GRE General TestQuantitative ReasoningMedium
A project manager is estimating task durations. Task A takes 'x' hours. Task B takes 5 hours less than twice the duration of Task A. Task C takes 3 hours more than Task A. If the total duration for all three tasks is 38 hours, what is the duration of Task B?
- A21 hours
- B8 hours
- C16 hours
- D11 hours
Show answer & explanationAnswer & explanation
Correct answer: A. 21 hours
Task A = x. Task B = 2x - 5. Task C = x + 3. Total = x + (2x - 5) + (x + 3) = 4x - 2. Set 4x - 2 = 38. Then 4x = 40, so x = 10. Task B = 2(10) - 5 = 20 - 5 = 15 hours.
Why the other options are wrong
- B. This is the value of x, the duration of Task A, not Task B.
- C. This is a common error resulting from incorrect setup or calculation.
- D. This is the duration of Task C (10+3=13), not Task B.
Translating Word Problems to Algebra
To solve word problems, assign variables to unknown quantities and translate the given relationships and conditions into algebraic equations.
- Use 'x' or another variable for the primary unknown.
- Translate phrases like 'twice a number' (2x), '5 less than' (x-5), '3 more than' (x+3).
- The word 'is' or 'equals' typically translates to '='.
Memory trick: Read, Define, Formulate, Solve, Check.