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•  FREE 1 hour demo session
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•  Session Topics can be selected by you
•  LIVE Training done using Skype/GTalk
•  Sample Tests given weekly

GRE/GMAT sample questions with solution

Substitution:

1. If  n is an even integer which one of the following is an odd integer?

   a) n²           b)  -2n-4      c) √(n² +2            d)n+1/2    e)2n²-3

       Sol: It is given that n is an even integer. Let n=2

             n² = 2²= 4 is an even integer. So choice a is eliminated.

            -2n-4 = -2*2 -4   = -4-4 = -8 is an even integer. So choice b is eliminated.

          √(n²+2 =√(2²+2 = √6  is not an integer. So choice c is eliminated.

          n+1/2 = 2+1/2 = 3/2 is not an integer. So choice d is eliminated.

          2n²-3 = 2* 2² – 3 = 8 -3 =5 is an odd integer. So choice e is the answer.

               For Live Training  Contact Me at resmysarath@gmail.com or call 1-2017411138

2.  If n is an integer, which of the following CANNOT be an integer?

       a) n-2/2              b)  √n         c) 2/n+1         d) √(n²+3     e) √(1/n²+2)

       Sol : Let n =0 . So n-2/2 = 0-2/2 = -1 which is an integer. So choice a is eliminated.

                √n = √0 =0 which is an integer. So choice b is eliminated.

              2/(n+1) = 2/(0+1) =2 which is an integer. So choice c is eliminated.

            Next, √(n²+3 = √(0²+3)  = √3 which is not an integer . So it may be the answer.

              √(1/n²+2) = √(1/2)  which is not an integer as well .

             So we choose another number say 1. Then √(n²+3) = √4 =2 which is  an integer .

            √(1/n²+2) = √(1/4) . Thus choice e is the answer.

          For Live Training  Contact Me at resmysarath@gmail.com or call 1-2017411138

3. If x, y and z are positive integers such that x< y < z and x + y + z =6, then what is the value of  

     z?

          a) 1       b) 2               c)3             d) 4               e) 5

          Sol :  From the given inequality x<y<z, it is clear that the positive integers x, y and z are

                   different  and are in increasing order of size.

                 Let x=1  y =2 and z= 3.   So 1< 2< 3 and  x+ y+z = 1+2+3 =6

                So z=3. Choice c is the answer.

            For Live Training  Contact Me at resmysarath@gmail.com or call 1-2017411138

4. By how much is the greatest of five consecutive even integers greater than the smallest

      among them?

      a) 1            b) 2               c)4                   d)8                  e) 10

          Sol:    Let the five consecutive even integers be 2, 4, 6, 8, 10

                   Largest no of these =10

                  Smallest no of these = 2

                 Difference =8

                So answer is d.

               For Live Training  Contact Me at resmysarath@gmail.com or call 1-2017411138

5. Which of the following could be an integer?

      a) The  average of two consecutive integers.

      b) The  average of three consecutive integers.

       c) The  average of four consecutive integers.

      d) The  average of six consecutive integers.

      e) The average of 6 and 9

       Sol:   choose any 2 consecutive integers,  say, 1 and 2.

               Average = 1+2/2 =1.5 is not an integer. So choice a is eliminated.

               choose any 3 consecutive integers,  say, 1 ,2 and 3.

               Averge = 1+2+3/3 =6/3 =2 is an integer. So choice b is the answer.

              For Live Training  Contact Me at resmysarath@gmail.com or call 1-2017411138

GRE : Sample Questions with Solution

1.  In how many different ways can the letters of the word ‘DETAILS’ be arranged in such a way that the  vowels occupy only the odd positions?

        a) 32        b) 48       c) 36    d) 60

          Sol :   There are 6 letters in the given word, out of wich there are 3 vowels and 3   

                      consonants.

                     3 vowels can be placed at any of the 3 places  marked 1, 3, 5.

                      No of ways of arranging the vowels = 3P3 = 3! =6

                     Also the 3 consonants can be arranged at the remaining 3 positions.

