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22. If x and y are he number of possibilities that A canassume such 'hat the unit digit of A and A aresame and the unit digit of A and A are samerespectively, then he value of x -y is (where A isa single digit number)(2) 2(4) 5(3) 3 |
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Answer» Given, A is a single digit number. if A = 1 then, A³ = 1³ = 1 , here you can see unit digit of A and A³ are same. if we take A = 2 then, A³ = 2³ = 8 , unit digits are not same.if we take A = 3 => A³ = 27 ( × )if we take A = 4 => A³ = 64 ( ✓ )if we take A = 5 => A³ = 125 (✓)if we take A = 6 => A³ = 216 (✓) if we take A = 7 => A³ = 343 ( × )if we take A = 8 => A³ = 512 ( × )if we take A = 9 => A³ = 729( ✓) hence, there are five possible solution where unit digits of A and A³ are same. so, x = 5 again, if we take A = 1 => A² = 1 and A³ = 1 (✓)if we take A = 2 => A² = 4 and A³ = 8 ( × )if we take A = 3 => A² = 9 and A³ = 27 ( × )if we take A = 4 => A² = 16 and A³ = 64 ( × )if we take A = 5 => A² = 25 and A³ = 125( ✓ )if we take A = 6 => A² = 36 and A³ = 216 ( ✓)if we take A = 7 => A² = 49 and A³ = 343 ( × )if we take A = 8 => A² = 64 and A³ = 512 ( × )if we take A = 9 => A² = 81 and A³ = 729 ( × )here we can see , there are three possible solution where unit digits of A² and A³ are same. so, y = 3 hence, x - y = 5 - 3 = 2 |
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