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

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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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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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There are N men in a group. Their average age is 20 years. Find N. [#permalink]
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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 freedom128 on 23 Nov 2019, 17:04.
Last edited by freedom128 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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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]
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]
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]
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
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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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Re: There are N men in a group. Their average age is 20 years. Find N. [#permalink]
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