                     No of ways these arrangements = 3P3 = 3! = 6

                     Total no of ways = 6*6 =36

          For Live Training  Contact Me at resmysarath@gmail.com or call 1-2017411138

2.  From a group of 7 men and 6 woman five  persons are to be selected to form a committee so that at least 3 men are there on te committee . In how many ways can it be done?

                  a) 564         b) 645    c)  735        d) 756

           Sol :  We may have  (3 men and 2 women ) or (4 men and 1 woman ) or(5 men only)

              Required no of ways = 7C3 * 6C2 + 7C4 * 6C1 +7C5

                                                   = 756

          For Live Training  Contact Me at resmysarath@gmail.com or call 1-2017411138

3. A  box  contains 2 white balls , 3 black balls and 4 red balls . In how many ways can 3 balls be   

   drawn    from the box, if at least one black ball is to be included in the draw?

            a) 32             b) 48          c) 64       d) 96

           Sol: we may have (1 black & 2 non-black ) or (2 black and 1 non black )  or 3 black

                 Required no of ways = 3C1 * 6C2 + 3C2 *   6C1   +  3C3

                                                      = 45+18+1=64

              For Live Training  Contact Me at resmysarath@gmail.com or call 1-2017411138

4. Two dice are thrown together . What  is the probability that the sum of the nos on the two

     faces is divisible by 4 or 6?

          a) 7/18    b) 5/ 18   c) 5/36    d) ½

           Sol :  n(S) = 6 * 6 =36

                     Let E be the event tat the sum of the nos on the two faces is divisible by 4 or 6 Then

                    E = {(1,3) ,(1, 5) , (2, 2), (2, 4) ,(2, 6), (3,1), (3,3) , (3,5), (4,2), (4,4), (5,1), (5,3),(6,2), 

                             (6,6)}

                  n(E) = 14

                   P(E) = n(E)/n(S) = 14/ 36 = 7/18

            For Live Training  Contact Me at resmysarath@gmail.com or call 1-2017411138

5.    A box contains 5 green, 4 yellow and 3 white marbles. Three marbles are drawn at

          random. What is the probability that they are not of the same colour?

         a) 3/44         b)3/55                c) 52/55                  d)41/44

            Sol:  Let S be the sample space. Then n(S) = no of ways of drawing 3 marbles out of 12.

                     = 12C3 = 220

                       Let E be the event of drawing 3 balls of the same colour.

                   Then E = events of drawing (3 balls out of 5) or (3 balls out of 4 ) or (3 balls out of 3)

ð  n(E) = 5C3 +4C3 +3C3 = 5C2 + 4C1 + 1 = 15

ð  P(E) = n(E)/n(S) = 15/220 = 3/44

Required probability = 1-(3/44) =41/44

For Live Training  Contact Me at resmysarath@gmail.com or call 1-2017411138

GRE / GMAT : Sample Questions with Solution

     Profit & Loss:

1. If CP = $ 56.25 and Gain = 20%    What is SP ?

            a) 65.70 b) 67.50  c)76.70   d) 56.50

     Sol:  SP = 120 % of  $ 56.25

                   = 120* 56.25 / 100

                   = 67.50

   For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

2.  If CP = $ 80 and Loss = 5% what is SP?

          a) 76  b) 67 c) 77 d)68

      Sol :  SP = 95% of $80

                     = 95 * 80 /100

                     = 76

               For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

3. A person incurs 5% loss by selling an article  for $ 1140 .At what price should the article be sold to   

       earn 5% profit ?

           a) 1200 b) 1260  c) 1270  d) 1400

       Sol : Let the new SP be x. Then

                (100 – Loss % ) : (1^st SP ) =  (100 + Gain % ) : (2^nd SP )

ð    (100-5)/1140 = (100+5)/x

ð  x = 105 * 1140 /95 = 1260

                    So New SP = $1260.

                For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

4.  A book was sold for $ 27.50 with a profit of 10% .If it were sold for $ 25.75 then what have been

         the percentage of profit  or loss ?

