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

It is currently 15 Nov 2019, 13:57

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

If all the N students of a class are classified into groups of either

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

Hide Tags

Find Similar Topics 
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3142
If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post Updated on: 12 Aug 2018, 23:52
29
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

11% (02:50) correct 89% (02:35) wrong based on 205 sessions

HideShow timer Statistics

e-GMAT Question of the Week #2

If all the N students of a class are classified into groups of either n, or (n+1), or (n+2) students, every time 3 students are left out and cannot be included in any of those groups formed. What is the value of N?

    1. N is between 7 and 70
    2. n is the smallest number with exactly 3 distinct factors


To access all the questions: Question of the Week: Consolidated List

Image

_________________

Originally posted by EgmatQuantExpert on 07 Jun 2018, 22:31.
Last edited by EgmatQuantExpert on 12 Aug 2018, 23:52, edited 5 times in total.
Most Helpful Expert Reply
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3142
If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 12 Jun 2018, 02:09
1
2

Solution



Given:
    • If all the N students of a class are classified into groups of either n, or (n + 1), or (n + 2) students, every time 3 students are left out and cannot be included in any of those groups formed

To find:
    • What is the value of N

Analysing Statement 1
    • As per the information provided in statement 1, N is between 7 and 70

As every time 3 students are left, the value of n is greater than 3
    • If we take n = 4, number of students = k. LCM (4, 5, 6) + 3 = 60k + 3
      o As N is between 7 and 70, the only possible value is 63, when k = 1

For any other values of n, the value of N does not lie in between 7 and 70

Hence, statement 1 is sufficient to answer

Analysing Statement 2
    • As per the information provided in statement 2, n us the smallest number with exactly 3 distinct factors

When a number has exactly 3 distinct factors, it is the square of a prime number

The smallest of such numbers = 4
Therefore, we can say the values of N will be in the form k. LCM (4, 5, 6) + 3 or 60k + 3
    • If k = 1, N = 63
    • If k = 2, N = 123
    • If k = 3, N = 183 and so on

As we don’t know the exact value of k, we can’t find out the exact value of N

Hence, statement 2 is not sufficient to answer

Hence, the correct answer is option A.

Answer: A

Important Observation


This question is an example where one can easily conclude that statement 1 is not sufficient or statement 2 is sufficient to answer, without observing the inferences present in the statements.

    • As per statement 1, in the given range only one value is possible. One needs to check whether any other possibilities exist or not - if not then this statement is giving us a unique answer, and hence, sufficient to answer.

    • As per statement 2, although one can conclude n = 4, it only helps us in obtaining the general form of N. the number 63 is only one of the possible cases and not necessarily the only case.

Image

_________________
General Discussion
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1271
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 07 Jun 2018, 22:53
If all the N students of a class are classified into groups of either n, or (n+1), or (n+2) students, every time 3 students are left out and cannot be included in any of those groups formed. What is the value of N?

Since all the N students of a class are classified into groups of either n, or (n+1), or (n+2) students, it means N = Multiple of LCM of n, (n+1), & (n+2).
since we do not know n, LCM cannot be found, only we know that LCM is multiple of 3! or 6

1. N is between 7 and 70.
since n is not known, N cannot be found. INSUFFICIENT

2. n is the smallest number with exactly 3 distinct factors
n = 2^2 = 4, So N is multiple of LCM of 4,5,6 or multiple of 60.
N can be 60, (57 is not divisible by 4,5,6) or 120 (57 is not divisible by 4,5,6).
Value of N cannot be uniquely determined, INSUFFICIENT

Combining Statement 1 & 2, we get N = multiple of LCM of 60 and N is between 7 and 70.
Hence N = 60.
SUFFICIENT

Answer C
_________________
Manager
Manager
avatar
B
Joined: 09 Oct 2015
Posts: 224
Re: If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 07 Jun 2018, 23:21
2
assuming this question means that the remainder when N is divided by n, n+1 or n+2 is 3, we can calculate N by finding out the LCM of these 3 numbers.

First of all n has to be greater than 3, as the remainder itself is 3.

