20. If a = 102, then find the value of a(a² - 3a + 3), Option : (a) 1030302 (b) 1010101 (c) 1000002  (d) 9999992

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If a = 102, then find the value of a(a² - 3a + 3).

• Take the digits of a=102


• Add them: 1+0+2=3

Let’s put a = 3.

3(3²−3⋅3+3) = 3(9−9+3) = 3×3 = 9

So for a=3, the result = 9.

Use the “digit-sum trick”

That means: whatever the real answer is, the sum of its digits must also equal 9.

Check given options

(a) 1030302 → digit sum = 1+0+3+0+3+0+2 = 9
(b) 10101014 → digit sum = 1+0+1+0+1+0+1+4 = 8
(c) 10000023 → digit sum = 1+0+0+0+0+0+2+3 = 6
(d) 99999922 → digit sum = 9+9+9+9+9+9+2+2 = 58→5+8=13→1+3 = 4 

(a) 1030302         (b) 1010101         (c) 1000002         (d) 9999992