Test: Time And Work- 1 - GRE MCQ

Step 1: Question statement and Inferences

The question asks for the number of minutes required for 6 identical printers to print 54 binders given that 3 printers take 2 minutes to print 9 binders. You can infer that the rate of printing does not change. 

Step 2: Finding required values

Number of binders printed by 3 printers in 2 minutes = 9

Number of binders printed by 3 printers in 1 minute = 9/2

Number of binders printed by 1 printer in 1 minute = 3/2

Number of binders printed by 6 printers in 1 minute = 3/2 × 6

Number of binders printed by 6 printers in x minutes = 9x

Step 3: Calculating the final answer

Put 9x = 54

x = 6 

Thus 6 printers will take 6 minutes to print 54 binders.

Answer: Option (E)

Step 1: Question statement and Inferences

The question is asking for the time needed for Mason to complete the job based on the time needed by Bill alone and by Bill and Mason working together.

You can infer that the rates in which they work do not change.

Step 2: Finding required values

Working alone, Bill can complete the design in 10 days.

Let the total amount of work involved in making the design be W

So, work done by Bill in 10 days = W

Work done by Bill in 1 day = W/10 

Let Mason working alone take d days to complete W amount of work

So, work done by Mason in d days = W

Work done by Mason in 1 day = W/d

When Bill and Mason work together,

They complete the work in 4 days

This means,

Work done by Bill and Mason in 4 days = W

Work done by Bill and Mason in 1 day = W/4

So,

W/10 + W/d = W/4

1/10 + 1/d = 1/4 

Step 3: Calculating the final answer

Solve for Mason’s time. First, subtract  from both sides:

1/d = 3/20 

Next, cross multiply:

3(d) = 20

Finally, divide both sides by 3:

d = 20/3

It would take Mason, working alone,   days to complete the design.

Answer: Option (C)

Step 1: Question statement and Inferences

We are given the time in which three workers Abe, Bosky, and Chris can finish a piece of work. Abe takes 12 hours to complete the work, Bosky takes 24 hours whereas Chris completes the work in 36 hours.

Now, we can easily find their respective rates of work.

Let’s say the total amount of work is W. Thus, the rate of work of the three workers:

Per the question statement the three workers work alternatively for an hour in turns. We have to find the minimum time in which the work can be completed:

Hence, only one of the workers will work on the job for an hour, then the second worker will work in place of him and then the third worker will replace him. This process continues till the job is completed.

Since any worker can start the job, the fastest worker should start the job to complete it in minimum time.

We know that Abe is the fastest worker, he finishes 1/12 part of the work in an hour, while Chris is the slowest, he finishes only 1/36 part of the work in an hour.

Thus, Abe should start the work, followed by Bosky followed by Chris.

Step 2: Finding required values

When each of Abe, Bosky, and Chris work for an hour, the amount of work completed at the end of the three hours:  

After 6 rounds of working together, the total time consumed will be = 3*6 = 18 hours

And the total work completed will be

Now, the remaining work is

Since now is Abe’s turn to work, he will complete the remaining 6/72W

 in one hour. 

Step 3: Calculating the final answer

So, the total number of hours taken to complete the job = 18 + 1 = 19 hours 

Answer: Option (B) 

The question is asking how long it would take 12 men and 15 women to complete a certain job. It tells you that 8 men complete this job in 12 days.

Let the total amount of work involved in completing the job be W.

Work done by 8 men in 12 days = W

Work done by 8 men in 1 day = W/12

Work done by 1 man in 1 day = W/96                      . . . Equation 1

So, work done by 12 men in 1 day = 12W/96 = W/8

Let one woman working alone complete the job in d days.

So, work done by 1 woman in 1 day =W/d                   . . . Equation 2

So, work done by 15 women in 1 day = 15W/d

Work done by 12 men and 15 women working together in 1 day = W/8 + 15W/d=(1/8+15/d)W

Once we know the value of d, we will be able to know the value of the coefficient of w in the above equation.

