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# [Smart Math] Arithmetic Problem 1

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

Evaluate $2.9999^{2}$

1. 8.99940001
2. 7.99940001
3. 8.9994011
4. 8.99940092
5. 9.00098641

### The Usual Method

Using the $(a-b)^{2}=a^{2}-2ab+b^{2}$, we get: $2.9999^{2}$ = $(3-0.0001)^{2}=3^{2}-2(3)(0.0001)+0.0001^{2}$
= 9-0.0006+0.00000001
= 8.99940001

(Ans: 1)

Estimated Time to arrive at the answer = 90 seconds

### Using Technique

Looking at the number, one can guess certain attributes of the answer.

Since, the question is squaring a number very close to 3, but less then that, the first digit of the answer should be a number close to 9 but less than that. Since, option ‘5’ is 9.00098641, it is eliminated.

Since 9 x 9 = 81 i.e. the last digit is 1, when we multiply, 2.9999 with 2.9999, the last digit has to be 1. Since, option ‘4’ has the last digit as 2, it is also eliminated.

Since, there are 4 digits after the decimal point, the answer should have 8 digits after the decimal. Since, option ‘3’ has 7 digits, it is also eliminated

Since, the squaring is of a number very close to 3, but less then that, the first digit should be the largest integer less than 9 i.e.8. Since, option ‘2’ has the first digit as 7, it is also eliminated.

This leaves us with only one option i.e ‘1’, which is the answer.

Estimated Time to arrive at the answer = 10 seconds
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