GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 12 Dec 2019, 01:26

### 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

# M and N are integers such that 6<M<N.What is the value of N?

Author Message
TAGS:

### Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 522
GPA: 2.81
M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

Updated on: 15 Jul 2016, 05:03
10
121
00:00

Difficulty:

75% (hard)

Question Stats:

59% (02:09) correct 41% (02:09) wrong based on 1395 sessions

### HideShow timer Statistics

M and N are integers such that 6<M<N.What is the value of N?

(1) The greatest common divisor of M and N is 6
(2) The least common multiple of M and N is 36

OG Q 2017 New Question (Book Question: 297)

Originally posted by AbdurRakib on 24 Jun 2016, 12:24.
Last edited by AbdurRakib on 15 Jul 2016, 05:03, edited 2 times in total.
Current Student
Joined: 22 Jun 2016
Posts: 223
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

24 Jun 2016, 13:43
23
10
Statement 1: greatest common divisor of M and N is 6. So, M and N are multiple of 6. But, an exact value of N cannot be determined. Insufficient!

Statement 2: LCM of M and N is 36. M can be 9 and N can be 12 or M can be 12 and N can be 18. Multiple possible answer. Insufficient!

Combining 1&2, M and N are multiple of 6 and LCM is 36. So the only possible values on M and N can be 12 and 18 respectively.
Sufficient!

##### General Discussion
Retired Moderator
Joined: 05 Jul 2006
Posts: 1380
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

14 Oct 2016, 14:15
9
4
AbdurRakib wrote:
M and N are integers such that 6<M<N.What is the value of N?

(1) The greatest common divisor of M and N is 6
(2) The least common multiple of M and N is 36

OG Q 2017 New Question (Book Question: 297)

Both together

LCM*HCF = MN ( each of m, n are multiple of 6 --- assume m = 6k , k is +ve integer )

N =36*6/ 6k thus N = 36/k , since N is a multiple of 6 then k can only be (1,2,3,6)

if k is 1 thus N= 36, M = 6, if k = 2 thus N= 18 and M = 12 , IF K=3 then N= 12 , M = 18 , IF K = 6 then N= 6 and M = 36) the only option that satisfy the constraint ( 6<M<N) is when K= 2 and N=18 , M=12

C
Manager
Joined: 23 May 2017
Posts: 231
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

29 Oct 2017, 09:30
6
1
M>6 and N>M

[1] GCD is 6 :
N= 6 * 3 & M = 6 * 2
N= 6 * 5 & M = 6 * 3

here number can be anything - as long as we multiply the number 6 by any of the prime numbers, the statement 2 will be satisfied

[2] LCM = 36 : 2 * 2 * 3 * 3 - N & M can only be formed with the combination of 2's or 3's
given m & n > 6 so possible values are
N= 2 * 3 * 3 & M = 2 * 2 * 3
N= 2 * 2 * 3 * 3 & M = 2 * 2 * 3
N= 2 * 2 * 3 * 3 & M = 2 * 3 * 3

Hence [1] & [2] individually not sufficient but together they yield the number N = 18 & M = 12
Manager
Joined: 22 Feb 2016
Posts: 81
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

14 Oct 2016, 08:19
2
hcf*LCM= a*b
statement1: only HCF is mentioned, multiple values are possible NS
Statement 2: Only LCM is mentioned , multiple values are possible NS

combining HCF*LCM= product of M*N
and we know M<N hence we can determine the values.

PS: please let me know if my approach is correct.
Intern
Joined: 19 Jul 2012
Posts: 27
Location: India
Concentration: Finance, Marketing
GMAT 1: 640 Q47 V32
GMAT 2: 660 Q49 V32
GPA: 3.6
WE: Project Management (Computer Software)
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

06 Nov 2016, 23:05
1
1
3
6*36=216=m*n
Both m & n are greater than 6
M<N can be satisfied under
Pairs (12,18),(9,24) and (8,27)
But only 12,18 can give gcf 6

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Intern
Joined: 18 Jun 2017
Posts: 3
M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

