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 500,000 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:

If n is a positive integer and n^2 is divisible by 72, then [#permalink]

Show Tags

09 Jan 2007, 00:21

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 1 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

2. If n is a positive integer and n^2 is divisible by 72, then the largest possible positive integer that must divide n is
A) 6
B) 12
C) 24
D) 36
E) 48

I get E on this one. Its a pain because I started with 12, the easy answer. 12 square is 144/72=2. 36 works but 48 square is 2304/72 is 32. Hence E. I dont know my squares that high, took a minute to do it longhand. Hope not to see it on the test.

E for me. This one took me a bit of time to figure out.

n^2 is divisible by 72

Prime Factors of 72 are 2^3*3^2

Hence n^2 = 2^2*3^2*2*k where k is any integer such that 2*k is a square
Let 2*k=j
Therefor the largest number that n is divisible by is 2*3*j=6*j i.e. some multiple of 6

Given the choices the bigggest multiple of 6 is 48 (6*8)i.e. 2*k =64

48^2 is divisible by 72. Hence the largest integer that divides n is 48. _________________

2. If n is a positive integer and n^2 is divisible by 72, then the largest possible positive integer that must divide n is A) 6 B) 12 C) 24 D) 36 E) 48

Surely, of the choices given, 48 is the largest # that could divide n, but 12 is the one that must divide n.

The wording is a bit tricky, watch out for must/could/cannot/etc.

Last edited by Andr359 on 09 Jan 2007, 21:40, edited 1 time in total.

My vote is for B. My approach was the same as Fig's.

n should be a multiple of 12. For any value of n, 12 should divide n. The other nos. MAY or MAY not depending on n.

For example if n=36 then n^2 is divisible by 72, n will not be divisible by 48 but will be divisible by 12. The question asks for the largest number that MUST divide n. So 12 should be the answer.

n^2 = ( (3)^2 * (2)^2 * 2 ) * k^2 => n = 3*2*sqrt(2)*k : non sense, as n is an integer, it forces k to not be an integer.

We must have an integer j such that : n^2 = ( (3)^2 * (2)^2 * 2 ) * 2 * j^2 <=> n = 3*2*2 * j <=> n = 12 * j

Fig, could you please explain the bolded sections in a little more detail.
For the first one, since n^2 is divisible by 72, shouldn't it be written as
n^2 = ( (3)^2 * (2)^2 * 2 ) * k : (where k is any integer)
The second one, I'm totally lost

n^2=72k=36*2k = 6^2*2k
2k needs to be the square of a number
k=2m^2, where m is a positive integer
therefore
n=12m

Therefore 12 is the largest possible number that must divide n. Other possible numbers that must divide n would be 1,2,3,4,6. Other possible numbers that may divide n could be anything, depend on what m is. _________________

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.

n^2=72k=36*2k = 6^2*2k 2k needs to be the square of a number k=2m^2, where m is a positive integer therefore n=12m

Therefore 12 is the largest possible number that must divide n. Other possible numbers that must divide n would be 1,2,3,4,6. Other possible numbers that may divide n could be anything, depend on what m is.

2. If n is a positive integer and n^2 is divisible by 72, then the largest possible positive integer that must divide n is A) 6 B) 12 C) 24 D) 36 E) 48

OA I have is B.

but for me the question is not properly worded as it says largest possible. is 12 the largest possible value that divide n? lets see....

(n^2)/72 = k
n^2 = 72k
n = 6 x sqrt(2k)

now, k could be a minimum of 2 or 2x2x2, 2x3x3, 2x4x4, 2x5x5, 2x6x6 or 2(n^2).

If k = 2, n = 12 and n is divisible by 12.
If k = 2x2x2, n = 24 and n is divisible by 24.
If k = 2x3x3, n = 36 and n is divisible by 36.
If k = 2x4x4, n = 48 and n is divisible by 48.
If k = 2x5x5, n = 60, and n is divisible by 60.

so we know that, n is a multiple of 12 and it is divisible by any number that is a multiple of 12.

If n is a positive integer and n^2 is divisible by 72, then the largest possible positive integer that must divide n is A) 6 B) 12 C) 24 D) 36 E) 48

The problem says the largest possible that must divide n. LetÂ´s solve step by step.
1) n^2 is multiple of 72 => n^2 = 72 * a (a = integer>=1)
2) n^2 = 2^3 * 3^2 * a = 2^2 * 3^2 * 2a
3) n = 2 * 3 * sqrt(2a)
4) n is integer => sqrt(2a) must be integer too. LetÂ´s say that sqrt(2a) = 2*k, k an integer. sqrt(2a) has to be even because an integer sqrt of an even number is always even as well (think 16 and 4, 36 and 6, 144 and 12, etc).
5) n = 2 * 3 * 2k = 4 * 3 * k = 12 * k. k could be 1, 5, 24, 8239823698298, any integer.
6) What is the largest +ve integer that must divide n?
7) Would it be 48? What if k = 5? n = 12 * 5 = 60; can 48 divide 60? No.
8) Which numbers must divide n = 12 * k? 2, 3, 4, 6, and 12.
The trick is to focus 1st on the "must", and only afterwards on the "largest".

gmatclubot

Re: PS: Value of n
[#permalink]
12 Jan 2007, 19:10