EXERCISE 7A (OBJECTIVE TYPE QUESTIONS IN 56 60 SOLUTION )

         56.       The sum of three consecutive multiples of 3 is 7. What is the largest number?

a)      21

b)      24

c)       27

d)      36

57.       What is the sum of two consecutive even numbers, the difference of whose squares is 84?

a)      34

b)      38

c)       42

d)      46

58.       The sum of the squares of three consecutive natural numbers is 2030. What is the middle number?

a)      25

b)      26

c)       27

d)      28

59.       There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first and twice the second is 36. The lager of the two is:

a)      6

b)      8

c)       9

d)      12

60.       In a two – digit number, the digit in the unit’s place is four times the digit in ten’s place and sum of the digits is equal to10. What is the number?

a)      14

b)      41

c)       82

d)      Data inadequate

e)      None of these

ANSWERS

56.C

57.C

58.B

59.C

60.E

SOLUTIONS

56.       Let the numbers be 3X, 3X + 3 and 3x + 6.

              Then, 3X + (3X +3) +(3x +| 6) = 72    9X = 63   X = 7.

              Largest number = 3X + 6= 27.

57.       Let the numbers be X and x + 2.

              Then, (X + 2)²- x²= 84    4X + 4 = 84        4X = 80     X = 20.

              Required sum = X + (X + 2) =2x + 2 = 42.

58.       Let the numbers be X, X + 1 and X + 2.

          Then, x² + (x + 1)² + ( X + 2)² = 2030     3X² + 6x – 2025 = 0

           x² + 2x – 675 = 0     (x + 27) (x – 25) = 0    X = 25.

          Middle number = (x + 1) = 26.

59.       Let the numbers be X and Y. Then, 2X + 3y = 39  .. (I) and 3X + 2y = 36 ….(II)

           On solving (I) and (II), we get: x = 6 and y = 9.

           Large number = 9.

60.       Let the ten’s digits be X. Then, unit’s digit = 4x.

              X + 4x = 10   5x = 10    X = 2

              So, tens digit = 2, Unit’s digit = 8.

             Hence, the required number is 28. 

1.