                         a)1 %  b)2%   c) 3%  d )5%

             Sol :  SP =  $ 27.50 profit = 10 %

                       So CP = 100* 27.50/110 = 25

                       When  SP  = $25.75 profit = 25.75 – 25 = 0.75

                      Profit % =( 0.75 * 100 /25 ) %   =   3%

            For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

5.  If the cost price is 96% of the selling price then what is the profit percentage ?

                a) 4% b)  3.17 %  c)4.27  %   d) 4.17%

               Sol :  Let  SP = $100 Then CP = 96  Profit = $4

               Profit % = (4 %100)/96 = 25/6 % = 4.17 %

                 For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

GRE /GMAT : Sample Questions with Solution

1. If 3/p = 6 and 3/q = 15 then p - q = ?

1. 1/3
2. 2/5
3. 3/10
4. 5/6
5. None of the above

Ans : C

Sol : 3/p = 6 so p=3/6 =1/2

        3/q = 15 so q=3/15=1/5

P – q = ½ - 1/5 =5-2/10 =3/10

For Live Training  Contact Me at  resmysarath@gmail.com or call 1-647-213-2378

    2.  If x⁴ = 16, then 4^x =

              a) 2   b) 4   c) 8   d) 16

x⁴ = 16    2* 2*2*2=16

2⁴ = 16   S x=2

4^x = 4²  = 16

For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

     3.  |-5| + |3| - |-5| =

             a) -2  b) -13  c) 8   d) 3  e) 2
          

          Sol: 

          Absolute value of  |-5|=5, |3| = 3

           |-5| + |3| - |-5| = 5 + 3 – 5 =  3

For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

     4. If 2x > 24 and 3x < 48, which of the following is a possible value for x?

          a) 12  b) 14  c) 16  d) 18

        Sol:  2x > 24  =>  2x/2  > 24/2  =>    x > 12

                3x < 48  =>   3x/3  <  48/3   =>  x <  16

         So from the given choices answers is 14

    For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

   5.  If a cube has a volume of 343 cubic inches, what is the length of one  side?

         A:7square inches B:30square inches C: 7inches D: 49 inches                          

        Sol: Volume of a cube = (length of one side )³  = 343

         So  (length of one side )³ = 7³

              Length of one side = 7 inches

   For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

    6.  If 3x - 6 = 14 - x, then x =

        A: 5       B: 3      C: 4     D: 8       E: 10

        Sol:  It is given that  3x - 6 = 14 – x

        3x – 6 -14 + x = 0

       4x – 20 =0

       4x = 20

        x= 5

   For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

7. Factor: a² -3a - 18

    A: (a - 3)(a - 9)   B: (a - 2)(a - 9)   C: (a + 3)(a + 6)  D: (a + 2)(a + 9)  E: (a - 6)(a + 3)

    It is given a² -3a – 18

   Let (a+ x) (a + y) = a² -3a – 18

    x+ y = -3

    xy = -18

   So  x= -6 and y = 3   factors are (a-6) and (a+ 3)

      For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

8.  If a = 2, then 3a + (a³)² =

    A: 73   B: 70    C: 7   D: 12    E: 27  

   Sol :  It is given a =2

     3a + (a³ ) ² = 3 * 2 + (2³ )² =6 + 8² = 6+ 64 = 70

   For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

9. If a camera purchased for $490 and sold for $460 find the loss percent?

a) 1%    b) 5%   c)  10%   d) 2%

Sol : CP = $490       SP = $465.50

Loss = (490-465.50) = $24.50

Loss % = 24.50* 100/490 = 5%

   For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

10 . A man buys an article for $ 27.50 and sells it for $ 28.60 . Find his gain percent?

a) 3%   b) 1%    c) 4%  d) 5%

Sol: CP = $ 27.50     SP= 28.60

Gain = SP- CP = 28.60 – 27.50 = 1.10

Gain %  = Gain * 100/CP = 1.10 * 100 /27.50 = 4 %

   For Live Training  Contact Me at resmysarath@gmail.com or call 1-647-213-2378

GRE /GMAT : Quantitative Comparison with solution

Directions:

In this section you will be given two quantities, one in column A and one in column B. You are to determine a relationship between the two quantities and mark.

