Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 27 Mar 2012
Posts: 6

If n is a positive integer and n^2 is divisible by 72, then [#permalink]
Show Tags
31 Mar 2012, 02:36
8
This post received KUDOS
54
This post was BOOKMARKED
Question Stats:
56% (01:50) correct
44% (01:07) wrong based on 1198 sessions
HideShow timer Statistics
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is A. 6 B. 12 C. 24 D. 36 E. 48 Can anyone explain it in very simple manner ?
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 39720

Re: OG 10 : PS 700 level Question [#permalink]
Show Tags
31 Mar 2012, 02:47
11
This post received KUDOS
Expert's post
32
This post was BOOKMARKED
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is A. 6 B. 12 C. 24 D. 36 E. 48 The largest positive integer that must divide \(n\), means for the least value of \(n\) which satisfies the given statement in the question. The lowest square of an integer, which is multiple of \(72\) is \(144\) > \(n^2=144=12^2=72*2\) > \(n_{min}=12\). Largest factor of \(12\) is \(12\). OR: Given: \(72k=n^2\), where \(k\) is an integer \(\geq1\) (as \(n\) is positive). \(72k=n^2\) > \(n=6\sqrt{2k}\), as \(n\) is an integer \(\sqrt{2k}\), also must be an integer. The lowest value of \(k\), for which \(\sqrt{2k}\) is an integer is when \(k=2\) > \(\sqrt{2k}=\sqrt{4}=2\) > \(n=6\sqrt{2k}=6*2=12\) Answer: B. Similar problem: divisionfactor88388.html#p666722Hope it's helps.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 09 Jul 2010
Posts: 121

Quantitative Review 2nd Edition Ques [#permalink]
Show Tags
21 Apr 2012, 14:04
Hi All
I have a confusion about this question
169. If n is a positive integer and n2 is divisible by 72, then the largest positive integerthat must divide n is (A) 6 (8) 12 (C) 24 (0) 36 (E) 48
If we are looking for largest positive integer that must divide n, why can it not be 48.
because if n2 = 72 * 32 then n will be 48 , so does this not mean n is divisible by 48.
Please explain.
Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 39720

Re: Quantitative Review 2nd Edition Ques [#permalink]
Show Tags
21 Apr 2012, 14:14
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Merging similar topics. raviram80 wrote: Hi All
I have a confusion about this question
169. If n is a positive integer and n2 is divisible by 72, then the largest positive integer that must divide n is (A) 6 (8) 12 (C) 24 (0) 36 (E) 48
If we are looking for largest positive integer that must divide n, why can it not be 48.
because if n2 = 72 * 32 then n will be 48 , so does this not mean n is divisible by 48.
Please explain.
Thanks The question asks about "the largest positive integer that MUST divide n", not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12. Complete solution of this question is given above. Please ask if anything remains unclear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 28 Feb 2012
Posts: 115
Concentration: Strategy, International Business
GPA: 3.9
WE: Marketing (Other)

Re: If n is a positive integer and n^2 is divisible by 72, then [#permalink]
Show Tags
14 Aug 2012, 22:50
2
This post received KUDOS
2
This post was BOOKMARKED
Normally i divide the number into the primes just to see how many more primes we need to satisfy the condition, so in our case: n^2/72=n*n/2^3*3^2, in order to have minimum in denominator we should try modify the smallest number. If we have one more 2 then the n*n will perfectly be devisible to 2^4*3^2 from here we see that the largest number is 2*2*3=12 Hope i explained my thought.
_________________
If you found my post useful and/or interesting  you are welcome to give kudos!



Intern
Joined: 15 Apr 2010
Posts: 49

Re: Quantitative Review 2nd Edition Ques [#permalink]
Show Tags
02 Nov 2012, 04:35
Bunuel wrote: Merging similar topics. raviram80 wrote: Hi All
I have a confusion about this question
169. If n is a positive integer and n2 is divisible by 72, then the largest positive integer that must divide n is (A) 6 (8) 12 (C) 24 (0) 36 (E) 48
If we are looking for largest positive integer that must divide n, why can it not be 48.
because if n2 = 72 * 32 then n will be 48 , so does this not mean n is divisible by 48.
Please explain.
Thanks The question asks about "the largest positive integer that MUST divide n", not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12. Complete solution of this question is given above. Please ask if anything remains unclear. I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48. I'm not a native speaker, so here is how I interpreted this question: "the largest positive integer that must divide n" = "the largest positive factor of n". Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here. I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 > true However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 > true So, I also notice that the keyword is "MUST", not "COULD". The question is, why is 48 not "MUST divide 48", but instead only "COULD divide 48"? I'm not clear right here. Why is 12 "MUST divide 12"? What's the difference between them? Thanks, Caten



