EXERCISE 7 A (OBJECTIVE TYPE QUESTIONS IN 61 70 SOLUTION )

66.       The sum of the digits of a two – digits number is 9 less than the number. Which of the following digits is at unit’s place of the number?

a)      1

b)      2

c)       4

d)       Data inadequate

67.       The difference between a two – digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers?

a)      3

b)      4

c)        9

d)      Cannot be determined

e)      None of these

68.       The difference between a two –digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers?

a)      29

b)      70

c)       92

d)      Cannot be determined

e)      None of these

69.       The sum of the digits of a two – digit number and the number obtained by interchanging the two digits is 63.Which is the smaller of the two numbers?

a)      5

b)      7

c)       9

d)      Data inadequate

e)      None of these

70.       If the digit in the unit’s place of a two – digit number is halved and the digit in the ten’s place is doubled, the number thus obtained is equal to the number obtained by interchanging the digits. Which of the following is definitely true?

a)      Sum of the digits is a two – digit number.

b)      Digit in the unit’s place is twice the digit in the ten’s place.

c)       Digits in the unit’s place and the ten’s place are equal.

d)      Digit in the unit’s place is half o f the digit in the ten’s place

e)      None of these.

ANSWERS

66. D

67. B

68. D

69. D

70. B

SOLUTION 

66.       Let the ten’s digit be x and unit’s digit be y. Then, (10X + y) – (X + y) = 9 on X =1. From this data, we cannot find y, the unit’s digit, so, the data is inadequate.

67.       Let the ten’s digit be X and unit’s digit be y.

               Then, (10x + y) – ( 10y + x) = 36    9 (X – Y ) – 36   x – y = 4.

68.       Let the ten’s digit be X and unit’s digit be y.

               Then, (10x + y) – (10y + X) = 63   9 ( x – Y ) = 63 x – y = 7

               Thus, none of the numbers an be determined.

69.       Let the ten’s digit be X and unit’s digit be y.

              Then, x + y = 1/5 [(10x + y) – 10y + x)]    5X + 5y = 9X – 9y 4X = 14y.

              Thus, the value of (X – y) cannot be determined from the given data.

70.       Let the ten’s digit be x and unit’s digit be y.

              Then, 10 x 2x + 1/2 y = 10y +x      20x – x = 10y – y/2    19X = 19/2 y    y = 2x.

               Thus, the units digit is twice the ten’s digit.