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

It is currently 15 Aug 2018, 17:27

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

Sets M and N contain exactly m and n elements, respectively.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 07 Dec 2015
Posts: 7
Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 25 Mar 2016, 05:17
5
24
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (00:44) correct 34% (00:40) wrong based on 750 sessions

HideShow timer Statistics

Sets M and N contain exactly m and n elements, respectively. What is the value of n?

(1) 7m=8n
(2) The intersection of M and N contains exactly 0.4m elements.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6521
Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 25 Mar 2016, 05:25
20
20
Gurshaans wrote:
Sets M and N contain exactly m and n elements, respectively. What is the value of n?

(1) 7m=8n
(2) The intersection of M and N contains exactly 0.4m elements.



Hi,

the Q asks us a numeric value for n..



However I gives us the ratio of m and n and II gives us the common elements in term of m again..
so NO numeric value of any kind to work on..
E

But lets see what each statements tells us..


May be helpful in some other Q..
(1) 7m=8n
m is a multiple of 8 and n is a multiple of 7

(2) The intersection of M and N contains exactly 0.4m elements.
this means common numbers are 0.4m..
so,
m has to be a multiple of 5, otherwise .4m will be decimal..


combined we can say
so both m and n are multiples of 5..
m is a multiple of 8*5=40
and n is a multiple of = 7*5=35

if we say we were told m <75.. we would have got our answer
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

General Discussion
Intern
Intern
avatar
Joined: 07 Dec 2015
Posts: 7
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 25 Mar 2016, 05:28
chetan2u Thank you!
Current Student
avatar
B
Joined: 16 Apr 2016
Posts: 1
GPA: 3.6
GMAT ToolKit User Reviews Badge
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 16 Apr 2016, 13:10
I'm a little confused - can you please explain what "the intersection of M and N contains exactly 0.4m elements" translates to algebraically? Would that mean N=0.4M? Since these are sets of numbers, it's also inherently assumed that the answer will be an integer, correct?
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6521
Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 16 Apr 2016, 20:52
3
1
jecharte wrote:
I'm a little confused - can you please explain what "the intersection of M and N contains exactly 0.4m elements" translates to algebraically? Would that mean N=0.4M? Since these are sets of numbers, it's also inherently assumed that the answer will be an integer, correct?


Hi,

Intersection of M and N consists of 0.4m elements in SET would be written as --
M\(\cap\)N = 0.4M..
so there are 0.4M elements common to M and N..
Since M and N are integers and common elements too should be integer, 0.4M should be integer..
so M has to be a multiple of 5 for 0.4M to be an integer..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Director
Director
User avatar
G
Joined: 24 Nov 2015
Posts: 554
Location: United States (LA)
Reviews Badge
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 17 Apr 2016, 05:33
after combining both statements we still don't get the answer.if we have extra info regarding m<75,then we would have got the answer as c.but correct option is E
Intern
Intern
avatar
Joined: 17 Jan 2016
Posts: 10
Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 07 May 2016, 09:21
1
chetan2u wrote:
Gurshaans wrote:
Sets M and N contain exactly m and n elements, respectively. What is the value of n?

(1) 7m=8n
(2) The intersection of M and N contains exactly 0.4m elements.



Hi,

the Q asks us a numeric value for n..



However I gives us the ratio of m and n and II gives us the common elements in term of m again..
so NO numeric value of any kind to work on..
E

But lets see what each statements tells us..


May be helpful in some other Q..
(1) 7m=8n
m is a multiple of 8 and n is a multiple of 7

(2) The intersection of M and N contains exactly 0.4m elements.
this means common numbers are 0.4m..
so,
m has to be a multiple of 5, otherwise .4m will be decimal..
so both m and n are multiples of 5..

combined we can say
m is a multiple of 8*5=40
and n is a multiple of = 7*5=35

if we say we were told m <75.. we would have got our answer


Why do both m and n need to be multiples of 5 ? Why also n ? Could you explain the "multiple of 5" part again please?
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6521
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 07 May 2016, 09:29
2
broilerc wrote:
chetan2u wrote:
Gurshaans wrote:
Sets M and N contain exactly m and n elements, respectively. What is the value of n?

(1) 7m=8n
(2) The intersection of M and N contains exactly 0.4m elements.



Hi,

the Q asks us a numeric value for n..



