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

**Problem**

**Problem**

What is the least number which must be subtracted from 10420 to make it a perfect square?

- 219
- 200
- 189
- 25
- 16

**The Usual Method**

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10420 can be written as:

10420 = 10000 + 420

The square root of 10000 = 100

Now, by trail and check method, check for squares of numbers greater than 100.

as 14400 > 10420 hence the square root should be < 120.

as 12100 > 10420 hence the square root should be < 110.

as 11025 > 10420 hence the square root should be < 105.

as 10404 < 10420 hence the required square root should be 102.

To bring 10420 to 10404, we have to subtract 10420 – 10404 = 16.

**(Ans: 5)**

*Estimated Time to arrive at the answer = 60 seconds.*

**Using Technique**

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Simply subtract each option from 10420 starting with the least number and check for perfect square as follows:

e. 10420 – 16 = 10404 = (Perfect Square)

(Note: We are taking option ‘5’ first as it is the one with the lowest number.)

No need to check any further.

Hence, option ‘5’.

**(Ans: 5)**

*Estimated Time to arrive at the answer = 10 seconds.*

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