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 Your Progress

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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: number properties. [#permalink]
16 Nov 2005, 07:23

laxieqv wrote:

find number of perfect squares which are also factors of n, a, b, and c are prime >2.

hmmm........... looks like you prepared/made this question. your question is little unclear. i am assuming it as "find the perfect squares that are also factors of n, a, b, and c and assuming that n, a, b, and c are different primes and are greater than 2".

a^4 can be selected in two ways i.e. a^2 and a^4 (assuming a^2 and a^2 in a^4 are same) = 2 ways
b^3 can be selected in 1 way i.e. b^2= 1 way
c^7 can be selected in 4 ways i.e. c^2, c^4 and c^6= 3 ways

they out to be: a^2.b^2.c^2 or a^4.b^2.c^4 or a^2.b^2.c^6..and so on.... i dont think we can count a^2.c^2.b^1 as a perfect square factor?...if we consider a^2*1 as a factor than this is a perfect square..b^2*1 is a perfect square factor...if we have a^2.b^2*1 also a factor etc...then 11 makes sense...

Re: number properties. [#permalink]
19 Nov 2005, 06:04

duttsit wrote:

laxieqv wrote:

A number n( positive integer) when factorised can be written as a^4*b^3*c^7.find number of perfect squares which are factors of n.a,b,c are prime >2.

n = a^4 * b^3 * c^7

a^4 has 4/2=2 perfect squares b^3 has 3/2=1 perfect squares c^7 has 7/2=3 perfect squares

a^4*b^3 has min(4,3)/2 = 3/2 = 1 perfect square b^3*c^7 has min(3,7)/2 = 3/2 = 1 perfect square c^7*a^4 has min(7,4)/2 = 4/2 = 2 perfect squares

a^4*b^3*c^7 has min(4,3,7)/2 = 3/2=1 perfect square

total: 11

OH MY GOD! Where have I come?????? How can you guys diligently solve such problems?? I cant even comprehend what such a problem means many a times! _________________

rahul..duttsit approach is very clear...if you cant follow it...try strenghthning your number properties skills...get your self a MGMAT number properties book...

basically the rule. is.prime^even is always a perfect square so we know that that N has prime factors a,b and c...so now all even powers of these factors would constitute a perfect square..

Hmmm let's see if this thinking is wrong.
For a we have 3 possibilities, a^0, a^2, a^4
For b we have 2 possibilities, b^0, b^2
For c we have 4 possibilities, c^0, c^2, c^4, c^6

So we would have 3*2*4=24 possibilities. The smallest of the perfect square factors would be 1, and the largest would be a^4b^2c^6. _________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Hmmm let's see if this thinking is wrong. For a we have 3 possibilities, a^0, a^2, a^4 For b we have 2 possibilities, b^0, b^2 For c we have 4 possibilities, c^0, c^2, c^4, c^6

So we would have 3*2*4=24 possibilities. The smallest of the perfect square factors would be 1, and the largest would be a^4b^2c^6.

a, b, and c, all, are prime and >2.

laxieqv wrote:

A number n( positive integer) when factorised can be written as a^4*b^3*c^7.find number of perfect squares which are factors of n.a,b,c are prime >2.

Last edited by HIMALAYA on 20 Nov 2005, 21:36, edited 1 time in total.

Well I understood he wants factors of n. And he says that a, b, c are primes that are greater than 2. Did I miss something? :hmm:

i think you are ok. i have been reading . (full stop) as , (coma).

laxieqv wrote:

A number n( positive integer) when factorised can be written as a^4*b^3*c^7. find number of perfect squares which are factors of n. a,b,c are prime >2.

different possible square factors:
a^2,a^4,b^2,c^2,c^4,c^6

Now for combinations of the above you can select one or less from each group therefore from the a group you can select none, a^2 or a^4 - 3 ways. from the b group you can select none or b^2 - 2 ways and from the c group you can select none, c^2, c^4 or c^6 - 4 ways.

Therefore total number of perfect squares that can be formed from the above are = 3*2*4 = 24 from which we will have to subtract one since one possibility was selecting none from each group. Therefore answer = 23.

Therefore total number of perfect squares that can be formed from the above are = 3*2*4 = 24 from which we will have to subtract one since one possibility was selecting none from each group. Therefore answer = 23.

does the bold part happen? ..i don't think so. Or do you mean the case of a^0 * b^0 * c^0 (= 1)? If so, this case should still be counted coz 1 is considered a perfect square. Btw, we all overlooked the case of a^0, b^0 and c^0 , which was brightly pointed out by sis Honghu

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...