First set- 4,5,6 LCM = 60. N= 60+3= 63.
Second set - 5,6,7 LCM= 210 . N = 210+3.
and so on

As A says N is between 7 and 70, only one set, i.e. 4 , 5 and 6 is suitable for this, hence the answer is A.

B says n( the first number) is a perfect square, i.e. n is 4,9,25,36, and so on. Multiple sets can be formed.

A should be the answer
Manager
Manager
avatar
B
Joined: 09 Oct 2015
Posts: 224
Re: If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 07 Jun 2018, 23:25
gmatbusters wrote:
If all the N students of a class are classified into groups of either n, or (n+1), or (n+2) students, every time 3 students are left out and cannot be included in any of those groups formed. What is the value of N?

Since all the N students of a class are classified into groups of either n, or (n+1), or (n+2) students, it means N = Multiple of LCM of n, (n+1), & (n+2).
since we do not know n, LCM cannot be found, only we know that LCM is multiple of 3! or 6

1. N is between 7 and 70.
since n is not known, N cannot be found. INSUFFICIENT

2. n is the smallest number with exactly 3 distinct factors
n = 2^2 = 4, So N is multiple of LCM of 4,5,6 or multiple of 60.
N can be 60, (57 is not divisible by 4,5,6) or 120 (57 is not divisible by 4,5,6).
Value of N cannot be uniquely determined, INSUFFICIENT

Combining Statement 1 & 2, we get N = multiple of LCM of 60 and N is between 7 and 70.

Hence N = 60.
SUFFICIENT

Answer C


for a) take examples. 4,5,6 or 5,6,7. You will see that only one set satisfies this requirement, i.e. 4,5,6
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1271
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 08 Jun 2018, 02:44
1
You are right, I missed it.
but N should be 60 not 63.

rahulkashyap wrote:
assuming this question means that the remainder when N is divided by n, n+1 or n+2 is 3, we can calculate N by finding out the LCM of these 3 numbers.

First of all n has to be greater than 3, as the remainder itself is 3.

First set- 4,5,6 LCM = 60. N= 60+3= 63.
Second set - 5,6,7 LCM= 210 . N = 210+3.
and so on

As A says N is between 7 and 70, only one set, i.e. 4 , 5 and 6 is suitable for this, hence the answer is A.

B says n( the first number) is a perfect square, i.e. n is 4,9,25,36, and so on. Multiple sets can be formed.

A should be the answer


Posted from my mobile device
_________________
Manager
Manager
avatar
B
Joined: 09 Oct 2015
Posts: 224
Re: If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 08 Jun 2018, 02:59
gmatbusters wrote:
You are right, I missed it.
but N should be 60 not 63.

rahulkashyap wrote:
assuming this question means that the remainder when N is divided by n, n+1 or n+2 is 3, we can calculate N by finding out the LCM of these 3 numbers.

First of all n has to be greater than 3, as the remainder itself is 3.

First set- 4,5,6 LCM = 60. N= 60+3= 63.
Second set - 5,6,7 LCM= 210 . N = 210+3.
and so on

As A says N is between 7 and 70, only one set, i.e. 4 , 5 and 6 is suitable for this, hence the answer is A.

B says n( the first number) is a perfect square, i.e. n is 4,9,25,36, and so on. Multiple sets can be formed.

A should be the answer


Posted from my mobile device



N has to be 63 and not 60, as 60 divided by 4,5 and 6 gives a remainder of 0. 63 gives a remainder of 3 when divided by all the 3 numbers, and that is what we need
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1271
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 08 Jun 2018, 04:19
yes it has to be multiple of 4, 5 and 6.

Question is that if 3 are removed, then it should not be divisible by n, n+1, n+2.

60-3 = 57 is not divisible by 4,5 or 6.

rahulkashyap wrote:
gmatbusters wrote:
You are right, I missed it.
but N should be 60 not 63.

rahulkashyap wrote:
assuming this question means that the remainder when N is divided by n, n+1 or n+2 is 3, we can calculate N by finding out the LCM of these 3 numbers.

First of all n has to be greater than 3, as the remainder itself is 3.

