It is actually very simple question but trick is hidden in its text. So lets try to solve this interesting puzzle.
From the question stem we know that,
Sum of Money = $ 200,000 = M
Number of beneficiaries = 4
Who are the beneficiaries?
Ans: One Spouse, and three childern
Lets assign the variables to these people.
Spouse = S
(Children in decreasing order of their age)
1st Child = Fc
2nd Child = Sc
3rd Child = Tc
So,
S + Fc + Sc + Tc = 200,000
Now let's take condition (1).
S = M/2 = $ 100,000
Fc = (1/4) (M/2) = M/8 = $ 12,500
Now the remaining money should be divided between Sc and Tc. But there is no condition provided how it should be divided among them. So, we can't say how much Tc is going to get.
Hence Statement (1), INSUFFICIENT.
I hope till now it must be clear to you why your selected answer is wrong.
Now let's concentrate on statement (2):
It states that two younger children (that is: Sc + Tc) receives $12,500 more than Fc.
Sc + Tc = Fc + 12,500
AND
It also states that the two younger children receives $62,500 less than spouse.
Sc + Tc = S - 62,500
Now as we know that, S + Fc + Sc + Tc = 200,000
Now as there are 4 variables in the above equation and both Fc and S are in a equal relation to Sc and Tc, so it means that both Sc and Tc going to share the equal amount of money. I know, its bit difficult to understand this concept, but this is the fact and you need to digest it.
So lets consider, Sc = Y. Therefore, Tc = Y
Hence,
2Y = Fc + 12500 ----> Equation 1
and
2Y = S - 62500 ----> Equation 2
and also,
2Y + S + Fc = 200000 ----> Equation 3
Now add equation 1 and equation 2,
4Y = S + Fc - 50000
It means, S + Fc = 4Y + 50000
Place the value in equation 3,
2Y + 4Y + 50000 = 200000
Now from here you can easily compute the value of Y (that is the youngest child's share).
Hence Statement (2) is alone SUFFICIENT.
Hope this helps...
Featured Course
