Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.134)

134. 

287 x 287 + 269 x 269 - 2 x 287 x 269 = ?

[A]. 534
[B]. 446
[C]. 354
[D]. 324
[E]. None of these

Answer: Option D

Explanation:

Given Exp. = a2 + b2 - 2ab, where a = 287 and b = 269
= (a - b)2 = (287 - 269)2
= (182)
= 324

Esai Arasi said: (Jun 9, 2016)  
Explain me in digit sum method.

Chethan Prabhu K said: (Mar 2, 2019)  
By Digit Sum method:

287 * 287 + 269 * 269 - 2 * 287 * 269.

Step 1 : Cancel all 9's and all combinations of 9.

It becomes
8 * 8 + 8 * 8 - 2 * 8 * 8 (287= 7+2 = 9, So cancel it)(269 = cancel 9, 2+6 =8)
64 + 64 - 2 * 64.

1 + 1 - 2 * 1(1 = 6+4 = 10 = 1 +0 = 1)
=> 0.

Check options = 324 = 3+2+4 = 9, 9 means 0 remember. So that's the answer.

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