Question 5 - Figure it out - Page 132, 133, 134 - Chapter 5 Class 8 - Number Play (Ganita Prakash)

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Question 5 If 48a23b is a multiple of 18, list all possible pairs of values for a and b.If a number is divisible by 18, it means It is divisible by 2 (must be even) It is divisible by 9 (sum of digits is divisible by 9). Note: We choose 2 & 9 because they have no common factors Divisibility by 2 Number is 48a23b Since the number has to be even. b can be 0, 2, 4, 6, 8 Divisibility by 9 Number is 48a23b Sum of digits = 4 + 8 + a + 2 + 3 + b = 17 + a + b The next multiples of 9 after 17 are 18, 27, 36 Finding pairs If Sum = 18 17+𝑎+𝑏=18 𝑎+𝑏=18−17 𝒂+𝒃=𝟏 Since 𝒃 is even, pair coud be 𝑏=0,𝑎=1. ∴ Pair: (𝒂=𝟏,𝒃=𝟎) If Sum =𝟐𝟕: 17+𝑎+𝑏=27 𝑎+𝑏=27−17 𝒂+𝒃=𝟏𝟎 We can have multiple cases here, like If 𝑏=2,𝑎=8 If 𝑏=4,𝑎=6 If 𝑏=6,𝑎=4 If 𝑏=8,𝑎=2 ( 𝑏=0 implies 𝑎=10, not a digit). Thus, the Possible pairs (𝑎,𝑏) are (𝟏,𝟎),(𝟖,𝟐),(𝟔,𝟒),(𝟒,𝟔),(𝟐,𝟖)