preparing for the GRE General Test?

Question

And I cannot for the life of me remember how to do these types of problems... someone help or at least point me in the right direction so I can find out.

If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?


2 minutes and 44 seconds
2 minutes and 58 seconds
3 minutes and 10 seconds
3 minutes and 26 seconds
4 minutes and 15 seconds

If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?


0.8 days
1.09 days
1.23 days
1.65 days
1.97 days

Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?


12 minutes
15 minutes
21 minutes
23 minutes
28 minutes

Answer 1

All these problems need to be considered using the fraction of the job each person completes per day....

Sam = 1/4
Lisa = 1/6
Tom = 1/2
Together 1/x (where x=number of days together)

So, working together,

1/4 + 1/6 + 1/2 = 1/x

and x = 1.09 days :)


That's the trick ... consider the fraction of the "work" done in a single time period (day, week, minute, etc)

Answer 2

If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

Let
x = time it takes with all working together

x/5 + x/10 + x/15 = 1
6x + 3x + 2x = 30
11x = 30
x = 30/11 min = 2 8/11 min = 2 min, 44 sec
_________

The others work the same way. Just be sure your units are consistent. For example, don't mix minutes and hours.

Answer 3

Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?


you have to use algebra for this one.
x/30+x/45+x/90= 1 (take note that i'm using minutes as the denominator.)

3x/90+2x/90+x/90=1
3x+2x+x= (90x1)

Its easy from here on.
6x = 90
x = 15

Answer 4

Remember that Work = Rate x Time. Since the unit of these types of problems is typically 1, you're looking at solving for Time which is just 1/Rate.

Take the 2nd example. You just need to derive the rates for each person, and sum them, then solve for X.

1/4x + 1/6x + 1/2x = 1

(3x + 2x + 6x)/12 = 1
11x = 12
x = 12/11

So 1.09 would be the answer.

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If you don't care about the formal way to approach this problem (and because the GRE is timed), you can start by just forming the equation (as we did above) and then plugging in the answers starting with the middle value. Your choice.

Answer 5

India had a near perfect match after Australia's first innings batting,i thought it was good first innings from Aussies but India scored so fast thanks to Dhawan and co and Australia's second innings capitulation that happened so quickly on the last day cannot be explained even by Ian Chappell.Batting for India clicked so well in this series,they had a near perfect match.Australia should've drawn this match but they ended up losing on the last day thanks to some poor batting in second innings.