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

 It is currently 22 Sep 2019, 03:21

### 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

# What are the last two digits of the number 7^45

Author Message
TAGS:

### Hide Tags

Intern
Joined: 03 Jul 2019
Posts: 33
Location: India
GPA: 3
WE: Sales (Venture Capital)
What are the last two digits of the number 7^45  [#permalink]

### Show Tags

23 Aug 2019, 11:11
2
00:00

Difficulty:

35% (medium)

Question Stats:

61% (01:04) correct 39% (01:17) wrong based on 33 sessions

### HideShow timer Statistics

What are the last two digits of the number 7^45

A 07
B 23
C 49
D 43
E 27
Director
Joined: 19 Oct 2018
Posts: 880
Location: India
Re: What are the last two digits of the number 7^45  [#permalink]

### Show Tags

23 Aug 2019, 13:41
The remainder when $$7^{45}$$ is divided by 100 is the last 2 digits of $$7^{45}$$.

$$7^2$$=49= 49 Mod 100
$$7^4$$= 2401= (01) mod 100

$$7^{4k}$$= 01 MOD 100
$$7^{4k+1}$$= (01*7) MOD 100= 07 MOD 100

45= 4*11+1, hence $$7^{45}$$= 07 MOD 100

A

AbdulMalikVT wrote:
What are the last two digits of the number 7^45

A 07
B 23
C 49
D 43
E 27
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4790
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: What are the last two digits of the number 7^45  [#permalink]

### Show Tags

24 Aug 2019, 02:19
AbdulMalikVT wrote:
What are the last two digits of the number 7^45

A 07
B 23
C 49
D 43
E 27

we can solve using 7 cyclicity ; 7,9,3,1
so for power 7^45 ; 7^4x+1 ; unit digit will be 3 and tens digit will be same as 7^4 ; 2401
IMO A: 07
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
SVP
Joined: 03 Jun 2019
Posts: 1540
Location: India
Re: What are the last two digits of the number 7^45  [#permalink]

### Show Tags

24 Aug 2019, 02:33
AbdulMalikVT wrote:
What are the last two digits of the number 7^45

A 07
B 23
C 49
D 43
E 27

What are the last two digits of the number 7^45?

= Rem[7^45/100]

7^2 = 49 = 50-1
7^4 = 49^2 = (50-1)^2 = 50^2 - 2*50 +1 = 2401

7^4k = 01mod100
7^44 = 01mod100
7^45 = 7*7^44 = 07mod100

IMO A
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Intern
Joined: 20 Aug 2017
Posts: 26
Re: What are the last two digits of the number 7^45  [#permalink]

### Show Tags

24 Aug 2019, 03:18
To find the last two digits we essentially need to find the remainder when divided by 100.

now, 7 follows cyclicity of 4 i.e. after the fourth power the unit digit gets repeated.

in this case we need last two digits.

7^4 = 2401. now last two digits are 01

so 7^44 = 7^4.
the product reduces to
(01)*7 = 07.

If you like my solution, do give kudos!
_________________
---------------------------------------------------------------------------------------
Nobody can defeat you, until you yourself give up!

If you like my solution, do give kudos!
Re: What are the last two digits of the number 7^45   [#permalink] 24 Aug 2019, 03:18
Display posts from previous: Sort by