AIC Placement Papers

AGRICULTURAL-INSURANCE-AIC -Model aptitude reasoning questions and answers. Aptitude,reasoning,english and professional test questions answers

AIC-Quantitative Aptitude

Directions (Q. Nos. 1 to 5) What will come in place of question mark (?) in the following questions?

 1. 348 ÷ 29 x 15 + 156 = (?)³ + 120

(1) 12

(2) 6    (Ans)

(3) 36

(4) 9

(5) None of these

Ans : 348 ÷ 29 x 15 + 156 = (?)³ + 120

⇒       12 x 15 + 156 = (?)³ + 120

⇒    180 + 156 - 120 = (?)³

⇒                    216 = (?)³

⇒                    (6)³ =  (?)³

∴                        ? = 6

2. (4 x 4)³ ÷ (512 ÷ 8)⁴ x (32 x 8)⁴ = (2 x 2)^{? + 4}

(1) 8

(2) 12

(3) 6   (Ans)

(4) 14

(5) None of these

Ans :  (4 x 4)³ ÷ (512 ÷ 8)⁴ x (32 x 8)⁴ = (2 x 2)^{? + 4}

⇒     (16)³ ÷ (64)⁴ x (256)⁴ = (4)^{? + 4}

⇒    (4)^2x3 ÷ (4)^3x4 x (4)^4x4  = (4)^{? + 4}

⇒          (4)⁶ ÷ (4)¹² x (4)¹⁶ = (4)^{? + 4}

⇒                        (4)^6-2+16 = (4)^{? + 4}

⇒                             (4)¹⁰  = (4)^{? + 4}

⇒                                 10 = ? + 4

∴                                   ? = 6

3. (2√392 - 21) + (√8 - 7)² = (?)²

(1) 4

(2) -4

(3) 12

(4) 2

(5) 6   (Ans)

Ans :  (2√392 - 21) + (√8 - 7)² = (?)²

⇒                 (2 x 14√2 - 21) + (√8 - 7)² = (?)²

⇒   28√2 - 21 + (√8)² - 2 x √8 x 7 + (7)² = (?)²

⇒                  28√2 - 21 + 8 - 28√2 + 49 = (?)²

⇒                                     - 21 + 8 + 49 = (?)²

⇒                                                     36 = (?)²

∴                                                       ? = 6

4. 1 1/4 + 1 1/6 - 1 1/8 = ? + 1 1/12

(1) 5/24    (Ans)

(2) 7/24

(3) 5/12

(4) 7/12

(5) None of these

Ans :   1 1/4 + 1 1/6 - 1 1/8 = ? + 1 1/12

⇒                 1 1/4 + 1 1/6 - 1 1/8 - 1 1/12  = ?            

⇒   (1 + 1 - 1 - 1) + (1/4 + 1/6 - 1/8 - 1/12) = ?

⇒   0 + (6 + 4 - 3 - 2/24) = ?   ⇒   0 + 5/24 = ?

 âˆ´                                                   ? = 5/24

5. 76% of 1285 = 35% of 1256 + ?

(1) 543

(2) 537   (Ans)

(3) 547

(4) 533

(5) None of these

Ans :   76% of 1285 = 35% of 1256 + ?

⇒                 976.6 = 439.6 + ?

⇒      976.6 - 439.6 = ?

∴                       ? = 537

Directions (Q. Nos. 6 to 10) What  approximate value will come in place of question mark (?) in the following questions? (You are not expected to calculate the exact value)

Solutions (6 to 10)

You can take approximate value of any number

6. 499.99 + 1999 ÷ 39.99 x 50.01 = ?

(1) 3200

(2) 2700

(3) 3000  (Ans)

(4) 2500

(5) 2400

Ans :   499.99 + 1999 ÷ 39.99 x 50.01 = ?

500 + 2000 ÷ 40 x 50 = ?

           500 + 50 x 50 = ?

               500 + 2500 = ?

                        3000 = ?

7. [(7.99)² - (13.001)² + '(4.01)³]² = ?

(1) -1800

(2) 1450

(3) -1660

(4) 1660 (Ans)

(5) -1450

Ans :   [(7.99)² - (13.001)² + '(4.01)³]² = ?

⇒                       [(8)² - (13)² + (4)³]² = ?

⇒                             [64 - 169 + 64]² = ?

⇒                                           (-41)²= ?

∴                                                  ? =  1681     (∵- x - ⇒ +)

                                                       ≈ 1660

8. 601/49 x 399/81 ÷ 29/201 = ?

(1) 520

(2) 360

(3) 460

(4) 500

(5) 420    (Ans)

Ans :  601/49 x 399/81 ÷ 29/201 = ?