29 Oct 2017, 09:02
1
If M and N are among 6, 12, 18 and 36 as well as 6 < M < N then M cannot be either 6 or 36 and N cannot be 6. The only test cases from to use are:

Case 1 - M = 12 , N = 18 , GCD = 6 , LCM = 36
Case 2 - M = 12 , N = 36 , GCD = 12 , LCM = 36
Case 3 - M = 18 , N = 36 , GCD = 18 , LCM = 36

The only case that satisfies the limitations of both statement 1 (GCD) and statement 2 (LCM) is case 1 and therefore N is 18 (answer again is C). Hope this helps explain why N cannot be 36
Manager
Joined: 18 Jul 2015
Posts: 84
GMAT 1: 530 Q43 V20
WE: Analyst (Consumer Products)
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

28 Sep 2019, 23:58
1
Inten21 wrote:
Bunuel

Can you please provide an elaborated Solution for this problem?

Would really appreciate it if you could explain in detail as to how to think and approach such tough LCM and GCF problems?

Also, can you link some more SIMILAR QUESTIONS if it is possible.

While your question is to Bunuel, I will try to share an detailed explanation that may help you as well as others.

What is the GCD - It is the product of the common terms with the least power (This is in my words and not a textbook perfect definition )

E.g. If there are two integers 12 and 16
Step-1: Break into prime factors. 12 would be $$2^2*3$$ and 16 would be $$2^4$$
Step-2: Identify common prime(s) i.e. 2
Step-3: Pick the common prime with the lowest power i.e. $$2^2$$ in our example and that is your GCD
GCD - $$2^2$$

Conceptually GCD is the largest number that can divide the 2 integers in question. Try to find an integer greater than 4 that divides both 12 and 16. You won't be able to find one!

What is LCM - It is the product of the common terms with the highest power (Again this is in my words and not a textbook perfect definition )

In the above example, pick out the highest power of all distinct primes i.e. $$2^4$$ and $$3^1$$
Hence LCM would be $$2^4*3^1 = 48$$
Conceptually LCM is the smallest multiple of the 2 integers in the question. Try to find an integer less than 48 that is a multiple of both 12 and 16. You won't be able to find one!

On to the question at hand:-

Info. provided in the question:
1. Both M and N are integers
2. Both are greater than 6
3. N is the greater than M ($$N>M$$, E.g. Least values of N could be 8 and that of M could be 7)

We are asked to determine the value of N

Statement-1: GCD (Greatest Common Divisor) of M and N is 6 (or $$2*3$$)

This states that 6 will be common to both M and N. Plus, as M and N are greater than 6 there will be other primes too. But this statement does not provide insight into those other primes and hence this statement is insufficient. Let me demonstrate that:

$$M = 2*3*5 = 30$$
$$N = 2*3*7 = 42$$

OR

$$M = 2*3*11 = 66$$
$$N = 2*3*13 = 78$$

Here GCD (M, N) is 6 but N can take different values while staying true to the 3 data points provided by the question stem.

Statement-2: LCM (Least Common Divisor) of M and N is 36 (or $$2^2*3^2$$)

Basis the definition of LCM, in which we consider the highest powers of all distinct primes, this statement provides information that 2 and 3 are the only primes carried by M and N. But it does not provide insight into the powers of 2 and 3 specific to M and N. E.g. in the examples below $$2^2$$ can be part of M in the first example and also part of N in the very last example, and hence this statement is insufficient.

$$M = 2*3*2 = 12$$
$$N = 2*3*3 = 18$$

$$M = 3*3 = 9$$
$$N = 2*3*2 = 12$$

Combining both statements:

When combining we need to ensure that:

1. $$N>M$$ - This one is the key!
2. N and M are greater than 6
3. From statement-1 we know that 6 is common to both M and N
4. From statement-2 we know that 2 and 3 are the only primes carried by M and N and their highest powers are 2 ($$2^2$$ and $$3^2$$)

$$M = 2*3*2 = 12$$
$$N = 2*3*3 = 18$$

You cannot do the below as it would violate the condition that N>M (pt. 1 i.e. Key).
$$M = 2*3*3 = 18$$
$$N = 2*3*2 = 12$$

Ans C (or $$N = 18$$)

While it sounds very simple, but as you can observe that the best approach to solving these questions and math questions in general is to list down the various possibilities in an organized fashion (one below another) in your notebook. The biggest mistakes happen when we ignore the data points provided in the question stem E.g. N>M or N,M>6 in this case.