However I gives us the ratio of m and n and II gives us the common elements in term of m again..
so NO numeric value of any kind to work on..
E

But lets see what each statements tells us..


May be helpful in some other Q..
(1) 7m=8n
m is a multiple of 8 and n is a multiple of 7

(2) The intersection of M and N contains exactly 0.4m elements.
this means common numbers are 0.4m..
so,
m has to be a multiple of 5, otherwise .4m will be decimal..
so both m and n are multiples of 5..

combined we can say
m is a multiple of 8*5=40
and n is a multiple of = 7*5=35

if we say we were told m <75.. we would have got our answer


Why do both m and n need to be multiples of 5 ? Why also n ? Could you explain the "multiple of 5" part again please?


hi
it may have been written in statement 2, But it is meant when both statements are combined..
As 8n = 7m.. so if m is multiple of 5 n has to be a multiple of 5..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
avatar
Joined: 17 Jan 2016
Posts: 10
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 07 May 2016, 09:33
chetan2u wrote:
hi
it may have been written in statement 2, But it is meant when both statements are combined..
As 8n = 7m.. so if m is multiple of 5 n has to be a multiple of 5..


thanks for the quick help! can you explain again why m is a multiple of 5 because of 0.4m ?
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6521
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 07 May 2016, 09:39
3
1
broilerc wrote:
chetan2u wrote:
hi
it may have been written in statement 2, But it is meant when both statements are combined..
As 8n = 7m.. so if m is multiple of 5 n has to be a multiple of 5..


thanks for the quick help! can you explain again why m is a multiple of 5 because of 0.4m ?


sure..
there are m and n elements..
Also there are 0.4m common elements...
Now these elements have to be integer.. MEANING we can't have 4.5 or 5.6 elements common, it has to be an integer say 3,4, or 5 etc..
When will 0.4*m be an integer, ONLY when m is a multiple of 5, say 5x..

so 0.4 *m = 0.4*5*x = 2x, hence an integer..
m could be anything 5,10,35 or 100 but it will surely be a multiple of 5..
Hope it helps
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
avatar
Joined: 07 Apr 2016
Posts: 1
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 12 Jun 2016, 06:33
Sir,

I have a question regarding the below solution by you. Specifically in the last line where if m,75 was mentioned we would have gotten our answer. How so?
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6521
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 12 Jun 2016, 06:40
1
prakhar4 wrote:
Sir,

I have a question regarding the below solution by you. Specifically in the last line where if m,75 was mentioned we would have gotten our answer. How so?


Hi Prakhar,

we have got m as a multiple of 40 and n as a multiple of 35...
since intersection is 0.4m, we can say that m and n are \(\neq{0}\)..

so if we were given m<75, ONLY 40 would have fit in as next multiple of 40 is 80, which would have >75..
and 7m = 8n....
so 7*40 = 8n......n =35


that is why suff..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
avatar
Joined: 20 May 2014
Posts: 8
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 20 Jun 2016, 17:23
The question is asking for a specific value of n.
Statement 1: This is a ratio, so clearly insufficient.
Statement 2: Another ratio, you don't know m and this statement says nothing about n.

1+2: From statement 1: \(m = \frac{8}{7}n\) and using statement 2: Intersection contains: \(0.4(\frac{8}{7}n)\) elements. Doesn't really tell you anything about n, so answer is E.
If you look at it from a higher level both statements give you some sort of ratio info, while the question is asking for a value. You can't get a value from just ratio info.
Current Student
avatar
Joined: 21 Apr 2016
Posts: 29
Location: United States
GMAT ToolKit User Reviews Badge
Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 29 Aug 2016, 12:27
chetan2u wrote:

if we say we were told m <75.. we would have got our answer


Great explanation, thank you!

However, I have one question about the above quoted bit...

After combining both statements, we know that
M---> Multiple of 7 AND a multiple of 5
N---> Multiple of 8
M/N are in the ratio of 8/7... So for ex if M = 7 x 5, then N= 8 x 5 (giving us values of M=35 and N=40)

Using this logic, we can have M= 7 x 10 , then N= 8 x 10 (giving us values of M=70 and N=80)

Therefore even if we were given m<75, we will still have 2 values..??

I think I am misunderstanding something maybe, can you please help to point out my misunderstanding?

Thanks :)
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6521
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 30 Aug 2016, 03:56
18967mba wrote:
chetan2u wrote:

if we say we were told m <75.. we would have got our answer


Great explanation, thank you!

