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Arithmetic Smart Math

[Smart Math] Arithmetic Problem 15

Here’s and example of a SMART MATH problem for ARITHMETIC.

Arithmetic

Problem

\frac{2^{5}\times 9^{2}}{8^{2}\times 3^{3}}=?

  1. \frac{1}{6}
  2. \frac{2}{3}
  3. \frac{3}{2}
  4. \frac{6}{1}
  5. \frac{1}{8}

The Usual Method

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\frac{2^{5}\times 9^{2}}{8^{2}\times 3^{3}}=\frac{2^{5}\times \left( 3^{2} \right)^{2}}{\left( 2^{3} \right)^{2}\times 3^{3}}=\frac{2^{5}\times 3^{4}}{2^{6}\times 3^{3}}=\frac{3}{2}

(Ans: 3)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

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Just by observing you can make out that the numerator has a higher value of power of base 3 and the denominator has a higher value of power of base 2. Hence, the answer has to have 3 in the numerator and 2 in the denominator. The only option satisfying these conditions is option ‘3’.

(Ans: 3)

Estimated Time to arrive at the answer = 5 seconds.
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