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

BTGmoderatorDC wrote:A sum of $200,000 from a certain estate was divided among a spouse and three children. How much 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 reminder
(2) Each of the two younger children received 12,500 more than the oldest child and 62500 less than the spouse

OA B

Source: Official Guide

Given: A sum of $200,000 was divided among a spouse and three children

Question: How much did the youngest child receive?

Let's take each statement one by one.

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

Say the total sum is $1. The spouse received $1/2; thus, the remainder = 1/2. Thus, the oldest child received 1/4 of 1/2 = $1/8. The sum remaining = 1/2 - 1/8 = 3/8 -- to be divided between the two younger children. We do not have any information about how the 3/8th part is divided between the two. Insufficient.

(2) Each of the two younger children received 12,500 more than the oldest child and 62500 less than the spouse.

Say Spouse gets $S, the oldest child gets $x, the younger child gets $y and the youngest child gets $z.

We have to get the value of z.

Thus, s + x + y + z = 200000

As per the information, y = z = x + 12500 = s - 62500

Plugging-in the value of y and z, in s + x + y + z = 200000, we get s + x + (x + 12500) + (x + 12500) = 200000

From x + 12500 = s - 62500, we get s = x + 75000

Plugging-in the value of s = x + 75000 in s + x + (x + 12500) + (x + 12500) = 200000, we get

(x + 75000) + x + (x + 12500) + (x + 12500) = 200000

This is a linear equation is x and is such that x does not vanish

, thus, we get the unique value of and from z = x + 12500, we get the unique value of z. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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