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Three business partners owned 100% of a certain company

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by rsarashi » Sat May 27, 2017 11:24 am
Three business partners owned 100% of a certain company. When they sold the company, one partner received exactly 5/8 of the proceeds of the sale and the other partners shared the remainder of the proceeds. How much money did the partner who received the smallest amount of the proceeds receive from the sale?

(1) The partner who received the smallest amount from the sale received exactly 1/5 the amount received by the partner who received the second largest amount.

(2) The partner who received the second largest amount from the sale received half of the two million dollars received by the partner who received the largest amount.

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Source: — Data Sufficiency |
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by GMATGuruNY » Sat May 27, 2017 11:49 am
rsarashi wrote:Three business partners owned 100% of a certain company. When they sold the company, one partner received exactly 5/8 of the proceeds of the sale and the other partners shared the remainder of the proceeds. How much money did the partner who received the smallest amount of the proceeds receive from the sale?

(1) The partner who received the smallest amount from the sale received exactly 1/5 the amount received by the partner who received the second largest amount.

(2) The partner who received the second largest amount from the sale received half of the two million dollars received by the partner who received the largest amount.
Since 5/8 is equal to MORE THAN HALF of the total amount, the partner who receives 5/8 of the proceeds receives the greatest amount.

Statement 1:
Since the only known values are FRACTIONS --- 5/8 and 1/5 -- the total proceeds from the sale can be any value.
Thus, it is not possible to determine the smallest amount received.
INSUFFICIENT.

Statement 2:
Second largest amount = (1/2)(largest amount) = (1/2)(2,000,000) = 1,000,000.
Since the two million dollars received by the partner who received the largest amount is equal to 5/8 of the total, we get:
2,000,000 = (5/8)T
T = (8*2,000,000)/5 = 8 * 400,000 = 3,200,000.
Thus:
Smallest amount = (total amount) - (largest amount) - (second largest amount) = 3,200,000 - 2,000,000 - 1,000,000 = 200,000.
SUFFICIENT.

The correct answer is B.
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by rsarashi » Sat May 27, 2017 9:40 pm
Since 5/8 is equal to MORE THAN HALF of the total amount, the partner who receives 5/8 of the proceeds receives the greatest amount.

Statement 1:
Since the only known values are FRACTIONS --- 5/8 and 1/5 -- the total proceeds from the sale can be any value.
Thus, it is not possible to determine the smallest amount received.
INSUFFICIENT.

Statement 2:
Second largest amount = (1/2)(largest amount) = (1/2)(2,000,000) = 1,000,000.
Since the two million dollars received by the partner who received the largest amount is equal to 5/8 of the total, we get:
2,000,000 = (5/8)T
T = (8*2,000,000)/5 = 8 * 400,000 = 3,200,000.
Thus:
Smallest amount = (total amount) - (largest amount) - (second largest amount) = 3,200,000 - 2,000,000 - 1,000,000 = 200,000.
SUFFICIENT.

The correct answer is B.
[/quote]

Hi GMATGuruNY ,

Thank you so much sir for your explanation.

Just a quick question, can we solve statement 1 by letting the total amount?

Let Highest be a, second be b, and third be c

Let total value be 400000

a = 5/8*400000 = 250000
so b+c = 150000 ......|

statement says c=1/5b ........||

from | & ||

b= 125000 and c = 25000

Now let value be 800000

so again c will be 25000

By this statement 1 is sufficient.

Please check and correct me if something is wrong.

Please help.
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by GMATGuruNY » Sun May 28, 2017 4:43 am
rsarashi wrote:Hi GMATGuruNY ,

Thank you so much sir for your explanation.

Just a quick question, can we solve statement 1 by letting the total amount?

Let Highest be a, second be b, and third be c

Let total value be 400000

a = 5/8*400000 = 250000
so b+c = 150000 ......|

statement says c=1/5b ........||

from | & ||

b= 125000 and c = 25000

Now let value be 800000

so again c will be 25000

By this statement 1 is sufficient.

Please check and correct me if something is wrong.

Please help.
The statement in red is untrue.

Case 2: Total amount = 800,000
In this case:
a = (5/8)(800,000) = 500,000.
b+c = 800,000 - 500,000 = 300,000.
Substituting b=5c into b+c = 300,000, we get:
5c + c = 300,000
6c = 300,000
c = 50,000.

Since c can different values -- 25000 in Case 1, 50000 in Case 2 -- Statement 1 is INSUFFICIENT.
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by rsarashi » Mon May 29, 2017 9:02 am
The statement in red is untrue.

Case 2: Total amount = 800,000
In this case:
a = (5/8)(800,000) = 500,000.
b+c = 800,000 - 500,000 = 300,000.
Substituting b=5c into b+c = 300,000, we get:
5c + c = 300,000
6c = 300,000
c = 50,000.

Since c can different values -- 25000 in Case 1, 50000 in Case 2 -- Statement 1 is INSUFFICIENT.
[/quote]

Hi GMATGuruNY ,

Thank you so much for correcting me sir.

Understood.
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