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3 children’s ages are consecutive even numbers. What is th

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3 children’s ages are consecutive even numbers. What is th

by Max@Math Revolution » Sat Feb 20, 2016 10:45 pm
3 children's ages are consecutive even numbers. What is the oldest child's age?

1) The youngest child is 2 years old.
2) After 6 years, their average age will be 2.5 times more than now.


* A solution will be posted in two days.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Tue Feb 23, 2016 5:40 pm
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.

3 children's ages are consecutive even numbers. What is the oldest child's age?

1) The youngest child is 2 years old.
2) After 6 years, their average age will be 2.5 times more than now.


In the original condition, their ages can be (2n-2), 2n,(2n+2), which makes 1 variable(n). In order to match with the number of equations, you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), n=2 is derived from 2n-2=2, which is unique and sufficient.
For 2), n=2 is derived from 2n+6=2.5(2n), which is unique and sufficient.
Therefore, D is the answer.


� 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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