Quantitative Aptitude-More exercise questions

Simplification-Exercise Questions

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1. If a * b  =  a + b , find the value of 5 * (5 * -2) :

                      ab

a. -3

b. -10

c. -1.66

d. 3/5 

 

2. If (a – b) is 9 more than (c + d) and (a + b) is 3 less than (c – d), then (a – c) is:

a. 6

b. 2

c. 3

d. None of these

 

3. The value of  1 + [1/(8 x 2)] + [1/(8 x 2²)] + [1/(8 x 2³)] is :

a. 71/64

b. 1/16

c. 1/4

d. None of these

 

4. If  a = b = c, then the value of  a + b + c  is :

        2     3    5                                 c

a. 1/√5

b. √2

c. 2

d. 5

 

5. When simplified, the product (1 – 1/2) (1 – 1/3) (1 – 1/4)…… (1 – 1/n) gives:

a. 1/n

b. 2/n

c. 2(n – 1)/n

d. 2/n(n + 1)

 

6. The value of  (x – y)³ + (y - z)³ + (z – x)³ is equal to :

                          12 (x – y) (y – z) (z – x)

a. 0

b. 1/12

c. 1

d. 1/4

7. The value of 99 95  x 99 is:

                           99    

a. 9989

b. 9896

c. 9890

d. 9809

 

8. (12)³ + (6)³ = 18

    (12)² + 6² - ?

a. 6

b. 18

c. 72

d. None of these

 

9. If a * b = 2a – 3b + ab, then 5 * 7 + 7 * 5 is equal to:

a. 33          

b. 36

c. 34

d. 38

 

10. If  x = a/(a – 1) and 1/(a – 1), then:

a. x is equal to y

b. x is equal to y only if a < 1

c. x is greater than y

d. x is greater than y only if a < 1

e. y is greater than x only if a < 1

 

11. If  a, b, c are integers; a² + b² = 45 and b² + c² = 40, then the values of a, b and c respectively are :

a. 2, 6, 3

b. 3, 2, 6

c. 5, 4, 3

d. None of these

 

12. A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less
     than  the correct one by 1206. Find the number to be multiplied.

a. 130

b. 132

c. 134

d. 136

 

13. In a garden, there are 12 rows and 14 columns of mango trees. The distance between two trees is 2
     metres and a distance of one metre is left from all sides of the boundary of the garden. The length of
     the garden is

a. 20m

b. 22m

c. 24m

d. 26m

 

14. In a group of donkeys and pigs, the numbers of legs are 16 more than twice the number of heads. The
      number of donkeys is

 a. 6

 b. 8

 c. 11

 d. 13

 

15. The value of 40 coins of 10 p and 20 p is Rs. 5.50. The number of 20 p coins is

a. 15

b. 25

c. 30  

d. 35

 

16. An enterprising businessman earns an income of Re 1 on the first day of his business. On every
     subsequent day, he earns an income which is just double of that made on the previous day. On the 20th
     day of business, he earns an income of:

 a. Rs 219

 b. Rs 220

 c. Rs 20²

 d. Rs 20

 

17. In an examination, a student scores 4 marks for every correct answer and loses 1mark for every wrong
     answer. If he attempts all 90 questions and secures 140 marks, the number of questions he attempts
     correctly, is:

 a. 35

 b. 40

 c. 42

 d. 46

 

18. Anitha had 80 currency notes in all, some of which are of  Rs 95 denomination and the remaining of Rs
    45 denomination. The total amount of all these currency notes was Rs. 4000. How much amount (in Rs)
    did she have in the denomination of Rs 45?

 a. 3500

 b. 72

 c. 2000

 d. None of these

 

19. How many 1/8s are there in 37 1/2?

a. 300

b. 400

c. 500

d. Can’t be determined

 

20. How many pieces of 0.85 metres can be cut from a rod 42.5 metres long?

a. 30

b. 40

c. 60

d. None of these

 

Answer & Explanations

 

1. Exp: (5 * -2) = 5 x (-2) = -10

                         5 + (-2)      3

 

             So, 5 * (5 * -2) = 5 * (-10/3) = 5 * (-10/3) = (-50/3) * (3/5) = -10.

