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

It is currently 08 Dec 2019, 01:24

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

There are N men in a group. Their average age is 20 years. Find N.

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 25 Jun 2014
Posts: 42
GMAT 1: 690 Q48 V37
WE: Operations (Computer Software)
There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

Show Tags

New post 24 Feb 2016, 10:29
6
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

29% (03:09) correct 71% (02:33) wrong based on 77 sessions

HideShow timer Statistics

There are N men in a group. Their average age is 20 years. Find N.

I ) If 2 men aged 22 years and 28 years join the group, the average age of the group increases by a prime number.

II) If 2 men aged 22 years and 28 years leave the group, the average age of the group decreases by a prime number.
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

Show Tags

New post 24 Feb 2016, 22:25
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There are N men in a group. Their average age is 20 years. Find N.

I ) If 2 men aged 22 years and 28 years join the group, the average age of the group increases by a prime number.

II) If 2 men aged 22 years and 28 years leave the group, the average age of the group decreases by a prime number.


In the original condition, there is 1 variable(n), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
(p=prime) For 1), 20n+50=(20+p)(n+2)=20n+40+pn+2p -> p(n+2)=10 -> p=2, n=3, which is unique and sufficient.
For 2), 20n-50=(20-p)(n-2)=20n-40-pn+2p -> p(n-2)=10 -> (p,n)=(2,7),(5,4), which is not unique and not sufficient.
Therefore, the answer is A.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Intern
avatar
Joined: 03 Sep 2014
Posts: 3
Schools: Duke '19 (S)
Re: There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

Show Tags

New post 24 Feb 2016, 22:34
1
Answer should be (A)

Statement A: If 2 men aged 22 years and 28 years join the group, the average age of the group increases by a prime number
Equation:
(20N + 50)/(N+2) can be {20 + 2, 20 +3}

It cannot be >= 25 as it would mean N <= 0

solving equations for N:
(20N + 50)/(N+2) = 22... (1)
(20N + 50)/(N+2) = 23... (2)

Only equation (1) results in integer value of N (=3)...
Hence statement A is sufficient.

Statement B:If 2 men aged 22 years and 28 years leave the group, the average age of the group decreases by a prime number

Similarly we can make equations for this statement as well:

(20N - 50)/(N-2) can be one of {20-2, 20-3, 20-5, 20-7, 20-11, 20-13, 20-17, 20-19} => {18,17, 15,13,9,7,3,1}

Solving each equation we get two integer values of N:
N=7 for 18
and N=4 for 15... clearly insufficient.

Hence Answer is (A)
Director
Director
User avatar
P
Joined: 18 Dec 2017
Posts: 826
Location: United States (KS)
Premium Member CAT Tests
Re: There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

Show Tags

New post 23 Nov 2019, 10:45
Mesto wrote:
There are N men in a group. Their average age is 20 years. Find N.

I ) If 2 men aged 22 years and 28 years join the group, the average age of the group increases by a prime number.

II) If 2 men aged 22 years and 28 years leave the group, the average age of the group decreases by a prime number.


I solved for A. Got N=3 considering the prime age increase as 2. For increase of 3, we got non integer N and for increase of 5 we nullify the equation. Trying greater values won't work.

Sufficient.

I was at 2 minutes mark. So answer is either A or D.

For Statement 2, we will decrease the value by prime number so (N+2) will be multiplied by 18,17,15 and so on. Since there are definitely more than likely values possible I marked A.
In the actual exam may be you should solve and get 2 values to confidently mark A
_________________
D-Day : 21st December 2019

The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long

Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic
You are missing on great learning if you don't know what this is: Project SC Butler
Senior Manager
Senior Manager
avatar
D
Joined: 30 Sep 2017
Posts: 451
GMAT 1: 720 Q49 V40
GPA: 3.8
Premium Member Reviews Badge
There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

Show Tags

New post Updated on: 23 Nov 2019, 22:40
There are N men in a group. Their average age is 20 years. Find N.

(1) If 2 men aged 22 years and 28 years join the group, the average age of the group increases by a prime number

Eq. (20N + 50)/(N+2) = 22, 23, or 25, where N is a positive integer. We only need to test 22, 23 and 25 to validate possible N value.

Only (20N + 50)/(N+2) = 22 yields a positive integer N (=3). The rests fail.

SUFFICIENT

(2) If 2 men aged 22 years and 28 years leave the group, the average age of the group decreases by a prime number

Eq. (20N - 50)/(N-2) =18, 17, or 15, where N is a positive integer. We only need to test 18, 17 and 15 to validate possible N value.

(20N - 50)/(N-2) = 18 or 15 yields a positive integer N. N can be 7 or 4.

NOT SUFFICIENT.

Hence ANSWER is (A)

Btw. Just a critique: this question is not GMAT-like, because N in both statements yields different result: 3 vs (7 or 4). Such thing actually never happens in real GMAT.

Posted from my mobile device

Originally posted by chondro48 on 23 Nov 2019, 17:04.
Last edited by chondro48 on 23 Nov 2019, 22:40, edited 1 time in total.
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8288
Re: There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

Show Tags

New post 23 Nov 2019, 20:46
There are N men in a group. Their average age is 20 years. Find N.

I ) If 2 men aged 22 years and 28 years join the group, the average age of the group increases by a prime number.
So 2 joining the group increases the average by \(\frac{(28-20)+(28-20)}{N+2}=\frac{10}{N+2}\)
Now this should be a prime number, that is 10/(N+2) is prime.
As 10=2*5, the increase can be 2 or 5, and also N+2=2...N=0 OR N+2=5....N=3
Sufficient

II) If 2 men aged 22 years and 28 years leave the group, the average age of the group decreases by a prime number.
In the similar manner as above 10/(N-2) should be prime.
So N-2=2...N=4 OR N-2=5.....N=7
Two possibilities....Insuff

A, but both statements give different possible answers
_________________
GMAT Club Bot
Re: There are N men in a group. Their average age is 20 years. Find N.   [#permalink] 23 Nov 2019, 20:46
Display posts from previous: Sort by

There are N men in a group. Their average age is 20 years. Find N.

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





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