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Zorluk: OrtaData Sufficiency

Two business partners, AA and BB, invested in a joint venture. What is the total profit earned by the business at the end of one year?

Statement I: Partner AA invested $6,000\$6,000 for the entire year, while Partner BB invested $9,000\$9,000 for 88 months.
Statement II: Partner AA's share of the annual profit is $2,400\$2,400.

Which of the following options correctly describes the sufficiency of the statements to answer the question?

  1. A
    Statement I alone is sufficient to answer the question, but Statement II alone is not sufficient.
  2. B
    Statement II alone is sufficient to answer the question, but Statement I alone is not sufficient.
  3. C
    Either Statement I alone or Statement II alone is sufficient to answer the question.
  4. D
    Neither Statement I nor Statement II is sufficient to answer the question.
  5. Both Statement I and Statement II together are sufficient to answer the question, but neither statement alone is sufficient.Cevap

Cevap

Both Statement I and Statement II together are sufficient to answer the question, but neither statement alone is sufficient.
Evaluating Statement I alone gives the profit-sharing ratio between Partner A and Partner B as (6000×12):(9000×8)=1:1(6000 \times 12) : (9000 \times 8) = 1 : 1, which is insufficient by itself to find the monetary profit. Statement II alone gives Partner A's profit share as $2,400\$2,400, which is also insufficient without knowing the proportion. Combining both statements shows that both partners receive equal shares, so total profit is $2,400×2=$4,800\$2,400 \times 2 = \$4,800. Therefore, both statements together are necessary and sufficient.

Adım Adım Çözüm

1
Evaluate Statement I alone
Profit sharing ratio of A to B = (6000×12):(9000×8)=72,000:72,000=1:1(6000 \times 12) : (9000 \times 8) = 72,000 : 72,000 = 1 : 1.
Profit is distributed in proportion to the product of capital invested and time period. Since no dollar amounts of profit are given, total profit cannot be determined from Statement I alone.
2
Evaluate Statement II alone
Partner A's profit share = $2,400\$2,400.
Without knowing Partner B's share or the ratio between their shares, the total profit cannot be calculated from Statement II alone.
3
Evaluate Statement I and Statement II together
Since ratio of shares is 1:11:1 and A's share is $2,400\$2,400, B's share is also $2,400\$2,400. Total profit = $2,400+$2,400=$4,800\$2,400 + \$2,400 = \$4,800.
Combining the ratio from Statement I and the monetary value from Statement II gives a unique answer to the question.

Anahtar Kavram

Partnership profit distribution ratio and data sufficiency evaluation
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Konular

Data Sufficiency

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