Hope it helps!
_________________
Cheers. Wishing Luck to Every GMAT Aspirant!
Manager
Joined: 23 Jan 2016
Posts: 180
Location: India
GPA: 3.2
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

10 Nov 2016, 23:00
Statement 1 tells us that between M and N, 2 and 3 are the lowest factors. However we do not know exactly who has 2 and who has 3; there can also be other factors between them. Insufficient.

Stamtement 2 tells us that 2^2 and 3^2 are the highest factors between M and N. However we do not know whether thats the only factors common between them or that there are lower factors of 2 and 3 between them than 2^2 and 2^3.

Combining both statements we understand that 2 and 3 are the lowest factors and 2^2 and 3^2 are the highest factors. So one of them must be 12 and the other must be 18. Since 6<M<N, N must be 18.

C
Intern
Joined: 08 Dec 2016
Posts: 32
Location: Italy
Schools: IESE '21
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

25 Jun 2017, 12:28
14101992 wrote:
Statement 1: greatest common divisor of M and N is 6. So, M and N are multiple of 6. But, an exact value of N cannot be determined. Insufficient!

Statement 2: LCM of M and N is 36. M can be 9 and N can be 12 or M can be 12 and N can be 18. Multiple possible answer. Insufficient!

Combining 1&2, M and N are multiple of 6 and LCM is 36. So the only possible values on M and N can be 12 and 18 respectively.
Sufficient!

Hi 14101992,

According the statement 2, LCM can be 36 as well.
The further constrain is given "by the formula (concept)": LCM*HCF = M*N --> 6*36, which tells that LCM cannot be 36 and so only M=12 and N=18 cen be the answer.

C is correct.

Hope it helps.

Matt
Intern
Joined: 25 Mar 2017
Posts: 1
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

10 Aug 2017, 19:35

Sent from my Nexus 6P using GMAT Club Forum mobile app
Status: It's now or never
Joined: 10 Feb 2017
Posts: 175
Location: India
GMAT 1: 650 Q40 V39
GPA: 3
WE: Consulting (Consulting)
M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

28 Aug 2017, 07:02
Statement 1 and 2: are clearly NOT SUFFICIENT. Can anyone explain the easiest way how together they are sufficient. I just had a lucky guess 'C' which was correct. Thanks.
_________________

Class of 2019: Mannheim Business School
Class 0f 2020: HHL Leipzig
Intern
Joined: 13 Aug 2018
Posts: 47
M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

28 Oct 2018, 01:39
AbdurRakib wrote:
M and N are integers such that 6<M<N.What is the value of N?

(1) The greatest common divisor of M and N is 6
(2) The least common multiple of M and N is 36

OG Q 2017 New Question (Book Question: 297)

Dear Bunuel, what is your take on this question?

Is there any way we could solve this question faster with a formula or something?

Because I kept thinking about what numbers could fit the statements and doing so took some time.

Thanks
Manager
Joined: 05 Oct 2017
Posts: 66
Location: India
Schools: GWU '21, Isenberg'21
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

10 Dec 2018, 05:43
2
It a Very good question !!!! some claps for GMAC

Lets understand what is being asked.

Here we suppose to find the value of N. a concrete , solid value of N

Statement 1 says GCD of M&N is 6 which means they are multiple of 6 or separated from each other by 6
so M&N can be 12 & 18 , 18 & 24 , 24 & 30 .........and so on (Hence Not sufficient)

Staement 2 says LCM of M&N is 36 means MAX value of N can be 36
so M&N can have value as 9 & 12 , 12 & 18 , 18 & 36 , 9 & 36 , 12 & 36 .(Hence Not sufficient)

On Combining we got 12 & 18 as our final answer because it is common in both.
GCD of 12 & 18 is 6 and LCM of 12 & 18 is 36
No other combination satisfy these condition

