Extra Questions
Question 1: If 51x3 is a multiple of 9, where x is a digits, then what is the value of x?
Solution: We have the sum of the digits of 51x3
= 5 + 1 + x + 3 = 9 + x
Since, 51x3 is divisible by 9.
∴ (9 + x) must be divisible by 9.
∴ (9 + x) must be equal to 0 or 9 or 18 or 27 or …
But x is a digit, then
9 + x = 9 ⇒ x = 0
9 + x = 18 ⇒ x = 9
x = 27 ⇒ x = 18, which is not possible.
∴ The required value of x = 0 or 9.
Question 2: If 27x is a multiple of 3 and x is a digit then find the value of x.
Solution: Sum of the digits of 27x
= 2 + 7 + x = 9 + x
Since, 27x is a multiple of 3,
∴ (9 + x) is divisible by 3.
⇒ 9 + x must be equal to 9 or 12 or 15
When 9 + x = 9 ⇒ x = 0
When 9 + x = 12 ⇒ x = 3
When 9 + x = 15 ⇒ x = 6
When 9 + x = 18 ⇒ x = 9
When 9 + x = 21 ⇒ x = 12, which is not possible. [∵ x is a digit]
The x can equal to 0, 3, 6 or 9.
Practice Exercise
Question 1. Write the following numbers in the generalized form:
(i) 65 (ii) 605
Answer: (i) 60 + 5 (ii) 600 + 0 + 5
Question 2. Write the following numbers in usual form:
(i) 7 x 100 + 10 x 5 + 9 x 1 (ii) 4 x 100 + 10 x 0 + 7 x 1
Answer: (i) 759 (ii) 407
Question 3. Is 307 divisible by 9?
Answer: No
Question 4. Is 1125 divisible by 3?
Answer: Yes
Question 5. Is 10011 divisible by 3?
Answer: Yes
Question 6. If 42x5 is a multiple of 9 and x is a digit, then find the value of x.
Answer: x = 7
Question 7. If 3x12 is a multiple of 3 and x is digit, then find the value of x.
Answer: x = 0 or 3 or 6 or 9
Question 8. If 35x is a multiple of 9 and x is digit, then find the value of x.
Answer: x = 1
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