1. If the quantity in column A is greater than the quantity in column B.
2. If the quantity in column B is greater than the quantity in column A.
3. If the quantities are equal.
4. If the comparison cannot be determined from the information that is given.

1. Quantity A: (-6)⁴ 
   Quantity B: (-6)⁵
1. if the quantity A is greater;
2. if the quantity B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Ans : A

Soln:  ( -6)⁴  =(-1 * 6)⁴ = (-1)⁴  * 6⁴ =  (-1)² * (-1)²   * 6⁴ =6⁴

               (-6)⁵ = (-1)⁵ * 6⁵  = -1 * 6⁵ =-6⁵

So Ans is A

2. Quantity A: Time to travel 95 miles at 50 miles per hour 
   Quantity B: Time to travel 125 miles at 60 miles per hour
1. Quantity A is greater
2. Quantity A equals Quantity B
3. Quantity B is greater
4. Relationship Indeterminate

Ans : C

Soln : Time = Distance/Speed

          For Case A     Time= 95/ 50 = 1.

          For Case B      Time= 125/60=2.

          So B>A

3. Quantity A: (9/13)² 
   Quantity B: (9/13)^1/2
1. Quantity A equals Quantity B
2. Relationship Indeterminate
3. Quantity B is greater
4. Quantity A is greater

Ans : C

  Soln :  a^1/m  = ^m√a

For Case A it is (9/13)²

For Case B it is (9/13)^1/2 = √(9/13)  

So B>A

4. Quantity A: 4 / 100 
   Quantity B: 0.012 / 3
1. Quantity B is greater
2. Quantity A equals Quantity B
3. Quantity A is greater
4. Relationship Indeterminate

Ans : C

    For Case A  :  4/100=0.04

   For Case B : 0.012 / 3 = 0.04

So A=B

5. x = 2y + 3 
   y = -2

Quantity A: x 
Quantity B: -1

1. if the quantity in Column A is greater;
2. if the quantity in Column B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given

Ans : C

x=2y+3 = 2(-2)+3 = -1

So both quantities are equal.

6. x + 2y > 8

Quantity A: 2x + 4y 
Quantity B: 20

1. if the quantity in Column A is greater;
2. if the quantity in Column B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Ans : D

x+2y > 8 => 2(x+2y) > 2(8)

  2x+4y > 16

So the relationship cannot be determined from the information given

7. Quantity A: The number of months in 7 years 
   Quantity B: The number of days in 12 weeks
1. if the quantity in Column A is greater;
2. if the quantity in Column B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given

Ans : C

The no of months in 7 years = 7* 12 months = 84 months

The no of days in 12 weeks = 12* 7 days = 84 days

So two quantities are equal.

8. Quantity A: 1-1/27 
   Quantity B: 8/9 + 1/81
1. if the quantity in is greater;
2. if the quantity in is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Ans : A

Case A 1-1/27 = 27-1/27 = 26/27=0.96

Case B 8/9 + 1/81

LCM of 9 and 81 is 81

So 8/9 + 1/81 = (8*9 +1)/81 = 73/81 =0.90

So A>B

9. r>s>0

Quantity A: rs/r 
Quantity B: rs/s

1. if the quantity A is greater;
2. if the quantity B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Ans : B

Case A rs/r and case B is rs/s

It is given that r>s

If you divide the same quantity by a smaller no the result will be greater.

10. Quantity A: 0.83 
    Quantity B: 0.81/3
1. Quantity B is greater
2. Relationship Indeterminate
3. Quantity A is greater
4. Quantity A equals Quantity B

Ans : C

Case A  0.83

Case B is 0.81/3 = 0.27

So A>B

Sample questions of GRE with solution

1  

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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