# How to solve maths multiple choice questions with short-cut method in no time?

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First of all, we should know what 'digital sum' is as we will use it to solve maths multiple choice questions quickly with a short-cut.

Digital sum of a number is nothing but the continuous addition of the digits in that number until finally a single-digit number is obtained.

For example, consider this number > 53549

we will add all the digits in the number > 5 + 3 + 5 + 4 + 9 = 26

but 26 is still a two-digit number and we need to get a single-digit number to be the digital sum.

So we will also add digits in 26 to get the digital sum.

2+6 = 8

So here 8 is finally the digital sum of the number 53549.

Now let us take a multiple choice question

**Example 1:** What is the square of 256?

**a) 65933 b) 65819 c) 65536 d) 65434 **

So the above multiple choice question has 4 options and we need to choose the correct answer.

The usual way of doing the multiplication of 256 * 256 and finding the answer will be a long and time-consuming process.

Instead, we can do this very quickly using the digital sum method.

For that, we will have to find the digital sum of 256^{2} and all the numbers in the choices. So let us do this.

256 * 256 => (2+5+6) * (2+5+6) => 13 * 13 => (1 + 3) * (1 + 3) => 16 => (1+6) => 7

So 7 is the digital sum of 256^{2}.

a) 65933 => 26 => 8 (this is the digital sum of the option 'a')

b) 65819 => 29 => 11 => 2 (this is the digital sum of the option 'b')

c) 65536 => 25 => 7 (this is the digital sum of the option 'c')

d) 65434 => 22 => 4 (this is the digital sum of the option 'd')

As you can see above the digital sum of 256^{2} is 7 which matches the digital sum of the option C. So clearly 'C' option is the correct answer.

But sometimes two options in the answer may have the same digital sum. In that case, it will be confusing to know the correct answer.

Here is an example of that.

**Example 2:** What is the square of 73?

**a) 5129 b) 5229 c) 5329 d) 5239 **

73 * 73 => (7+3) * (7+3) => 10 * 10 = (1+0) * (1+0) = 1

So digital sum of 73^{2} is 1.

a) 5129 => 17 => 8 (this is the digital sum of the option 'a')

b) 5229 => 18 => 9 (this is the digital sum of the option 'b')

c) 5329 => 19 => 10 => 1 (this is the digital sum of the option 'c')

d) 5239 => 19 => 10 => 1 (this is the digital sum of the option 'd')

Here the digital sum of both the options c and d is same which is 1 and matches with the digital sum of the square of 73. However, both cannot be the correct answer.

But since we are finding the square of 73 the result will be a perfect square. In the value 73 if we multiply the end digit 3 by itself we will get 9. You can check any perfect square ending with the value 9 has an even number in the 10th place (the digit before the last digit).

For example,

49 (7 * 7)

169 (13 * 13)

289 (17 * 17)

You can check 49, 169 and 289 all these perfect square values have an even number (4,6 and 8) at the 2nd digit from the right (10th place).

In the options, C and D the values are 5329 and 5239 but only C option has even number in the 10th place (digit before the last digit). So, without any doubt option C is the correct answer.

To know more about the digital sum and solving problems with it watch this youtube video > youtube.com/watch?v=BhF7vZGm5IE

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**Written by:** Rajesh Bihani ( Find me on Google+ )