“ Math is just not my cup of tea. Humse na ho payga”. How many of you have felt the same at some point in your life? If you have been there and done that, then join the league.

I remember getting a score between 50-60 consistently in Math throughout middle school. My problem was not with understanding concepts but speed and accuracy always held me back. When I was in 8th standard, an angel came into my life and changed my perception forever. It was ‘shortcuts’ that magically transformed my life and Math has been my favorite since then!

Shortcuts can improve your accuracy and help you arrive at solutions at lightning fast speed! These shortcuts can further help you make educated guesses by allowing you to eliminate wrong answers especially in competitive exams and standardized tests.

We at Pedagoge, have curated a list of 7 math tricks/shortcuts that can help you solve complicated problems in minutes.

1)** To find the complement of a number (difference from the next highest power of 10)**

Subtract all but the unit digits of the number from 9 and subtract the unit place from 10.

For e.g. to know complement of 32,056 (its difference from 100,000) :

9-3 = 6; 9-2 = 7; 9-0 = 9; 9-5 = 4; 10-6 = 4;

The result is 67,944.

2)** Number Series Questions**

You are asked to find the pattern of a series.

Let’s take an example : **16, 26, 6, 46, -34, ? **

There is a pattern in the difference between the numbers in the series. Every consecutive difference is multiplied by -2.

3) **Squaring any two digit number.**

Use this simple method and find the square of any two digit number in seconds.

Let me explain this trick by taking examples

### 67^2 = [6^2][7^2]+20*6*7 = 3649+840 = 4489

### Take one more example

### 97^2 = [9^2][7^2]+20*9*7 = 8149+1260 = 9409

### Here [] is not an operation, it is only a separation between initial 2 and last 2 digits

4) **Application of Alligation Technique in Time and Distance Questions**

Example: A man travels part of his journey by bicycle at 20 Km/h and remaining distance by car at speed of 70 Km/h covering the entire journey at an average speed of 50 Km/h. What is the ratio of distance covered by bicycle and car?

**Solution. **As you can see in the picture, weighted average speed is 50 km/h so we keep it in the middle. Average speed of bicycle and car is taken as in visual components. We take the average speed of bicycle on the left side and average speed of car on the right side (rule of thumb). By solving this simple alligation we find that ratio of time the man takes to complete the journey by bicycle and car is 2:3. But here we need to find the ratio of distance covered, so 2*20= 40 and for car 3*70=210. Ratio comes out to be 4:21.

5) **To find the squares of numbers near numbers of which squares are known**

Example:

To find 41^2, Add 40+41 to 1600 = 1681

To find 59^2, Subtract 60^2-(60+59) = 3481

6) **To find out the sum of 3-digit nos. formed with a set of given digits**

This is given by (sum of digits)*(no. of digits-1)!*1111..1(i.e, based on the number of digits)

Example –

Find the sum of all 3 digit numbers formed by using 2,4,6,7 and 9.

Sum = (2+4+6+7+9)*(5-1)!*11111 (since 5 digits are there)

=28*24*11111

=7466592

7) **“Minimum of all” regions in Venn Diagrams **

In a survey conducted among 100 men in a company, 100 men use brand A, 75 use brand B, 80 use brand C, 90 use brand D & 60 use brand E of the same product. What is the minimum possible number of men using all the 5 brands, if all the 100 men use at least one of these brands?

Solution:

Step 1: Sum of the difference from 100 = (100-100) + (100-75)+(100-80)+(100-90)+(100-60) = 95

Step 2: Again take the difference from 100 = 5

We hope these shortcuts/tricks help you score well in school, college or competitive exams like CAT, GMAT, GRE, XAT, JEE, SSC etc. To seek the right guidance on Mathematics from the best teachers in Kolkata, visit Pedagoge.