BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

integers

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pm
Location: Gandhinagar
Thanked: 41 times
Followed by:2 members

integers

by shashank.ism » Tue Feb 09, 2010 7:12 am
How many integers exist such that not only are they multiples of 2008^2008 but also are factors of
2008^2020?

a 12
b 481
c 587
d 2008^(12)
e 637
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pm
Location: Arabian Sea
Thanked: 125 times
Followed by:2 members

by ajith » Tue Feb 09, 2010 9:40 am
shashank.ism wrote:How many integers exist such that not only are they multiples of 2008^2008 but also are factors of
2008^2020?

a 12
b 481
c 587
d 2008^(12)
e 637
2008^2020/2008^2008 = 2008^12

Now the question is equivalent to how many factors are there for 2008^12

2008^12 = (8*251)^12
= 2^36 *251^12
No of factors = 37*13

481
B
Always borrow money from a pessimist, he doesn't expect to be paid back.
Top
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 am
Thanked: 137 times
Followed by:5 members

by thephoenix » Tue Feb 09, 2010 9:48 am
How many integers exist such that not only are they multiples of 2008^2008 but also are factors of
2008^2020?

multiples of 2008^2008 --->K=x* 2008^2008

factors of 2008^2020--->2008^2020*x/k---->2008^(2020-2008)=2008^12

2008^12=[(2^3)*251]^12=2^36 251^12

hence soln is 37*13=481
Top
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pm
Location: Gandhinagar
Thanked: 41 times
Followed by:2 members

by shashank.ism » Tue Feb 09, 2010 9:55 am
Nice approach to solve the problem..
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Tue Feb 09, 2010 1:42 pm
ajith wrote:
shashank.ism wrote:How many integers exist such that not only are they multiples of 2008^2008 but also are factors of
2008^2020?

a 12
b 481
c 587
d 2008^(12)
e 637
2008^2020/2008^2008 = 2008^12

Now the question is equivalent to how many factors are there for 2008^12

2008^12 = (8*251)^12
= 2^36 *251^12
No of factors = 37*13

481
B
Superb approach to solve the problem.
I had gone nuts figuring out how to solve the problem.

Can, you explain this step?

= 2^36 *251^12
No of factors = 37*13
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
Post new topic Post Reply
• Page 1 of 1