                                                         5 + (-10/3)

2. Exp: (a – b) – (c + d) = 9 and (c – d) – (a + b) = 3

          => (a – c) – (b + d) = 9 and (c – a) – (b + d) = 3

          => (b + d) = (a – c) – 9 and (b + d) = (c – a) – 3

          => (a – c) – 9 = (c – a) – 3 => 2(a – c) = 6 => (a – c) = 3

3. Exp:  8 x 2³ + 2² + 2 + 1 = 64 + 4 + 2 + 1 = 71/64.

                  8 x 2³                         64

4. Exp:  a = b = c = k (say). Then, a = 2k, b = 3k, c = 5k.

            2     3    5

 

          a + b + c = 2k + 3k + 5k = 10k = 2.

              c                   5k              5k           

5. Exp: 1/2 x 2/3 x 3/4 x …..x (n – 1)/n = 1/n

6. Exp: Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³

                                                              = 3 (x – y) (y – z) (z – x).

 

             3 (x – y) (y – z) (z – x) = 1/4.

             12(x – y) (y – z) (z – x)

7. Exp: (100 – 4/99) x 99 = 9900 – 4 = 9896.

8. Exp: Let (12)³ + (6)³ = 18. Then,

                (12)² + 6² - ?

 

          12³ + 6³ = 12² + 6² - x   =>  12² + 6² - 12 * 6 = 12² * 6² - x  =>  x = 12 * 6 = 72.

           12 + 6

9. Exp: 5 * 7 + 7 * 5 = (2 * 5 – 5 * 7 + 5* 7) + (2 * 7 – 5 * 5 + 7 * 5)

                               = (10 + 14 – 25 + 35) = 34.

10. Exp: x = a/(a – 1) = 1 + 1/(a – 1) = 1 + y.   Therefore,  x > y

11. Exp: a² + b² = 45 ….(1)  and b² + c² = 40

            Subtracting, we get: a² - c² = 5   =>   (a + c) (a – c) = 5.

           (a + c) = 5 and (a – c) = 1.

           Solving we get: a = 3, c = 2. Putting c = 2 in (ii), we get b = 6.

12. Exp: Let the required number be x. Then,

            43x – 34x = 1206 or 9x = 1206 or x = 134.

            Required number = 134.

13. Exp: Each row contains 14 plants.

            Leaving 2 corner plants, 12 plants in between have (12 x 2) metres & 1 metre on each side is left.

            Length = (24 + 2) m = 26m.

14. Exp: Let the number of donkeys be x and the number of pigs be y. Then,

            4x + 2y = 2(x + y) = 16 or 2x + (2x + 2y) = (2x + 2y) +16

    or 2x = 16 or x = 8.

14. Exp: Let the number of 20 paise coins be x.

            Then, number of 10 paise coins = (40 – x).

            10(40 – x) + 20x = 550 or 10x = 150 or x = 15.

16. Exp: 2nd day he earns = 2 = 2(2 – 1)

            3rd day he earns = 2(3 – 1)

            On 20th day he earns 2(20 -1) = 219 rupees

17. Exp: Let the number of correct answers be x.

            Number of incorrect answers = (90 – x).

            4x – (90 – x) = 140 or 5x = 230 or x = 46.

18. Exp: Let the number of 45-rupee notes = x

            Then, the number of 95-rupee notes = (80 – x)

            45x + 95(80 – x) = 4000 or x + 2(80 – x) = 95 or x = 72.

19. Exp: Required number = (75/2) = (75/2 x 8/1) = 300.

                             (1/8)

20. Exp: Number of pieces = 42.5 = 42.50 = 4250 = 50.

                                        0.85     0.85        85

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