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# [Smart Math] Arithmetic Problem 19

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

### Problem

$\frac{4}{4+\frac{0.4-4.04}{4\times 0.91}}=?$

1. 1.3
2. 3.7
3. 16
4. 4.5
5. 5.6

### The Usual Method

Simplifying the expression we get:

$\frac{4}{4+\frac{0.4-4.04}{4\times 0.91}}=\frac{4}{4+\frac{\left( -3.64 \right)}{3.64}}=\frac{4}{4-1}=\frac{4}{3}=1.33$

(Ans: 1)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

Observe that the term (0.4 – 4.04) will yield a negative value. Hence the term $\left( \frac{0.4-4.04}{4\times 0.91} \right)$ will also be negative number slightly more than 1. Hence, 4 + (some negative number slightly more than 1) = a number slightly less than 4 = x
Hence, $\frac{4}{x}$ will yield a value slightly more than 1. Hence option ‘1’.