Amount received by the youngest child

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Deepthi Subbu: Master | Next Rank: 500 Posts; Posts: 298; Joined: Tue Feb 16, 2010 1:09 am; Thanked: 2 times; Followed by:1 members

Amount received by the youngest child

by Deepthi Subbu » Tue Jan 18, 2011 10:27 pm

A sum of 200000 from a certain estate was divided among a spouse and 3 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 younger children received $12500 more than the oldest child and $62500 less than the spouse.

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Source: Beat The GMAT — Data Sufficiency | Tue Jan 18, 2011 10:27 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Tue Jan 18, 2011 11:57 pm

Deepthi Subbu wrote:A sum of 200000 from a certain estate was divided among a spouse and 3 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 younger children received $12500 more than the oldest child and $62500 less than the spouse.

Statement 1: From this statement we can only determine the total received by the two younger children.

Not sufficient

Statement 2: This implies both of the younger children received same amount, say $ x. Hence, the oldest children received $ (x - 12,500) and the spouse received $ (x + 62, 500).

Therefore, [(x + 62,500) + (x - 12,500) + x + x] = 200,000
=> (4x + 50,000) = 200,000

We can easily determine x from this linear equation in x.

Sufficient

The correct answer is B.

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aleph777: Master | Next Rank: 500 Posts; Posts: 131; Joined: Fri Jun 18, 2010 10:19 am; Location: New York, NY; Thanked: 10 times

by aleph777 » Wed Jan 19, 2011 6:42 am

Anurag,

I arrived at the same conclusion as you, but with slightly different numbers.

I thought that if EACH child receives $12500 more than the oldest and $62500 less than the spouse, then you'd end up with this equation in the end:

4x + 125000 - 25000 = 200000

I doubled the numbers provided in the second statement because I thought you need to take into account the fact that those are the differences for EACH of the youngest children. So, we need to combine them in order to determine the specific take of one child.

Can you explain why you only take into account the differences once?

Thanks!

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Jan 19, 2011 6:56 am

aleph777 wrote:I thought that if EACH child receives $12500 more than the oldest and $62500 less than the spouse, then you'd end up with this equation in the end:

4x + 125000 - 25000 = 200000

I doubled the numbers provided in the second statement because I thought you need to take into account the fact that those are the differences for EACH of the youngest children. So, we need to combine them in order to determine the specific take of one child.

No.
Second statement says, "Each of the younger children received $12500 more than the oldest child...". Which means the take of the oldest child is $12,500 less than each of the younger child. It is true that this amount is the difference between the take of oldest child and the younger ones. But difference from each of them simultaneously not sequentially.

Now if you assume that the take of each younger child is $ x, then according to you, the take of oldest child is $ (x - 25,000). Right? Now that what happens to second statement? We are ended up with each younger child getting $25,000 more than the oldest child! Which is obviously not true.