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\((250-3)^2=250^2-2*250*3+03^2\)
\(250^2\)=62500 has 2 trailing 0's
2*250*3=1500 has 2 trailing 0's.

Hence last 2 digits of \((250-3)^2\) must be same as that of \(03^2\)

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Last 2 digits of \(201^2\)= \(01^2=01\)
Last 2 digits of \(202^2\)= \(02^2=04\)
Last 2 digits of \(203^2\)=\(03^2=09\)
Last 2 digits of \(204^2\)= \(04^2=16\)
Last 2 digits of \(246^2\) or \((250-04)^2\)= \(04^2=16\)
Last 2 digits of \(247^2\)or \((250-03)^2\)=\(03^2=09\)
Last 2 digits of \(248^2\)or \((250-02)^2= 02^2=04\)
Last 2 digits of \(249^2\) or \((250-01)^2= 01^2=01\)

last two digits of \((201*202*203*204*246*247*248*249)^2\)= last 2 digits of [01*04*09*16*16*09*04*01]=76


Bunuel
What is the last two digits of \((201*202*203*204*246*247*248*249)^2\) ?

A. 10
B. 16
C. 36
D. 56
E. 76

Could you please explain how is (250-03)^2 = 03^2

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