The reciprocal of this coefficient will be equal to the total time taken by 12 men and 15 women to complete the task.

So, we need to find the value of d.

Step 3: Analyze Statement 1

20 women can do the same job in 10 days.

Work done by 20 women in 10 days = W

Work done by 20 women in 1 day = W/10

Work done by 1 woman in 1 day =W/200                  . . . Equation 3

Comparing Equation 3 with Equation 2:

d=200

Thus, Statement 1 is sufficient to arrive at a unique value of the time taken by 12 men and 15 women

to complete the job

Step 4: Analyze Statement 2

24 men and 5 women can complete the same job in 40/11 days.

Work done by 24 men and 5 women in 40/11 days = W

Work done by 24 men and 5 women in 1 day = 

Using Equations 1 and 2 we can write:

Thus, we have a linear equation in d.

By solving this equation, we will be able to find the value of d

Thus, Statement 2 too is sufficient to arrive at a unique answer.

Step 5: Analyze Both Statements Together (if needed)

You get unique answers in steps 3 and 4, so this step is not required

Answer: Option (D)

Step 1: Question statement and Inferences

The question asks for the amount of time that the three friends, working together at their respective rates, will take to complete the thesis. You are given the rates of each friend, and you can infer that the rates are consistent. In other words, the women typing will consistently complete the same number of chapters per hour.

Step 2: Finding required values

Use the rates that the three friends type. Per each hour, Suzy, Marie, and Leslie type 3, 5, and 6 chapters each, respectively.  The thesis contains 28 chapters total.

Step 3: Calculating the final answer

In the first hour working together, Suzy, Marie, and Leslie type 3, 5, and 6 chapters each, thus typing a total of 14 chapters together. In the second hour, they type the same number of chapters, for a total of 14. At the end of this second hour, they have typed 28 chapters, which is the entire thesis.

Working together, it will take the three friends 2 hours to type the thesis.

Answer: Option (D)

Step 1: Question statement and Inferences

This is a problem involving two different rates of work. We will first solve for these individual rates of work, and then, we will find the combined rate of work by adding the individual rates of work. Once we know the combined rate of work, we will be able to find the total time taken to complete the work.

Step 2: Finding required values

Let the total amount of work be W

Work done by 20 men in 5 days = W

Now considering the women:

Work done by 10 women in 4 days = W

So, work done by 2 men and 8 women in 1 day =

Step 3: Calculating the final answer

Total time taken to complete W amount of work = 50/11  days

Looking at the answer choices, we see that Option D is correct

Steps 1 & 2: Understand Question and Draw Inferences

The question asks for the number of days it will take Jeff to complete the report. You need to know the portion of the report, whether as a fraction or a percent, that Jeff can complete in a single day.

We are also given that he completes the same percent of his report every day.

Step 3: Analyze Statement 1

(1) Jeff can complete 10% of the report in 2 days.

If Jeff completes 10% of the report in 2 days, then he completes 5% in one day. At this rate, it will take Jeff 20 days to complete the report. 

Statement 1 is sufficient.

Step 4: Analyze Statement 2

(2) After 7 days, there was still 65% of the report to be completed.

If 65% of the report remains after 7 days, then Jeff has completed 35% during these 7 days. AT this rate, he completes 5% in one day, and it will take him 20 days to complete the report. 

Statement 2 is sufficient.

Step 5: Analyze Both Statements Together (if needed)

You get unique answers in steps 3 and 4, so this step is not required

Answer: Option (D)

Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15

Amount of work P can do in 1 day = 1/16
Amount of work Q can do in 1 day = 1/12 
Amount of work P, Q and R can together do in 1 day = 1/4
Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48
=> Hence R can do the job on 48/5 days = 9 (3/5) days

Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him
Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 × 1/5 = 1
i.e, the work will be done in 15 days