A sum of $270,000 from a certain estate was divided among four childre

Question

A sum of $270,000 from a certain estate was divided among four children. How much of the estate did the oldest child receive?
 
(1) The two younger children together received half of the estate.
(2) The oldest and the youngest of the children together received $175,000.

RR88 · Answer

Option E

270,000$ to be divided among 4 children : A, B, C & D  .
How much A got?

I: C + D = 135,000
i.e., A + B = 135,000. Insufficient.

II: A + D = 175,000
i.e., B + C = 95,000. Insufficient.

I + II: 
C + D = 135,000
A + B = 135,000
A + D = 175,000
B + C = 95,000
Insufficient.

kanaav · Answer

Hi  Bunuel  is it safe to say the option is not c because it doesn't state the in the first stem, the estate was divided equally?

Bunuel · Answer

This is not the only reason. If we knew that the estate was divided equally, then we would not need the statements to answer the question.

When combined we have:

a + b + c + d = 270 (from the stem) (the order is from oldest to youngest)
c + d = 135 (from the first statement)
a + d = 175 (from the second statement)

We want the value of a, which we cannot get from the equation above.

amanvermagmat · Answer

Statement 1. The older two children received the other half (1/2 * 270000 = 135000 combined) but we don't know how that was divided between those two. So Insufficient.

Statement 2. Sum total of eldest and youngest is 175000, but again we don't know how that 175000 has been divided between them. So Insufficient.

Combining the two statements: Youngest and second youngest together have 135000, but out of this how much youngest one has we don't know. So we cannot answer the share of youngest and eldest out of the 175000 that they have together.

Insufficient still. Hence  E answer

JeffTargetTestPrep · Answer

We can let a = the amount received by the oldest child, b = the amount received by the second oldest, c = the amount received by the third oldest, and d = the amount received by the fourth oldest. Since the total was 270,000, we have:

a + b + c + d = 270,000

We need to determine the value of a.

Statement One Alone:

The two younger children together received half of the estate.

Since the two younger children received half of the estate, c + d = 135,000. However, we still cannot determine the value of a. Statement one alone is not sufficient.

Statement Two Alone:

The oldest and the youngest of the children together received $175,000.

Since the oldest and the youngest of the children together received $175,000, a + d = 175,000. However, we still cannot determine a.

Statements One and Two Together:

We have the following three equations:

a + b + c + d = 270,000

c + d = 135,000

a + d = 175,000

However, without any further information on b, we cannot determine a.

Answer: E

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A sum of $270,000 from a certain estate was divided among four childre

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