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A sum of $200,000 from a certain estate was divided

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A sum of $200,000 from a certain estate was divided

by late4thing » Fri Oct 16, 2015 8:38 am
A sum of $200,000 from a certain estate was divided among a spouse and three children. How much of the estate did the youngest child receive?

(1) The spouse received 1/2 of the sum from the estate, and the oldest child received 1/4 of the remainder.
(2) Each of the two younger children received $12,500 more than the oldest child and $62,500 less than the spouse.


Please explain.
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by [email protected] » Fri Oct 16, 2015 10:07 am
Hi late4thing,

Certain Quant questions become easier to deal with IF you can find a way to work with fewer variables.

After reading the initial prompt, there are 4 variables: the spouse and each of the 3 children. We're told that the sum of those 4 numbers is $200,000. We're asked for the amount that the YOUNGEST child received.

I'm going to list the initial variables as...
V = spouse
X = oldest child
Y = middle child
Z = youngest child

So, V+X+Y+Z = 200,000 and we're trying to figure out the value of Z.

1) The spouse received 1/2 of the sum from the estate, and the oldest child received 1/4 of the remainder.

From this, we know that...
V = (1/2)(200,000) = 100,000
X = (1/4)(100,000) = 25,000

This leaves us with Y+Z = 75,000 but we do NOT know the value of Z.
Fact 1 is INSUFFICIENT

2) Each of the two younger children received $12,500 more than the oldest child and $62,500 less than the spouse.

With this information, we can actually write a gigantic equation with just ONE variable.

The two youngest children received the same amount, so Z = Y.

They received 12,500 more than the oldest child, so Z = Y = X+12,500.

They received 62,500 less than the spouse, so Z = Y = X+12,500 = V - 62,500

All of this can be rewritten; instead of...

V+X+Y+Z = 200,000

we have....

(Z+62,500) + (Z-12,500) + Z + Z = 200,000

This is one variable and one equation, so we can solve it (and there will be just one answer).
Fact 2 is SUFFICIENT

Final Answer: B

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by MartyMurray » Fri Oct 16, 2015 9:12 pm
late4thing wrote:A sum of $200,000 from a certain estate was divided among a spouse and three children. How much of the estate did the youngest child receive?

(1) The spouse received 1/2 of the sum from the estate, and the oldest child received 1/4 of the remainder.
(2) Each of the two younger children received $12,500 more than the oldest child and $62,500 less than the spouse.
Statement 1 tells us that 3/4 of the estate went to two of the inheritors. 1/4 is left and we don't have any indication of how much of that 1/4 went to each of the other children.

So Statement 1 is insufficient.

Statement 2 tells us that the two younger children got the same amount. The two younger children includes the youngest. So we are good so far.

We could make the mistake of thinking that we should combine the information that the two younger children got the same amount with the information in Statement 1 and choose C, but let's see if Statement 2 works on its own. It looks as if it will.

Let's see what happens if we clearly outline what Statement 2 is telling us.

Calling the amount the younger children got Y, we get Y + Y + (Y - 12,500) + (Y + 62,500) = 200,000.

So 4Y + 50,000 = 200,000.

We could figure out Y from this. So Statement 2 on its own is sufficient and the answer is B.
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by Max@Math Revolution » Wed Oct 21, 2015 11:20 am
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.

A sum of $200,000 from a certain estate was divided among a spouse and three children. How much of the estate did the youngest child receive?

(1) The spouse received 1/2 of the sum from the estate, and the oldest child received 1/4 of the remainder.
(2) Each of the two younger children received $12,500 more than the oldest child and $62,500 less than the spouse.

In the original condition, the age is arranged x(child)<y(child)<z(child)<s(spouse), and x+y+z+s=200,000, and we want to know the value of x
There are 4 variables, which requires us to have 4 equations. One is given from the original condition, so we require 3 more.
From condition 2, x=12,500+z, x=s-62,500, x=y, so 3 equations are given so this is sufficient.
For condition 1, s=(x+y+z+s)/2, z=(x+y+z+s)/2(1/4). This only gives 2 equations so is insufficient, and the answer becomes (B).

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