Sample questions of GRE with solution

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1                        Questions   Related  to   Chain rule ,  Time & Work

    1)  If 6 workers can build 4 cars in 2 days, then how many days would it take 8 workers to

           build 6 cars?

         (A) 5/3

         (B) 9/4

         (C) 8/3

        (D) 11/4

        (E) 10/3

      Ans: more workers  less no of days     (indirect proportion)

              More cars more days                     (direct proportion)

       Ratio of workers=  8:6   

    Ratio of cars       =4:6

    Ratio of days  = 2:x

           6*6*2=8*4*x

        X=(6*6*2)/8*4

           = 9/4

22)     If 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to

          build 5 cars?

         Ans : more workers  less no of days     (indirect proportion)

                        More cars more days                     (direct proportion)

                     Ratio of workers=  5:7

         Ratio of cars       =7:5

         Ratio of days  = 7:x

                      5*7*x=7*5*7

                      X=7*5*7/5*7

                        =7

33     If 5 men and 9 women can do a piece of work in 19 days how many days will take 3men and 6 women to do the same work?

Let required no be X

5 men = 9 women => 1man =9/5 women

3 men and 6 women = 3*9/5 +6 =27+30/5=57/5

More women less no of days  (indirect proportion)

57/5:9=19:x

X=9*19*5/57=15             

44     A man completes  5/8  of a job in 10 days. At this rate how many more days will it take him to finish the job?

a)      5  b) 6  c) 7  d) 71/2

Ans  Work done =5/8     Balance work = (1- 5/8)=3/8

 Less work Less days (Direct Proportion )

Let the required no of days be x.

Then 5/8:3/8=10:x

5/8*x=3/8*10

X=3*8*10/5*8

 =6 days
 5)      3 pumps , working  8 hours a day  can empty a tank in 2 days , how many hours a day must  4

               pu mps    work to empty the tank in 1 day?

                a) 9      b) 10     c) 11   d) 12

Ans:  Let the required number of working hours per day be x

         More pumps Less working hours per day    (Indirect Proportion )

        Less days, More Working Hours per day       (Indirect Proportion )

               Pumps      4:3

                                                   ::    8: x

                 Days         1:2  

                4*1*x=3*2*8

                        X=3*2*8/4

                         =12

56)      If the cost of x metres  of  wire is d dollars , then what is the cost of  y metres of wire at the same rate?

a)      xy/d     b) xd      c) yd    d)yd/x

Cost of x metres =  d

Cost of 1 metre = d/x

Cost of y metres = (d/x)y=dy/x

67)      In   a camp, 95 men had provision for  200 days , After 5 days 30 men left  the camp. For how many days will the remaining food last now?

a)      180   b) 285      c)   139  18/19 d) none of these

Ans:  Let the remaining food will last for x days.

95  men had provisions for 195 days . 65 men had provision for x days.

Less men ,More days      (Indirect Proportion )

65 : 95 :: 195 : x    =>  65*x=95*195

X  =95*195/65

   =285

78)      A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is 14cm. How many times can it go round a cylinder with radius 20 cm ?

a)      40    b)49   c)  100   d)None of these

Ans :  Let the required number of rounds be x

More radius , Less rounds    (Indirectly Proportional)

20:14 :: 70:x  =>  20*x=14*70

X = 14*70/20

=49

89)    If 3/5 of a cistern is filled in 1 minute, how much more time will be required to fill the rest of it?

a)      30 sec    b) 40 sec     c)  36 sec     d) 24 sec

Let the required time be x seconds.

Part Filled = 3/5  , Remaining part = (1-3/5) = 2/5

Less part , Less time (Direct proportion)

3/5  : 2/5 :: 60 : x =>  3/5*x =2/5*60

= > x=40

910)    If 7 spiders make 7 webs, then 1 spider will make 1 web in how many days?

a)      1  b)7/2   c) 7   d) 49

Ans :  Let the required no of days be x. Then

Less spiders, More days     (Indirect Proportion)

Less webs , Less days          (Direct Proportion)

Spiders   1  :  7

                                  ::  7:x

Webs      7 :   1

1*7*x= 7*1*7

x =  7*7*1 /  1*7

 =  7

111)   400 persons  working 9 hours per day complete  ¼  th of the work in 10 days. The no of additional persons working 8 hours per day , required to complete the remaining work in 20 days, is :

a)      675    b) 275    c) 250    d) 225

Ans:  Let the no of persons completing te work in 20 days be x.

Work done = ¼    Remaining work = (1- ¼  ) = ¾

Less  hours  per  day , More men required   ( Indirect Proportion)

More work , More men required                   ( Direct proportion )

More days , Less men required                      ( Indirect Proportion)

Hours per day    8 :  9

Work                   ¼  : ¾      : :   400:x

Days                   20 : 10

8 * ¼  * 20 * x = 9 * ¾ * 10 * 400

x = 9 * 3* 10* 400*4 /  8 * 20 * 4

 =675

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