxx5 (result of 6-1)
- xxxxxxx9
__________
xxxxxx6 (result of 5-9)

Not the prettiest but does the job.

Kudos [?]: 42 [0], given: 0

Intern
Joined: 15 May 2012
Posts: 2

Kudos [?]: [0], given: 1

Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

21 May 2012, 19:56
I'm sorry..but I am still not getting it...how did you get 16? I understood the -10..but not 16

Kudos [?]: [0], given: 1

Intern
Joined: 28 Feb 2012
Posts: 26

Kudos [?]: 46 [1], given: 1

Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

21 May 2012, 20:12
1
KUDOS
Ok Let me try to explain this.

If you need to subtract 7 from 234 then as you know 7 is greater than 4 so you will take one carry from 10th place integer and you will subtract 7 from 14 to get 7. So result of this subtraction is 227.

Same way we know the last digit of the expression is 6 but this less than 10 so we have take carry from 10th place. So it becomes 16.

Kudos [?]: 46 [1], given: 1

Senior Manager
Joined: 30 Jun 2011
Posts: 267

Kudos [?]: 88 [0], given: 20

Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

22 May 2012, 01:43
1
This post was
BOOKMARKED
neetutiwari wrote:
I'm sorry..but I am still not getting it...how did you get 16? I understood the -10..but not 16

see below multiplicity table

4n+1 4n+2 4n+3 4n
1 1 1 1
2 4 8 6
3 9 9 1
4 6 4 6
5 5 5 5
6 6 6 6
7 9 3 1
8 4 2 6
9 1 9 1

All numbers from 1-9 repeat their units digit after a cycle of 4. i.e. 3^2 will have same units digit as 3^6 and form above table we see that 9 would be that digit.

Similarly,
6^15 will have units digit=6
7^4 will have units digit=1
9^3 will have units digit=9

So 6 - 1 - 9 = -4 (+10 from borrow) = 6

Kudos [?]: 88 [0], given: 20

Moderator
Joined: 01 Sep 2010
Posts: 3355

Kudos [?]: 9041 [0], given: 1152

Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

22 May 2012, 04:36
1
This post was
BOOKMARKED
also you can see in this way:

6-9 = -4 but our six is a number in our equation that end with unit digit 5 infact to obtain the number of our answer choices subtracting 9 we have a number that must with unit digit of 5

A) 8 -> to get 8 you have 17 - 9= 8 but unit digit is 7 wrong

B) 7 -> 16-9 = 7 but unit digit is 6

C) 6 -> 15-9= 6
_________________

Kudos [?]: 9041 [0], given: 1152

Current Student
Joined: 06 Sep 2013
Posts: 1980

Kudos [?]: 719 [0], given: 355

Concentration: Finance
Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

22 Nov 2013, 11:01
AnkitK wrote:
What is the units digit of 6^15 - 7^4 - 9^3?

A) 8
B) 7
C) 6
D) 5
E) 4

6-1-9 = -4. Bottow 10
Units digit is then 6.

Hope it helps
Cheers!
J

Kudos [?]: 719 [0], given: 355

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2616 [1], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

26 Feb 2014, 01:57
1
KUDOS
1
This post was
BOOKMARKED
6^15 - 7^4 - 9^3

Rewrite as 6^15 - (7^4 + 9^3 )

6^15 would give units digit as 6

7^4 would give units digit as 1

9^3 would give units digit as 9

(7^4 + 9^3 ) gives 9+1 = 10 so 0 is the units digit

6^15 - (7^4 + 9^3 ) gives 6-0 = 6 as the units digit

_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2616 [1], given: 193

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16764

Kudos [?]: 273 [0], given: 0

Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

21 Jun 2015, 23:02
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16764

Kudos [?]: 273 [0], given: 0

Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]

### Show Tags

19 Sep 2016, 17:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Re: What is the units digit of 6^15 - 7^4 - 9^3?   [#permalink] 19 Sep 2016, 17:40
Display posts from previous: Sort by