Math Expert
Joined: 02 Sep 2009
Posts: 39720

Re: Quantitative Review 2nd Edition Ques [#permalink]
Show Tags
02 Nov 2012, 04:53
catennacio wrote: Bunuel wrote: Merging similar topics. raviram80 wrote: Hi All
I have a confusion about this question
169. If n is a positive integer and n2 is divisible by 72, then the largest positive integer that must divide n is (A) 6 (8) 12 (C) 24 (0) 36 (E) 48
If we are looking for largest positive integer that must divide n, why can it not be 48.
because if n2 = 72 * 32 then n will be 48 , so does this not mean n is divisible by 48.
Please explain.
Thanks The question asks about "the largest positive integer that MUST divide n", not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12. Complete solution of this question is given above. Please ask if anything remains unclear. I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48. I'm not a native speaker, so here is how I interpreted this question: "the largest positive integer that must divide n" = "the largest positive factor of n". Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here. I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 > true However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 > true So, I also notice that the keyword is "MUST", not "COULD". The question is, why is 48 not "MUST divide 48", but instead only "COULD divide 48"? I'm not clear right here. Why is 12 "MUST divide 12"? What's the difference between them? Thanks, Caten Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus n must be divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72. Now, ask yourself: if n=12, is n divisible by 48? No. So, n is not always divisible by 48. Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 10 Jan 2011
Posts: 237
Location: India
GMAT Date: 07162012
GPA: 3.4
WE: Consulting (Consulting)

Re: If n is a positive integer and n^2 is divisible by 72, then [#permalink]
Show Tags
02 Nov 2012, 05:20
2
This post received KUDOS
I approach this problem by prime factorisation. any square must have 2 pairs of prime factors. prime factorisation of 72 has 2*2, 3*3 and 2. n^2 must have one more 2 as a prime factor. Hence lasrgest number which must devide n is 2*3*2 = 12
_________________
Analyze why option A in SC wrong



Intern
Joined: 15 Apr 2010
Posts: 49

Re: Quantitative Review 2nd Edition Ques [#permalink]
Show Tags
02 Nov 2012, 08:49
Bunuel wrote: Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus n must be divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.
Now, ask yourself: if n=12, is n divisible by 48? No. So, n is not always divisible by 48.
Hope it's clear.
Thank you very much Bunuel. Very clear now. Now I understand what "must" means. It means it will be always true regardless of n. As you said (and I chose), when n = 24 or 36 or 48, the answer 48 can divide 48, but cannot divide 12. So the "must" here is not maintained. In this case we have to choose the largest factor of the least possible value of n to ensure that largest factor is also a factor of other values of n. Therefore the least value of n is 12, the largest factor of 12 is also 12. This factor also divides other n values, for all n such that n^2 = 72k. My mistake was that I didn't understand the "must" wording and didn't check whether my answer 48 can divide ALL possible values of n, including n=12. This is what "must" mean. Again, thanks so much! Caten



Math Expert
Joined: 02 Sep 2009
Posts: 39720

Re: Quantitative Review 2nd Edition Ques [#permalink]
Show Tags
02 Nov 2012, 08:53
catennacio wrote: Bunuel wrote: Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus n must be divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.
Now, ask yourself: if n=12, is n divisible by 48? No. So, n is not always divisible by 48.
Hope it's clear.
Thank you very much Bunuel. Very clear now. Now I understand what "must" means. It means it will be always true regardless of n. As you said (and I chose), when n = 24 or 36 or 48, the answer 48 can divide 48, but cannot divide 24 and 36. So the "must" here is not maintained. In this case we have to choose the largest factor of the least possible value of n to ensure that largest factor also a factor of other values of n. Therefore the least value of n is 12, the largest factor of 12 is also 12. This factor also divides other n values, for all n such that n^2 = 72k. My mistake was that I didn't understand the "must" wording and didn't check whether my answer 48 can divide ALL possible values of n, including n=12. This is what "must" mean. Again, thanks so much! Caten More must/could be true questions from our question banks ( viewforumtags.php) here: search.php?search_id=tag&tag_id=193Hope it helps.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 04 Oct 2011
Posts: 218
Location: India
Concentration: Entrepreneurship, International Business
GPA: 3

