# GRE® Quant Practice | Rates Q5

#### GRE Quantitative Comparison Questions | Work Time

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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#### 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)

#### 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. #### 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 #### GRE Online Course - QuantTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GRE Live Online Classes Next Batch December 15, 2023 ## Additional Practice Questions in Rates | Time Speed Distance & Work Time Pipes Cisterns ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 93800 48484
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