Examkin

Soru

Zorluk: OrtaRates, Ratios, Percentages, and Applied Word Problems

A commercial law firm charges clients for services rendered by its Senior Partners and Associate Partners. Last month, the firm billed a total of $450,000 across all client accounts. What was the ratio of the total amount billed for Senior Partner hours to the total amount billed for Associate Partner hours?

(1) Senior Partners billed at an hourly rate that was 50 percent higher than the hourly rate billed by Associate Partners.
(2) Senior Partners accounted for 40 percent of the total number of hours billed by the firm last month.

  1. A
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. B
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.Cevap
  4. D
    EACH statement ALONE is sufficient.
  5. E
    Statements (1) and (2) TOGETHER are NOT sufficient.

Cevap

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
The correct option is the statement indicating both statements together are sufficient, but neither alone is sufficient. Statement (1) provides the ratio of hourly billing rates (3:23:2), and Statement (2) provides the ratio of total hours billed (2:32:3). Multiplying rate ratio by hours ratio gives the ratio of total amounts billed (1:11:1), yielding a single unique value.

Adım Adım Çözüm

1
Rephrase the target question mathematically
Let RSR_S and RAR_A be the hourly rates for Senior and Associate Partners, respectively. Let HSH_S and HAH_A be the hours billed by Senior and Associate Partners, respectively. Total billing ratio is Senior BillingAssociate Billing=RS⋅HSRA⋅HA=(RSRA)⋅(HSHA)\frac{\text{Senior Billing}}{\text{Associate Billing}} = \frac{R_S \cdot H_S}{R_A \cdot H_A} = \left(\frac{R_S}{R_A}\right) \cdot \left(\frac{H_S}{H_A}\right).
Total revenue for each group is the product of hourly rate and hours billed.
2
Evaluate Statement (1) independently
Statement (1) gives RS=1.50RA  ⟹  RSRA=32R_S = 1.50 R_A \implies \frac{R_S}{R_A} = \frac{3}{2}. Without HSHA\frac{H_S}{H_A}, the target ratio cannot be evaluated.
Statement (1) alone is NOT sufficient.
3
Evaluate Statement (2) independently
Statement (2) gives HS=0.40(HS+HA)  ⟹  0.60HS=0.40HA  ⟹  HSHA=23H_S = 0.40 (H_S + H_A) \implies 0.60 H_S = 0.40 H_A \implies \frac{H_S}{H_A} = \frac{2}{3}. Without RSRA\frac{R_S}{R_A}, the target ratio cannot be evaluated.
Statement (2) alone is NOT sufficient.
4
Evaluate Statements (1) and (2) combined
Multiplying the two ratios yields Senior BillingAssociate Billing=(32)⋅(23)=1\frac{\text{Senior Billing}}{\text{Associate Billing}} = \left(\frac{3}{2}\right) \cdot \left(\frac{2}{3}\right) = 1. The ratio is uniquely determined as 1:11:1.
Both statements together are SUFFICIENT.

Anahtar Kavram

Data Sufficiency stems asking for a ratio can be solved by finding the relative ratios of constituent factors (Rate Ratio × Quantity Ratio) without needing absolute numerical quantities.
Tahmini Süre:2m 0s
Bu soruyu puanla

Konular

Rates, Ratios, Percentages, and Applied Word Problems

Bu konudan daha fazla soru