GRE General TestQuantitative ReasoningMedium
A project manager is estimating task durations. Task A takes 'x' hours. Task B takes 5 hours longer than Task A. Task C takes twice as long as Task B. If the total duration for all three tasks is 65 hours, which equation correctly represents the total duration?
- Ax + (x + 5) + (x + 5)/2 = 65
- Bx + 5x + 2(5x) = 65
- Cx + (x + 5) + 2(x + 5) = 65
- Dx + (x + 5) + 2x = 65
Show answer & explanationAnswer & explanation
Correct answer: C. x + (x + 5) + 2(x + 5) = 65
Task A is x. Task B is x + 5. Task C is twice Task B, so 2(x + 5). Summing these expressions should equal 65.
Why the other options are wrong
- A. This incorrectly represents Task C as half of Task B, not twice.
- B. This incorrectly represents Task B as 5x and Task C as 2(5x).
- D. This incorrectly represents Task C as 2x instead of twice Task B (2(x+5)).
Translating Word Problems to Algebra
Converting verbal descriptions of relationships and quantities into mathematical equations using variables.
- Identify unknown quantities and assign variables.
- Translate keywords into mathematical operations (e.g., 'is' means '=', 'longer than' means '+').
- Formulate equations based on the problem's conditions.
Memory trick: Words to Math: Assign variables, translate keywords, then build the equation brick by brick.