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Math Expert V
Joined: 02 Sep 2009
Posts: 58465
Mr. Evans' will states that each of his children will receive an equal  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 48% (01:51) correct 52% (01:38) wrong based on 44 sessions

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Mr. Evans' will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 5 children and 6 grandchildren, then approximately what percentage of Mr. Evans' estate will each grandchild receive?

A. 20%
B. 17%
C. 4.0%
D. 3.3%
E. 2.8%

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Senior SC Moderator V
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Mr. Evans' will states that each of his children will receive an equal  [#permalink]

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Bunuel wrote:
Mr. Evans' will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 5 children and 6 grandchildren, then approximately what percentage of Mr. Evans' estate will each grandchild receive?

A. 20%
B. 17%
C. 4.0%
D. 3.3%
E. 2.8%

This question's wording can be very tricky.

1) we need at least 5 shares

-- Mr. E has five children, and "each of his children will receive an equal share of his estate..."
--That means: each one of 5 children gets an equal share
--It does NOT mean: the estate is divided into 5 parts (that leads to trap answer D)

2) We need more than 5 shares. The set of grandchildren is like a sixth child.
-- Mr. E's grandchildren "split a portion . . . equal to the share received by each of his children."
-- That means: his grandchildren, as a set, also get one share equal to that of one child
-- It does NOT mean: the estate is divided into 5 equal parts, AND THEN 6 grandchildren share $$\frac{1}{5}$$

Where is the other $$\frac{1}{5}$$ coming from if the estate has been divided already?
Will one of the children hand over his or her fifth to the grandchildren? NO

3) We must divide the estate into SIX equal portions**

• 5 children each get 1 portion; $$\frac{5}{6}$$ of total estate
• One set of grandchildren receives 1 portion, $$\frac{1}{6}$$ of total estate

4) What portion does each (one) grandchild get?
• One set of 6 grandchildren gets $$\frac{1}{6}$$ portion
• Each grandchild's portion is $$\frac{\frac{1}{6}}{6} = \frac{1}{36}$$

5) What percentage of Mr. Evans's estate does each (one) grandchild receive?
• A portion is a part of a whole
• Percentage: $$\frac{Part}{Whole} * 100$$

$$\frac{1}{36}*100\approx{.0277}*100\approx{2.8}$$ percent

**
Let X = a portion, C = one child, G = the set of grandchildren

The estate gets divided this way:
X |X |X |X |X |X
C |C |C |C|C |G

Once you realize you need 6 portions, if the fractions aren't clear, you can assign values

Let the estate be worth $72 X = $$\frac{72}{6}$$ =$12
The set of grandchildren receives X = $12 There are 6 grandchildren Each grandchild receives $$\frac{12}{6}$$ =$2

What percentage of the estate does each grandchild receive?
Percentage: $$\frac{Part}{Whole} * 100$$
$$\frac{2}{72} * 100 = \frac{1}{36} * 100\approx{.0277}*100 \approx{2.8}$$ percent

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Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver Mr. Evans' will states that each of his children will receive an equal   [#permalink] 20 Jan 2018, 15:14
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