## RS Aggarwal Class 8 Math Fifth Chapter Playing with Numbers Exercise 5D Solution

## EXERCISE 5D

### OBJECTIVE QUESTIONS

#### Tick (√) the correct answer in each of the following:

**(1) If 5×6 is exactly divisible by 3, then the least value of x is**

Ans: (b) 1

5 + x + 6 = (11 + x) must be divisible by 3.

This happens when x = 1 or 4 or 7.

Since x is digit, it cannot be more than 9.

∴ x = 1

**(2) If 64y8 is exactly by 3, then the least value of y is**

Ans: (a) 0

6 + 4 + y + 8 = 18 + y

This is divisible by 3 as y is equal to 0.

**(3) If 7×8 is exactly divisible by 9, then the least value of y is**

Ans: (c) 3

7 + x + 8 = 15 + x

18 is divisible by 9.

Therefore, 15 + x = 18

⇒ x = 3

**(4) If 37y4 is exactly divisible by 9, then the least value of y is**

Ans: (d) 4

3 + 7 + y + 4 = 14 + y

∴ 14 y = 18

⇒ y = 18 – 14 = 4

**(5) If 4xy7 is exactly divisible by 3, then the least value of (x + y) is**

Ans: (a) 1

4 + x + y +7 = 11 + (x + y)

⇒ 11 + (x + y) = 12

⇒ (x + y) = 12 – 11 = 1

**(6) If x7y5z is exactly divisible by 3, then the least value of (x + y) is**

Ans: (d) 3

x + 7 + y + 5 = (x + y) + 12

This sum is divisible by 3 is x + y + 12 is 12 or 15.

∴ x + y + 12 = 12

⇒ x + y = 12 – 12 = 0

But x + y cannot be 0 because x and y will habe to be 0.

∴ x + y + 12 = 15

⇒ x + y = 15 – 12 = 3

**(7) If x4y5z exactly divisible by 9, then the least value of (x + y + z) is**

Ans: (c) 9

X + 4 + y + 5 + z = 9 + (x + y + z)

This equation is equal to 0 for the number x4y5z to be divisible by 9.

But x is the first digit, so it can’t be 0.

∴ x + 4 + y + 5 +z = 18

⇒ x + y + z = 18 – 9 = 9

**(8) If 1A2B5 is exactly divisible by 9, then the least value of (A + B) is**

Ans: (b) 1

1 +A + 2 + B + 5 = (A + B) + 8

The number is divisible by 9 is (A + B) = 1

**(9) If the 4-digit number x27y is exactly divisible by 9, then the least value of 9x + y) is**

Ans: (d) 9

X + 2 + 7 + y = (x + y) + 9

This sum will be divisible by 9, if (x + y) is 0.

Since, x is the first digit it can never be 0.

∴ x + y + 9 = 18

⇒ x + y = 9