GRE® Quant Practice | Rates Q5

The GRE maths sample question given below is a Quantitative Comparison question in Rates. This GRE sample question helps you understand the relation between Work done and time taken to complete the work.

Question 5: P and Q take 4 hours to complete a task. P, Q, and R take 2 hours to complete the task.

Quantity A	Quantity B
Time taken by P alone to complete the task.	Time taken by R alone to complete the task.

1. Quantity A is greater
2. Quantity B is greater
3. The two quantities are equal
4. Cannot be determined

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Video Explanation

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Explanatory Answer

Step 1: Frame Equations for information given in the Question Stem

Let the time taken by P alone, Q alone, and R alone be p, q, and r hours respectively.
So, in 1 hour P will complete \\frac{1}{p})
So, in 1 hour Q will complete \\frac{1}{q})
So, in 1 hour R will complete \\frac{1}{r})

Information 1: P and Q complete the task in 4 hours.
Therefore, P and Q will complete \\frac{1}{4})^th of the task in 1 hour.
Fraction of work done by P and Q in 1 hour is \\frac{1}{p}) + \\frac{1}{q}) = \\frac{1}{4}) ..... (1)

P, Q, and R complete the task in 2 hours
Therefore, P, Q, and R will complete \\frac{1}{2}) the task in 1 hour.
Fraction of work done by P, Q, and R in 1 hour is \\frac{1}{p}) + \\frac{1}{q}) + \\frac{1}{r}) = \\frac{1}{2}) ..... (2)

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Step 2: Solve Equations (1) and (2)

Subtract equation (1) from equation (2)
\\frac{1}{p}) + \\frac{1}{q}) + \\frac{1}{r}) - \\frac{1}{p}) - \\frac{1}{q}) = \\frac{1}{2}) - \\frac{1}{4})
⇒ \\frac{1}{r}) = \\frac{1}{2}) - \\frac{1}{4})
So, r = 4

R alone takes 4 hours. to complete the task.
It is given that, P and Q together take 4 hours.
Therefore, each of P and Q alone will take more than 4 hours.

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Step 3: The comparison

Quantity A: Time taken by P alone to complete the task. We know P takes more than 4 hours
Quantity B: Time taken by R alone to complete the task. R takes 4 hours to complete the task.
Quantity A > Quantity B

Choice A is the correct answer for this GRE Quantitative Comparison Question