However, I have one question about the above quoted bit...

After combining both statements, we know that
M---> Multiple of 7 AND a multiple of 5
N---> Multiple of 8
M/N are in the ratio of 8/7... So for ex if M = 7 x 5, then N= 8 x 5 (giving us values of M=35 and N=40)

Using this logic, we can have M= 7 x 10 , then N= 8 x 10 (giving us values of M=70 and N=80)

Therefore even if we were given m<75, we will still have 2 values..??

I think I am misunderstanding something maybe, can you please help to point out my misunderstanding?

Thanks :)


Hi,
you have understood the method but going wrong on inference from 7m=8n...
This tells us that n and NOT m, is multiple of7.....
M is s multiple of 8, as m= n*8/7....so n is multiple of 7
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Current Student
avatar
Joined: 21 Apr 2016
Posts: 29
Location: United States
GMAT ToolKit User Reviews Badge
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 30 Aug 2016, 04:57
chetan2u wrote:
18967mba wrote:
chetan2u wrote:

if we say we were told m <75.. we would have got our answer


Great explanation, thank you!

However, I have one question about the above quoted bit...

After combining both statements, we know that
M---> Multiple of 7 AND a multiple of 5
N---> Multiple of 8
M/N are in the ratio of 8/7... So for ex if M = 7 x 5, then N= 8 x 5 (giving us values of M=35 and N=40)

Using this logic, we can have M= 7 x 10 , then N= 8 x 10 (giving us values of M=70 and N=80)

Therefore even if we were given m<75, we will still have 2 values..??

I think I am misunderstanding something maybe, can you please help to point out my misunderstanding?

Thanks :)


Hi,
you have understood the method but going wrong on inference from 7m=8n...
This tells us that n and NOT m, is multiple of7.....
M is s multiple of 8, as m= n*8/7....so n is multiple of 7


Yes! Thank you!! I understand now why if m<75, we would have a unique ans..
Because if M was 8x(2)x5 = 80, that is > 75! Therefore, we are only left with M=8x(1)x5 = 40! (And subsequently N=7x(1)x5 = 35!
:)
Manager
Manager
avatar
B
Joined: 08 Nov 2015
Posts: 80
GMAT 1: 460 Q32 V22
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 08 Jan 2017, 00:06
Lettherebelight wrote:
Sets M and N contain exactly m and n elements, respectively. What is the value of n?

(1) 7m=8n
(2) The intersection of M and N contains exactly 0.4m elements.


From 1, the LCM of 7 and 8 is 56, so you can plugin either 8 or 7 in the first equation to get the value. However since LCM is 56, the value can be any multiple of 56.
For example 7(*8*4) = 8(*7*4), n can be any value 7, 14, 28 etc hence not sufficient.

From 2, intersection of both elements is 0.4m and we know nothing about the value of m hence this not sufficient as well.

Taking 1 and 2, does not help us in answering the question. Hence insufficient.

Answer is E.
Manager
Manager
avatar
S
Joined: 17 Aug 2015
Posts: 115
GMAT 1: 650 Q49 V29
Reviews Badge
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 23 Mar 2017, 19:14
1 ) n= 7, 14,21, 28,35, ... 70........105

m= 8, 16, 24,32, 40......80 ----- 120


2) common = .4m and it should be integer so it can be integer for m= 40 , 80, 120 so on... so n can be 35, 70, 105.... multiple value

answer is E
Intern
Intern
avatar
B
Joined: 24 Sep 2017
Posts: 20
Location: Brazil
GMAT 1: 710 Q49 V37
WE: General Management (Computer Software)
Re: Sets M and N contain exactly m and n elements, respectively.  [#permalink]

Show Tags

New post 17 Dec 2017, 11:38
Hello,

Another way to see the second statement:
(1) m : n = 8 : 7
(2) Think about groups, so: m + (n - 0.4m) = T (total of elements) => 0.6m + n = T

(1-2) Substitute (1) in (2): 0.6 x 8n/7 = T
n and T are variables, but we have just one equation to solve it. Hence, insufficient.

Best,
Re: Sets M and N contain exactly m and n elements, respectively. &nbs [#permalink] 17 Dec 2017, 11:38
Display posts from previous: Sort by

Sets M and N contain exactly m and n elements, respectively.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.