Re: Number Properties question [#permalink]
Show Tags
11 Jan 2013, 23:31
taurean wrote: If n is a positive integer and \(n^2\) is divisible by 72, then the largest positive integer that must divide n is a) 6 b) 12 c) 24 d) 36 e) 48 IMO B. 72 prime factors are \(2^3 * 3^2\) \(n^2\) divisible by 72 is 144 ==> (\(2^4 * 3^2\)). So n is 12 largest positive integer divides 12 must be 12 itself pls correct me if im wrong
_________________
GMAT  Practice, Patience, Persistence Kudos if u like
Last edited by shanmugamgsn on 12 Jan 2013, 00:43, edited 1 time in total.



Current Student
Joined: 27 Jun 2012
Posts: 411
Concentration: Strategy, Finance

Re: Number Properties question [#permalink]
Show Tags
11 Jan 2013, 23:34
shanmugamgsn wrote: taurean wrote: If n is a positive integer and \(n^2\) is divisible by 72, then the largest positive integer that must divide n is a) 6 b) 12 c) 24 d) 36 e) 48 IMO B. 72 prime factors are \(2^2 * 3^2\)\(n^2\) divisible by 72 is 144 ==> (\(2^3 * 3^2\)). So n is 12 largest positive integer divides 12 must be 12 itself pls correct me if im wrong Correction: Prime factorization for 72 is \(2^3 * 3^2\)  there are 3 twos. Also your solution needs further reasoning. 12 is not the only number n can take.
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here



Manager
Joined: 04 Oct 2011
Posts: 218
Location: India
Concentration: Entrepreneurship, International Business
GPA: 3

Re: Number Properties question [#permalink]
Show Tags
12 Jan 2013, 00:45
PraPon wrote: shanmugamgsn wrote: taurean wrote: If n is a positive integer and \(n^2\) is divisible by 72, then the largest positive integer that must divide n is a) 6 b) 12 c) 24 d) 36 e) 48 IMO B. 72 prime factors are \(2^2 * 3^2\)\(n^2\) divisible by 72 is 144 ==> (\(2^3 * 3^2\)). So n is 12 largest positive integer divides 12 must be 12 itself pls correct me if im wrong Correction: Prime factorization for 72 is \(2^3 * 3^2\)  there are 3 twos. Also your solution needs further reasoning. 12 is not the only number n can take. ya it was a typo.. I corrected it... Why 12 cannot be solution here? Ya only 12 is not number greater than and divisible by 72, but it is first number ! So i choose it
_________________
GMAT  Practice, Patience, Persistence Kudos if u like



Manager
Joined: 13 Feb 2012
Posts: 145
Location: Italy
Concentration: General Management, Entrepreneurship
GPA: 3.1
WE: Sales (Transportation)

Re: If n is a positive integer and n^2 is divisible by 72, then [#permalink]
Show Tags
12 Jan 2013, 06:35
The language used in this problem is one of the things that might get you under timed conditions; "the greatest... that must" is the LEAST, just like Bunuel explained and it is very important to have this sort of Gmat wording clear in mind. Other than that it's not too difficult.
_________________
"The Burnout"  My Debrief
Kudos if I helped you
Andy



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629

Re: Quant Review 2E  Q#169 [#permalink]
Show Tags
11 Aug 2013, 08:13
anshuman09 wrote: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is (A) 6 (B) 12 (C) 24 (D) 36 (E) 48
Please let me know why 48 can't be the answer? Firstly , is there any specific reason for contesting 48 as an answer? Nonetheless, if\(n^2\) is divisible by 72, then n must have a prime factorization of the kind : \(2^2*3*.....(more primes)\). Now the power of 2 has to be atleast 2, because 72 contains \(2^3\). Thus, n = 12*some primes. Thus, 12 is the largest positive integer which WILL/MUST divide n. Hope this helps.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Intern
Joined: 02 Aug 2013
Posts: 2

Re: Quant Review 2E  Q#169 [#permalink]
Show Tags
11 Aug 2013, 11:55
mau5 wrote: anshuman09 wrote: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is (A) 6 (B) 12 (C) 24 (D) 36 (E) 48
Please let me know why 48 can't be the answer? Firstly , is there any specific reason for contesting 48 as an answer? Nonetheless, if\(n^2\) is divisible by 72, then n must have a prime factorization of the kind : \(2^2*3*.....(more primes)\). Now the power of 2 has to be atleast 2, because 72 contains \(2^3\). Thus, n = 12*some primes. Thus, 12 is the largest positive integer which WILL/MUST divide n. Hope this helps. Thanks mate for the reply.. But If we choose the value of n as 48 then n^2 (48 * 48) will also be divisible by 72. As the same thing is happening in case of n=12, as you have explained. Since we have to choose the largest value of n, why cant 48 be the right value of n?