Option C is correct choice

Hope that Helps!!!!
_________________
Intern
Joined: 04 May 2018
Posts: 4
Concentration: Technology, Strategy
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

11 Dec 2018, 10:17
Statement 1: The GCD of M and N is 6. Therefore, M and N must contain 2*3 and may or may not contain any other number
M = 2 * 3 * 7 (any other number or nothing at all)
N = 2 * 3 * 5 (any other number or nothing at all) --- INSUFFICIENT

Statement 2: The LCM of M and N is 36. Therefore, M and N can take the following forms:
M = 2 * 3 * 2 = 12
N = 2 * 3 * 3 = 18

OR

M = 2 * 3 * 2 = 12
N = 2 * 3 * 2 * 3 = 36

--- INSUFFICIENT

Together (1) & (2)
only 1 possibility ,
M = 2 * 3 * 2 = 12
N = 2 * 3 * 3 = 18

Intern
Joined: 15 Jun 2018
Posts: 1
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

28 Jun 2019, 06:13
matt882 wrote:
14101992 wrote:
Statement 1: greatest common divisor of M and N is 6. So, M and N are multiple of 6. But, an exact value of N cannot be determined. Insufficient!

Statement 2: LCM of M and N is 36. M can be 9 and N can be 12 or M can be 12 and N can be 18. Multiple possible answer. Insufficient!

Combining 1&2, M and N are multiple of 6 and LCM is 36. So the only possible values on M and N can be 12 and 18 respectively.
Sufficient!

Hi 14101992,

According the statement 2, LCM can be 36 as well.
The further constrain is given "by the formula (concept)": LCM*HCF = M*N --> 6*36, which tells that LCM cannot be 36 and so only M=12 and N=18 cen be the answer.

C is correct.

Hope it helps.

Matt

Why can't the LCM be 36?
Manager
Joined: 20 Oct 2018
Posts: 147
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

01 Jul 2019, 10:52
I will try to simplify amins309's explanation to some extent:

Statement 1: The GCD of M and N is 6. Therefore, M and N must contain 2*3 and may or may not contain any other number
M = 2 * 3 * 7 (any other number or nothing at all)
N = 2 * 3 * 5 (any other number or nothing at all) --- INSUFFICIENT

Statement 2: The LCM of M and N is 36. Therefore, M and N can take the following forms:
M = 2 * 3 * 2 = 12 N=2*3*3 = 18
M = 2 * 3 * 3 = 18 N=2*2*3*3 = 36
M = 2*3*3 = 18 N= 2*2*3*3 = 36

--- INSUFFICIENT

Together (1) & (2)

In addition to this we use one more property: LCM*HCF = product of two numbers (M*N)
LCM*HCF = 36*6 = 6*6*6 ---- (1)
now in case M=12 and N= 36 --> M*N = 6*6*6*2 is not equal to (1)
Similar to M = 18 and N=36 ---> M*N = 6*6*6*3

While M = 12 and N = 18 ---> M*N = 6*6*6 = LCM*HCF
Manager
Joined: 18 Jan 2017
Posts: 127
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

05 Sep 2019, 05:50
Bunuel

Can you please provide an elaborated Solution for this problem?

Would really appreciate it if you could explain in detail as to how to think and approach such tough LCM and GCF problems?

Also, can you link some more SIMILAR QUESTIONS if it is possible.

Intern
Joined: 16 Jul 2019
Posts: 1
Re: M and N are integers such that 6<M<N.What is the value of N?  [#permalink]

### Show Tags

05 Sep 2019, 10:51
S1: if hcf is 6, let m=6a, n=6b, where a & b relatively prime.
=>6<6a<6b
=>1<a<b
Not sufficient

S2: if lcm is 36, 6ab=36;
=> ab=6,
=> a=2, b=3
=> m=2*hcf, n=3*hcf
=> Not sufficient

with S1+S2;
m=12, n=18
Sufficient
Re: M and N are integers such that 6<M<N.What is the value of N?   [#permalink] 05 Sep 2019, 10:51
Display posts from previous: Sort by