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gvosough: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Wed Apr 28, 2010 9:42 am

by gvosough » Tue Oct 04, 2011 3:11 pm

if 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to build 5?

A) 1
B) 5
C) 7
D) 25
E) 35

Answer: C

Can s.o. plz explain thank

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Source: Beat The GMAT — Problem Solving | Tue Oct 04, 2011 3:11 pm

GmatMathPro: GMAT Instructor; Posts: 349; Joined: Wed Sep 28, 2011 3:38 pmFollowed by: 54 members; Location: Austin, TX; Thanked: 236 times; GMAT Score:770

by GmatMathPro » Tue Oct 04, 2011 3:31 pm

Let W=number of workers, C=number of cars to build, and D=number of days to finish the job.

Think about how changing C and W will affect how long it will take to finish the job. Obviously, the more workers you have the better. If you increase the number of people working, the amount of time it takes to finish the job decreases. For example, if you double W, D should be cut in half. If you triple W, D should be multiplied by 1/3. Mathematically, we would say W and D vary inversely. With C and D, though, the more cars to be built, the longer it should take. If you double the number of cars, it should double the number of days. Mathematically, we would say D and C vary directly.

So, if we go from 7 workers to 5 workers, and 7 cars to 5 cars, we've multiplied W by 5/7, which would have the effect of multiplying D by 7/5, the reciprocal factor. However, we've also multiplied the number of cars by 5/7, which has the effect of multiplying D by 5/7. The (7/5)*(5/7) cancel out, so D is unaffected.

If you like formulas, once you establish that W varies inversely with D and C varies directly with D, you could set up the following equation: D=kC/W, where k is some non-zero constant. Now, plug in the initial values of W, C, D to solve for the constant, k. You should get k=7. Now the formula is D=7C/W. PLug in the new values of C and W, C=5 and W=5 to get [spoiler]D=7[/spoiler]

Pete Ackley
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Oct 04, 2011 4:30 pm

gvosough wrote:if 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to build 5?

A) 1
B) 5
C) 7
D) 25
E) 35

Answer: C

Can s.o. plz explain thank

Let rate per worker = 1 unit per day.
Rate for 7 workers = 7 units per day.
Over 7 days, work produced = 7*7 = 49 units.
Since 49 units = 7 cars, each car = 49/7 = 7 units.
Thus, 5 cars = 5*7 = 35 units.
Rate for 5 workers = 5 units per day.
Time needed = w/r = 35/5 = 7 days.

The correct answer is C.

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edvhou812: Master | Next Rank: 500 Posts; Posts: 143; Joined: Sat Nov 06, 2010 9:06 pmFollowed by: 1 member; Thanked: 10 times

by edvhou812 » Tue Oct 04, 2011 8:49 pm

If 7 workers can build 7 cars in 7 days, then 7 workers must be able to build 1 car in 1 day. If 7 workers can build a car in one day, then each worker completes 1/7 of the car in that day.

The rate of completion for five workers per day is 1/7+1/7+1/7+1/7+1/7=5/7. So 5 workers complete 5/7 of a car in one day. To answer the question, we create the following equation:

5/7x=5
x=5/1*7/5=35/5=7

So it will take 5 workers, that complete 5/7 of a car per day, 7 days to build 5 cars.

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Tue Oct 04, 2011 10:27 pm

use this ratio

Original # of workers*#of days taken/Work done = New #of workers required *# of days taken/Work done

7*7/7 = 5*W/5 ; W=7

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Wed Oct 05, 2011 4:49 am

gvosough wrote:if 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to build 5 cars ?

A) 1
B) 5
C) 7
D) 25
E) 35

Answer: C

Can s.o. plz explain thank

If we carefully look at the above problem then we can see that the question given shows us to find the number of days taken to do the work and here efficiency ( Rate of doing work Per unit time ) , remains the same .

Total work done by 7 men in 7 days is - 7 cars

7 * 7 { Total work = No of men * No of days }

Thus 49 men days = 7 cars

So 1 men day = 1/7 man day ( Efficiency )

We also know that

Total work = No of men * No of days * efficiency of the workers

so , 5 = 5 * d * 1/7

So , d * 1/7 = 1

or , d = 7....

Abhishek

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svd.kumar: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Tue Sep 21, 2010 7:38 am; Thanked: 4 times

by svd.kumar » Wed Oct 05, 2011 5:53 am

Try This way of thinking

Try to calculate the rate i.e 1 worker per 1 day

7 Workers in 7 Days builds 7 cars
1 Worker in 7 days builds 7/7 = 1 car
1 Worker in 1 day builds 1/7 car (rate)

Which means
Workers * Days * rate (Rate per day per worker) = number of cars (7 * 7 * 1/7 = 7)

So for 5 workers for 5 cars , let d be days
5 * d * 1/7 = 5
d = 7

Answer = 7

Thanks,
SVD

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