First set- 4,5,6 LCM = 60. N= 60+3= 63.
Second set - 5,6,7 LCM= 210 . N = 210+3.
and so on

As A says N is between 7 and 70, only one set, i.e. 4 , 5 and 6 is suitable for this, hence the answer is A.

B says n( the first number) is a perfect square, i.e. n is 4,9,25,36, and so on. Multiple sets can be formed.

A should be the answer


Posted from my mobile device



N has to be 63 and not 60, as 60 divided by 4,5 and 6 gives a remainder of 0. 63 gives a remainder of 3 when divided by all the 3 numbers, and that is what we need

_________________
Manager
Manager
avatar
B
Joined: 09 Oct 2015
Posts: 224
Re: If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 08 Jun 2018, 04:28
57 does not give the same remainder (3) when it is divided by 4,5, and 6 individually
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1271
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 08 Jun 2018, 05:02
Manager
Manager
avatar
B
Joined: 02 Jul 2017
Posts: 67
CAT Tests
Re: If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 08 Jun 2018, 09:55
Given : Total students are N , if we divide them in three groups of n ,(n+1) & (n+2) ..every time 3 students are left or remainder is 3 and it can not be included in any group ..that means n>3 .

Approach : N=L.C.M of{ n ,(n+1) & (n+2) }+3

or N-3 = L.C.M of { n ,(n+1) & (n+2) }

Let us check individual statements
Statement 1: N is B/W 7 and 70 ; or N-3 is B/W 4 & 67
minimum possible value of n can be 4 ..as inferred from the problem statement
With n=4 we have N-3= LCM of 4 ,5 & 6 ...=60 ..satisfies the constraint ...let us keep
Let us check for n=5 N-3=LCM of 5,6 & 7 ...=210 ...does not satisfy the constraint ...
We can say only possible value of n is 4 ...and hence N is 63...statement 1 is sufficient ..

Let us see statement 2 ..which gives additional information of n is the smallest number with exactly three distinct factors ..inferring n must be a positive integer as number of students can be a positive integer only ..
n=P1^a*P2^b.. ..number of distinct factors are (a+1)(b+1)=1*3
a+1=1 ; and b+1=3
a=0 and b=2...power is two and the smallest prime number is 2 ...hence n must be 2^2=4....hence statement 2 alone is sufficient ..
N is = LCM of 4 , 5 & 6 +3 =63
Hence answer is D ..

Please kudos my effort/post if it helps ..
Director
Director
User avatar
P
Joined: 14 Dec 2017
Posts: 510
Location: India
Re: If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 08 Jun 2018, 10:23
EgmatQuantExpert wrote:
e-GMAT Question of the Week #2

If all the N students of a class are classified into groups of either n, or (n+1), or (n+2) students, every time 3 students are left out and cannot be included in any of those groups formed. What is the value of N?

    1. N is between 7 and 70
    2. n is the smallest number with exactly 3 distinct factors


Given N = nk + 3
N = (n+1)p + 3
N = (n+2)q + 3

Hence N = LCM of (n, (n+1), (n+2)) * x + 3

Also n>3, lets say n =4, then LCM of (4,5,6) is 60, hence N = 60x + 3 = 63, 123, 183,...etc.
lets say n = 5, then LCM of (5,6,7) = 210, hence N = 210x +3 = 213, 423,...etc,
similarly for other consecutive numbers.

Statement 1: 7<N<70
From our upfront work, we can see that N = 60(1) + 3 = 63, is the only # that satisfies constraint of statement 1.

Hence Statement 1 alone is Sufficient.

Statement 2:
n is the smallest number with three distinct factors.

Hence n is a square of a prime number & since it needs to be the smallest, \(n = 2^2 = 4\)
So from our upfront work, we can say N = 60x + 3 = 63, 123, 183,...etc.

Statement 2 gives multiple values of N.

Hence Statement 2 alone is Insufficient.

Answer A.
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13585
Re: If all the N students of a class are classified into groups of either  [#permalink]

Show Tags

New post 29 Jun 2019, 06:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: If all the N students of a class are classified into groups of either   [#permalink] 29 Jun 2019, 06:33
Display posts from previous: Sort by

If all the N students of a class are classified into groups of either

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





cron

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