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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.
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.
24 Feb 2016, 22:25
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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.
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.
24 Feb 2016, 22:34
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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)
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)