⇒       601/49 x 399/81 x 201/29 = ?

⇒       600/50 x 400/80 x 200/30 = ?

∴        400 = ?

           420 ≈ ?

9. 441.01 - 232.99 + 1649.99 = ? + 1225.92

(1) 600

(2) 630   (Ans)

(3) 660

(4) 690

(5) 720

Ans :  441.01 - 232.99 + 1649.99 = ? + 1225.92

⇒         441 - 233 + 1650 - 1226  = ?

⇒                           2091 - 1459 = ?

∴                                          ? = 623 ≈ 630

10. (21.5% of 999)^1/3 + (43% of 601)^1/2 = ?

(1) 18

(2) 22  (Ans)

(3) 26

(4) 30

(5) 33

Ans :  (21.5% of 999)^1/3 + (43% of 601)^1/2 = ?

         (1000 X 21.5%)^1/3 + (600 X 43%)^1/2 = ?

                                 (215)^1/3 + (258)^1/2 = ?

                                 (216)^1/3 + (256)^1/2 = ?

                                (6)^3X1/3 + (16)^2X1/2 = ?

                                                  6 + 16 = ?

                                                        22 = ?

Directions (Q. Nos. 11 to 15) What will come in place of question mark (?) in the following number series?

11. 15  21  39  77  143  (?)

(1) 243

(2) 240

(3) 253

(4) 245

(5) None of these  (Ans)

12. 33  39  57  87  129  (?)8

(1) 183  (Ans)

(2) 177

(3) 189

(4) 199

(5)

13. 15  19  83  119  631  (?)

(1) 731  (Ans)

(2) 693

(3) 712

(4) 683

(5) None of these

 14. 19  26  40  68  124  (?)

(1) 246

(2) 238

(3) 236    (Ans)

(4) 256

(5) None of these

15. 43  69  58  84  73 (?)

(1) 62

(2) 98

(3) 109

(4) 63

(5) None of these   (Ans)

Directions (Q. Nos. 16 to 20) In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer

(1) if x > y

(2) if x ≥ y

(3) if x < y

(4) if x ≤ y

(5) if x = y or the relationship cannot be established

Ans :

16. I.  x² - 11x + 24 = 0

       II.  2y² - 9y + 9 = 0
 

Ans :2     I.  x² - 11x + 24 = 0

              x² - 8x - 3x + 24 = 0

            x (x - 8) - 3 (x - 8) = 0

                    (x - 8)(x - 3) = 0

∴        x = 8 or 3
 

II.      2y² - 9y + 9 = 0

    2y² - 6y - 3y + 9 = 0

 2y(y - 3) - 3 (y - 3) = 0

       (2y - 3) (y - 3) = 0

∴        y = 3/2 or 3

So,      x ≥ y

17. I.  x³ * 13 =  x² * 247 

       II.  y^1/3 * 14  = 294 ÷ y^2/3
 

Ans :3    I.  x³ * 13 =  x² * 247 

or x³ / x²  = 247/13

x = 19

II.          y^1/3 * 14  = 294 ÷ y^2/3    

or,   (y)^1/3 * (y)^2/3  = 294/14

or,          (y)^1/3+2/3 = 21

∴                      y = 21

So,                     y > x

18. I. 12 *  4 / x^4/7 -  3 * 4 / x^4/7 =  x^10/7

       II.  y³ + 783 = 999
 

Ans : 4     I. 12 *  4 / x^4/7 -  3 * 4 / x^4/7 =  x^10/7

or,         48 - 12 = (x)^10/7 * (x)^4/7

or,         36 = (x)⁷     = (x)²

∴           x = ±6
 

II.          y³ + 783 = 999

                     y³ = 999 - 783

                     y³ = 216

∴                  y = ±6

∴                  y ≥ x

19. I. √500 x + √402 = 0

       II. √360 y + (200)^1/2 = 0
 

Ans : 5      I. √500 x + √402 = 0

or,                           √500 x = - √402

By squaring both sides, we get

         500 x²  = 402

                 x = √402 /500 = ± 0.897

II.√360 y + (200)^1/2 = 0

or,              (200)^1/2 = - √360 y

By squaring both sides, we get

    = (-√360 y)²

                200 = 360 y²

                    y = √200/360 = ± 0.75

relationship cannot established.

20. I. (17)² + 114 ÷ 18 = x

       II. (26)² - 18 * 21 = y

Ans :3        I. (17)² + 114 ÷ 18 = x

                                 289 + 8 = x

∴                                        x = 297

II. (26)² - 18 * 21 = y

           676 - 378 = y

∴                298 = y

So,                  y > x