Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 21 Dec 2014, 21:38

### 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 remainder when 7^74-5^74 is divided by 24? Is

Author Message
TAGS:
Manager
Joined: 04 Sep 2007
Posts: 215
Followers: 1

Kudos [?]: 8 [0], given: 0

What is the remainder when 7^74-5^74 is divided by 24? Is [#permalink]  03 Jul 2008, 12:19
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
What is the remainder when 7^74-5^74 is divided by 24?

Is there an easy way to solve this?
Director
Joined: 01 Jan 2008
Posts: 629
Followers: 3

Kudos [?]: 136 [0], given: 1

Re: PS: What is the easiest way to solve? [#permalink]  03 Jul 2008, 13:20
wizardofwashington wrote:
What is the remainder when 7^74-5^74 is divided by 24?

Is there an easy way to solve this?

easiest way for me: 7^74 - 5^74 = (49)^37-25^37 = (24*2+1)^37 - (24+1)^37 -> remainder is 1^37 - 1^37 = 0
Director
Joined: 12 Apr 2008
Posts: 501
Location: Eastern Europe
Schools: Oxford
Followers: 11

Kudos [?]: 167 [0], given: 4

Re: PS: What is the easiest way to solve? [#permalink]  03 Jul 2008, 13:45

It may be useful to remember that a^n-b^n is always divisible by (a-b).

So, when we write 49^37-25^37, we can note that 49-25=24, and thus, the expression can be evenly divided by 24.
Manager
Joined: 04 Sep 2007
Posts: 215
Followers: 1

Kudos [?]: 8 [0], given: 0

Re: PS: What is the easiest way to solve? [#permalink]  03 Jul 2008, 13:57
greenoak wrote:

It may be useful to remember that a^n-b^n is always divisible by (a-b).

So, when we write 49^37-25^37, we can note that 49-25=24, and thus, the expression can be evenly divided by 24.

Thanks, guys. Appreciate your quick response.
VP
Joined: 03 Apr 2007
Posts: 1377
Followers: 3

Kudos [?]: 221 [0], given: 10

Re: PS: What is the easiest way to solve? [#permalink]  04 Jul 2008, 21:58
greenoak wrote:

It may be useful to remember that a^n-b^n is always divisible by (a-b).

So, when we write 49^37-25^37, we can note that 49-25=24, and thus, the expression can be evenly divided by 24.

Ditto
SVP
Joined: 29 Aug 2007
Posts: 2499
Followers: 56

Kudos [?]: 530 [0], given: 19

Re: PS: What is the easiest way to solve? [#permalink]  04 Jul 2008, 22:20
maratikus wrote:
wizardofwashington wrote:
What is the remainder when 7^74-5^74 is divided by 24?

Is there an easy way to solve this?

easiest way for me: 7^74 - 5^74 = (49)^37-25^37 = (24*2+1)^37 - (24+1)^37 -> remainder is 1^37 - 1^37 = 0

I like your approach. however i figured out as under:

7^1 - 5^1 = 2 so reminder = 2.
7^2 - 5^2 = 24 ...... so reminder 0.
7^3 - 5^3 = 48 ...... so reminder 0.
7^4 - 5^4 = 218 ....... so reminder = 2

similarly;
7^73 - 5^73 should have a reminder of 2.
7^74 - 5^74 should have a reminder of 0.
_________________
Re: PS: What is the easiest way to solve?   [#permalink] 04 Jul 2008, 22:20
Similar topics Replies Last post
Similar
Topics:
What is the remainder when a is divided by 4? 0 07 Aug 2013, 23:10
5 What is the remainder when a is divided by 4? 7 19 Dec 2010, 14:22
A number when divided by a divisor leaves a remainder of 24. 0 16 Oct 2013, 12:23
25 A number when divided by a divisor leaves a remainder of 24. 26 07 Apr 2007, 22:45
Do j and k yield the same remainder when divided by 24? (1) 2 12 Jul 2006, 15:54
Display posts from previous: Sort by