Math Expert
Joined: 02 Sep 2009
Posts: 39720

Re: Quant Review 2E  Q#169 [#permalink]
Show Tags
11 Aug 2013, 12:12
anshuman09 wrote: mau5 wrote: anshuman09 wrote: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is (A) 6 (B) 12 (C) 24 (D) 36 (E) 48
Please let me know why 48 can't be the answer? Firstly , is there any specific reason for contesting 48 as an answer? Nonetheless, if\(n^2\) is divisible by 72, then n must have a prime factorization of the kind : \(2^2*3*.....(more primes)\). Now the power of 2 has to be atleast 2, because 72 contains \(2^3\). Thus, n = 12*some primes. Thus, 12 is the largest positive integer which WILL/MUST divide n. Hope this helps. Thanks mate for the reply.. But If we choose the value of n as 48 then n^2 (48 * 48) will also be divisible by 72. As the same thing is happening in case of n=12, as you have explained. Since we have to choose the largest value of n, why cant 48 be the right value of n? Check here: ifnisapositiveintegerandn2isdivisibleby72then129929.html#p1067773
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 02 Aug 2013
Posts: 2

Re: Quant Review 2E  Q#169 [#permalink]
Show Tags
11 Aug 2013, 12:17
Thanks a lot Bunuel. Now I got it. My understanding is:
possible values of n = 12, 24, 36 and 48. But it is 12 that can divide all the possible values of n. If we consider 48, it will not divide 12, 24 and 36. Hence, 12 is the value that MUST divide n.
Thanks again.



Senior Manager
Joined: 10 Jul 2013
Posts: 334

Re: Quant Review 2E  Q#169 [#permalink]
Show Tags
12 Aug 2013, 15:36
anshuman09 wrote: mau5 wrote: anshuman09 wrote: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is (A) 6 (B) 12 (C) 24 (D) 36 (E) 48
Please let me know why 48 can't be the answer? Firstly , is there any specific reason for contesting 48 as an answer? Nonetheless, if\(n^2\) is divisible by 72, then n must have a prime factorization of the kind : \(2^2*3*.....(more primes)\). Now the power of 2 has to be atleast 2, because 72 contains \(2^3\). Thus, n = 12*some primes. Thus, 12 is the largest positive integer which WILL/MUST divide n. Hope this helps. Thanks mate for the reply.. But If we choose the value of n as 48 then n^2 (48 * 48) will also be divisible by 72. As the same thing is happening in case of n=12, as you have explained. Since we have to choose the largest value of n, why cant 48 be the right value of n? 12 must divide n , 24,36,48 may divide n . n^2 / 72, here n can be 12, 36,48....... but to be divided by 72, n should be at least 12. (12^2 = 144) so 12 is must and the rest are may or could............ below 12 not possible. At least 12..........
_________________
Asif vai.....



Manager
Joined: 16 Jan 2011
Posts: 103

Re: If n is a positive integer and n^2 is divisible by 72, then [#permalink]
Show Tags
13 Aug 2013, 10:32
1
This post was BOOKMARKED
n^2/72 > n*n/(2^3*3^2) >(n/2*3)*(n/2*3)*1/2 > means that n/6*1/2 > 12




Re: If n is a positive integer and n^2 is divisible by 72, then
[#permalink]
13 Aug 2013, 10:32



Go to page
1 2
Next
[ 40 posts ]





Similar topics 
Author 
Replies 
Last post 
Similar Topics:


57


If n is a positive integer, then (2^n)^{2} + (2^{n})^2 is equal to

lpetroski 
20 
22 Jun 2017, 10:03 

51


If n is a positive integer and n^2 is divisible by 72, then

Bunuel 
14 
18 Apr 2017, 07:43 

45


If n is a positive integer and n^2 is divisible by 96, then

enigma123 
11 
25 Jan 2017, 09:40 

23


If (n2)! = (n! + (n1)!)/99, and n is a positive integer, then n=?

gettinit 
16 
23 Apr 2017, 19:52 

71


If n is a positive integer and n^2 is divisible by 72, then

asyahamed 
18 
30 Mar 2017, 16:37 



