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

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There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

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24 Feb 2016, 10:29
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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.
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Re: There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

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24 Feb 2016, 22:34
1

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.

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There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

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Updated on: 23 Nov 2019, 22:40
1
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.

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.
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Re: There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

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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.

 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.
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Re: There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

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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
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Re: There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

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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
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Re: There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

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20 Dec 2019, 05:45
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.

Average=Sum/Num of terms
20=x/n, x=20n

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

(22+28+20n)/(n+2)=20+p, 50+20n=(20+p)(n+2), 50+20n=20n+40+pn+2p,
10=pn+2p, 10=p(n+2), n+2=10/p; 10/p=integer, so p={5 or 2};
p=5: n+2=10/p, n+2=10/5, n+2=2, n=0; invalid.
p=2: n+2=10/p, n+2=10/2, n+2=5, n=3; valid.

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

(20n-50)/(n-2)=20-p, 20n-50=(20-p)(n-2), -50=-40-pn+2p,
-10=-pn+2p, -10/p=p(2-n), 2-n=-10/p; -10/p=integer, so p={5 or 2};
p=5: 2-n=-10/p, 2-n=-2, n=2+2=4; valid.
p=2: 2-n=-10/p, 2-n=-5, n=2+5=7; valid.

Ans (A)
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Re: There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

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25 Dec 2019, 01:10
chetan2u 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.
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

Hello,

Can you explain me why do you do the calculation ?

I mean I know that 10/(N-2) and 10/(N+2) should be prime => so they are divisible by themselves of one.

But why did you do : N+2 = 2... N = 0 OR N+2 = 5
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Re: There are N men in a group. Their average age is 20 years. Find N.  [#permalink]

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25 Dec 2019, 17:37
Let me explain this concept.
K is prime no.

St. 1

10 = k(n+2)
10= (1*10) or (2*5)

So (1, 10) will not be applicable here.
Now 2*5 = k(n+2)
N is positive integer and n+2 is greater than 2 clearly.
Therefore, k = 2, n+2 = 5 which will give you n= 3

Sufficient.

St. 2
Simplified version.
10= k(n-2)
Again here (1,10) will not be correct.
Now 2*5 = k(n-2)
If k =2, n will be 7
If k=5 n will be 4

Not sufficient.

CharlesGSE wrote:
chetan2u 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.
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

Hello,

Can you explain me why do you do the calculation ?

I mean I know that 10/(N-2) and 10/(N+2) should be prime => so they are divisible by themselves of one.

But why did you do : N+2 = 2... N = 0 OR N+2 = 5
Re: There are N men in a group. Their average age is 20 years. Find N.   [#permalink] 25 Dec 2019, 17:37
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