**Want to crack Quants?…Then get your Numbers right!**

Various entrance examinations for MBA mandatorily have a section on Quantitative Ability popularly called Quants. Be it any examination, Numbers is an important topic among other significant topics like Time, Speed & Distance, Geometry, Time & Work, Permutation & Combination etc.

Why should an aspirant lay stress on this topic?

The reasons are as follows:

- It is the most fundamental part of Quants
- The number of questions in competitive examinations from this topic is high
- It helps in learning how to calculate fast
- Sometimes, even for solving questions on other quantitative topics, these concepts are helpful.

Therefore the first topic that should be covered adequately during preparation is Numbers!

This article will help you tackle the disadvantage of paucity of time. The different types of questions covered under this topic are easily found in sample test papers. But how can one solve them quickly?

The answer to the question lies in the very basics – Addition, Subtraction, Multiplication and Division. Quant is all about these four basic concepts. What is it that we need to do differently to gain advantage in terms of time?

Let us see a few time saving techniques:

- Addition:

**Q. 23476 + 34987**

In place of adding the digits of the 2 numbers individually, taking two digits at a time makes the process faster. So 76+87 = 70+80+6+7 = 150+6+7= 150+13 = 163. (For Mental calculation). Hence last 2 digits are 63 n 1 carry (similar to single digit addition method). Next, 34+49+1(carry) = 30+40+4+9+1=70+4+10=84(Mental calculation). Last, 2+3=5.

Therefore Answer is **58463.**

- Subtraction:

**Q. 4567 – 2334**

Again, taking 2 digits at a time, 67-34=67-30-4=37-4=33 (Mental calculation). Then, 45-23=45-20-3=22.

Answer is **2233.**

- Multiplication:

**Q. 34*76**

In place of multiplying by one digit at a time and then adding the products of each stage, the following method gives the product in one step only.

Units digit – 4*6=24 -> 4 carry 2

Tens digit – Cross multiply (3*6) + (7*4) + 2(carry) = 48 -> 8 carry 4

3 4

7 6

Hundreds place – 3*7 + 4(carry) = 25

Answer is **2584**

** **

**Q. 299*20**

The above method can be used.

Or 299*20 = (300-1) * 20 = (300*20) – 20 = 6000 – 20 = 5980.

Answer is **5980**

- Division:

**Q. 786 / 125**

For divisor ending in 25, the method to be used is,

Find the power to which 5 has to be raised to get the divisor : 5^3 = 125. So power = 3

Multiply the dividend by 2 ^ (The calculated power) : 786 * (2^3) = 6288

Divide the result by 10 ^ (The calculated power) : 6288/(10^3) = 6.288

Answer is **6.288**

Note: For multiplication by a number ending in 25, find the power first, then multiply the dividend by 10^(calculated power) and finally divide the result by 2^(calculated power).

Once these methods are employed, calculations can be sped up, keeping accuracy intact!

Now let us look at an introductory concept of Number Theory with the help of an example.

**Q. What is the number of zeros at the end of 75!**

Calculating 75! is difficult. But, it is possible to find the number of zeros at the end of 75!. It means that we have to find out how many times is 75! divisible by 10.

It is possible to find the number of times a factorial of a number is divisible by a prime number. As 10 = 2*5, therefore we can find the number of times 2 can divide it and the number of times 5 can divide it. A factorial contains a series of consecutive numbers. 2 can devide every alternate number in the series, where as 5 can divide every 5^{th} number. So number of times 75! Will be divisible by 5 will be less than that of 2. Hence we will only find how many times it is divisible by 5 as equal number of 2s and 5s are required to make 10s.

The method to calculate this is to divide 75 by 5 till it is no longer divisible.

5 |
75 |

5 |
15 |

3 |

Then, the result after every step should be added to get the number. In this case it is 15 + 3 = 18.

So, the number 10s will also be 18

Answer is **18**

For more concepts related to Number Theory, keep following the website. Other important concepts of this topic would be at your reach soon!

[…] the shortcuts of addition, subtraction, multiplication & division, from the article ‘Crack Quanta with us’, he may proceed with the following concepts used in number […]