prabsahi wrote:

Have been your follower for a long time on beat the gmat!!Big fan of yours..cant afford so your posts are Bible

.. good to have you here Sir.

I think you mistyped the bold part .(just rewriting)

.

\(11^{11}-9^9 = 11^{11} -

(11-2)^{09} ≈ 11^{11} - 11^9 = 11^9(11^2 - 1) ≈ (11^9)(11^2) = 11^{11}\)

Press Kudos if it helps!!Fixed!

Thanks for catching the typo.

Another way to approach this problem:

10¹¹ (100,000,000,000) is 100 TIMES the value of 10⁹ (1,000,000,000).

Implication:

11¹¹ must be MORE THAN 100 TIMES the value of 9⁹.

Since 9⁹ is so small when compared to 11¹¹, we can ignore the value of 9⁹ when we approximate:

11¹¹ - 9⁹ ≈ 11¹¹

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