If $a, b,$ and $c$ represent the number of unique digits in the decimal representation of

If $a, b,$ and $c$ represent the number of unique digits in the decimal representation of $\dfrac1{2^6\times 5^2},\dfrac1{2^3\times 5^3},\dfrac1{2^2\times 5^5}$ respectively, which of the following is true?

A) $a>b>c$
B) $a=2b+c$
C) $a=4(c-b)$
D) $a=b^2+c^2+2$
E) $a^2=2(b^2+c^2)$

Answer: E

Source: e-GMAT

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