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# [Smart Math] Arithmetic Problem 2

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

Simplify 1/[1+1/{1+1/(1+1/4)}]

1. 3/14
2. 14/3
3. 7/3
4. 14/9
5. 9/14

### The Usual Method

First solving (…), we get: 1 + 1/4 = 5/4

Now Solving {…}, we get: 1+ 1/(5/4) = 9/5

Now Solving […], we get: 1 + 1/(9/5) = 14/9

Hence, answer is 1/(14/9) = 9/14

(Ans: 5)

Estimated Time to arrive at the answer = 60 seconds

### Using Technique

Just solve the 1st level bracket i.e. (…), we get: 1 + 1/4 = 5/4.
5 > 4 or Numerator > Denominator

Also, since, there are three division operation further left, in the final answer, the Numerator < Denominator. This eliminates options ‘2’, ‘3’ and ‘4’.

Also, note that if in the first level of operation, we get the numerator and denominator as 5 and 4 respectively, and that further operations involve addition, the final answer will have a value greater than 5 and 4. This eliminates option ‘1’. Hence ‘5’ is the final answer.

(Ans: 5)

Estimated Time to arrive at the answer = 10 seconds

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