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

 It is currently 15 Dec 2019, 21:44 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # What is the units digit of 9^19 - 7^15?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59730
What is the units digit of 9^19 - 7^15?  [#permalink]

### Show Tags 00:00

Difficulty:   25% (medium)

Question Stats: 75% (01:01) correct 25% (01:24) wrong based on 77 sessions

### HideShow timer Statistics

Competition Mode Question

What is the units digit of $$9^{19} - 7^{15}$$?

A. 2
B. 4
C. 5
D. 6
E. 7

_________________
Intern  B
Joined: 10 Jul 2018
Posts: 5
Re: What is the units digit of 9^19 - 7^15?  [#permalink]

### Show Tags

Cyclic order of 9 raised to the power is [1,9]

Cyclic order of 9 raised to the power is [9,3,1,7]

So, the difference of the said expression is 2

Posted from my mobile device
Director  P
Joined: 18 May 2019
Posts: 557
Re: What is the units digit of 9^19 - 7^15?  [#permalink]

### Show Tags

1
9^19 - 7^15

9^1 = 9 unit digit = 9
9^2 = 81 unit digit = 1
9^3 = 729 unit digit = 9
9^4= 6561 unit digit = 1
hence cyclisity of the powers of 9 is 2

7^1= 7 unit digit =7
7^2= 49 unit digit =9
7^3= 343 unit digit =3
7^4= 2401 unit digit =1
7^5=16807 unit digit =7
hence cyclisity of the powers of 7 is 4

9^19 - 7^15 = (9^18)*9 - (7^12)*7^3
=1*9 - 1*3 = 9-3 =6

Hence D.
Senior Manager  P
Joined: 07 Mar 2019
Posts: 462
Location: India
GMAT 1: 580 Q43 V27 WE: Sales (Energy and Utilities)
Re: What is the units digit of 9^19 - 7^15?  [#permalink]

### Show Tags

1
What is the units digit of $$9^{19}−7^{15}$$?

A. 2
B. 4
C. 5
D. 6
E. 7

For $$9^{19}$$ unit digit would be 9 as odd power of 9 gives 9 as unit digit(even power gives one)

For $$7^{15}$$ unit power would be 3 since 7 raised to power which is a multiple of 3 gives 3 as unit digit.

Hence unit place of $$9^{19}−7^{15}$$ = Unit place of $$9^{19}$$ - Unit place of $$7^{15}$$
= 9 - 3
= 6

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Manager  G
Joined: 17 Jan 2019
Posts: 127
Re: What is the units digit of 9^19 - 7^15?  [#permalink]

### Show Tags

1
1
What is the units digit of 9^19 - 7^15?

9^1=9
9^2=81
9^3= _ _ 9
the pattern is _9,_1,_9,_1
19/2=8 R1
therefore the unit digit of 9^19 is 9

7^1=7
7^2=49
7^3=_ _ 3
7^4= _ _ _ 1
7^5= _ _ _ _ _ 7
the pattern is _7, _9,_3,_1
15/4=3 R3
therefore the unit digit of 7^15 is 3

9-3= 6

D
Director  P
Joined: 24 Nov 2016
Posts: 973
Location: United States
Re: What is the units digit of 9^19 - 7^15?  [#permalink]

### Show Tags

1
Quote:
What is the units digit of $$9^{19}−7^{15}$$?

A. 2
B. 4
C. 5
D. 6
E. 7

$$units:9^{19}…cycles(9)=[9,1]=2…remainder:19/2=1…units:1st=$$; or,
$$units:9^{19}=(3^2)^{19}=3^{38}…cycles(3)=[3,9,7,1]=4…remainder:38/4=2…units:2nd=$$
$$units:7^{15}…cycles(7)=[7,9,3,1]=4…remainder:15/4=3…units:3rd=$$
$$units:9^{19}−7^{15}=9-3=6$$

Intern  B
Joined: 08 Jul 2017
Posts: 1
Re: What is the units digit of 9^19 - 7^15?  [#permalink]

### Show Tags

Ans D.. Use cyclicity concept
Senior Manager  P
Joined: 25 Jul 2018
Posts: 403
Re: What is the units digit of 9^19 - 7^15?  [#permalink]

### Show Tags

1
9^1=9
9^2=.1
...
These units digits are repeated in every two terms.
—> If the power of 9 is odd, units digit ends with 9.
—> if the power of 9 is even, units digit ends with 1.
——>Units digit of 9^19 ends with 9

7^1=7
7^2=.9
7^3=..3
7^4=..1
These units digits are repeated in every four terms.
—> units digit of 7^15 is the same as that of 7^3 —> ...3

—> ...9 —3=...6

Posted from my mobile device
Senior Manager  G
Joined: 29 Jun 2019
Posts: 470
Re: What is the units digit of 9^19 - 7^15?  [#permalink]

### Show Tags

.....9-.....3=....6
Hence, option D

Posted from my mobile device
_________________
Always waiting
Intern  B
Joined: 15 Aug 2017
Posts: 24
Re: What is the units digit of 9^19 - 7^15?  [#permalink]

### Show Tags

1
The powers of 9 have the following pattern:
9^1 = 9
9^2 = 81
9^3 = 729
9^4 = 6,561
9^5 = 59,049

As you can see, all even powers will have a units digit of 1 and odd powers will have a units digit of 9.

9^19, 19 is odd so units digit is 9.

Powers of 7 repeat itself after 4 transitions, for example:
7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2,401
7^5 = 16,807

We see that after the fourth power the pattern starts over again, so:
7^15, we take 15 and divide it by four leaving us with 3, the units digit is the 3rd in the repeating list -> 3.

9-3 = 6

IMO
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8715
Location: United States (CA)
Re: What is the units digit of 9^19 - 7^15?  [#permalink]

### Show Tags

1
Bunuel wrote:

Competition Mode Question

What is the units digit of $$9^{19} - 7^{15}$$?

A. 2
B. 4
C. 5
D. 6
E. 7

The patter of units digits for a base of 9 is:

9^1 = 9

9^2 = 1

9^3 = 9

So, 9 raised to an odd power results in a units digit of 9.

The pattern of units digits for a base of 7 is:

7^1 = 7

7^2 = 9

7^3 = 3

7^4 = 1

7^5 = 7

Thus, we see that 7^4n (where n is an integer) has a units digit of 1. Thus, 7^16 has a units digit of 1, and 7^15 has a units digit of 3. Thus, the units digit of 9^19 - 7^15 is 9 - 3 = 6.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: What is the units digit of 9^19 - 7^15?   [#permalink] 11 Oct 2019, 15:54
Display posts from previous: Sort by

# What is the units digit of 9^19 - 7^15?  