Quantitative Aptitude: Maths Tricks | Set 1 (Squares of numbers)

3

The written round for most companies contains questions from quants(Quantitative Aptitude). There are two factors which determines score in quants, speed and accuracy. In this post we discuss certain tricks to improve upon the former i.e. speed.

We start with something simple : Squares

1. Squares of numbers 91-100:
Algorithm:
Step 1: Subtract the given number from 100. Let it be x.
Step 2: Subtract x from the given number.
Step 3: Square x.
Step 4: Combine (or concatenate) numbers from step 2 and step 3 to obtain result.

Let us understand how to compute this with an example:

97^2  Step 1: 100-97 = 3  Step 2: 97-3 = 94  Step 3: 3^2 = 09  Final result: From step 2 and step 3 :97^2 = 9409
Let us try another example:

91^2  Step 1: 100-9 = 91  Step 2: 91-9 = 82  Step 3: 9^2 = 81  Final Result: From step 2 and step 3 : 91^2 = 8281

2. Squares of numbers 101-109
Algorithm:
Step 1: Subtract the given number from 100.Let it be x.
Step 2: Add x to the given number.
Step 3: Square x.
Step 4: Combine (or concatenate) number from step 2 and step 3 to obtain result.

Let us understand how to compute this with an example:

102^2  Step 1: 102-100 = 2  Step 2: 102+2 = 104  Step 3: 2^2 = 04  Final result: From step 2 and step 3 : 102^2=10404
Let us try another example:

107^2  Step 1: 107-100 = 7  Step 2: 107+7 = 114  Step 3: 7^2 = 49  Final Result: From step 2 and step 3 : 107^2 = 11449

3. Squares of numbers 51-60:
Algorithm:
Step 1: Subtract 50 from the given number.Let it be x.
Step 2: Add x to 25.
Step 3: Square x.
Step 4: Combine (or concatenate) number from step 2 and step 3 to obtain result.

Let us understand how to compute this with an example:

53^2  Step 1: 53-50 = 3  Step 2: 25+3 = 28  Step 3: 3^2 = 09  Final result: From step 2 and step 3 :53^2 = 2809
Let us try another example:

55^2  Step 1: 55-50 = 5  Step 2: 25+5 = 30  Step 3: 5^2 = 3025  Final Result: From step 2 and step 3 : 55^2 = 3025

4. Squares of numbers 41-50:
Algorithm:
Step 1 : Subtract the given number from 50.Let it be x.
Step 2 : Subtract x from 25.
Step 3 : Square x.
Step 4 : Combine (or concatenate) number from step 2 and step 3 to obtain result.

Let us understand how to compute this with an example:

46^2  Step 1: 50-46 = 4  Step 2: 25-4 = 21  Step 3: 4^2 = 16  Final result: From step 2 and step 3 :41^2 = 2116
Let us try another example:

42^2  Step 1: 50-42 = 8  Step 2: 25-8 = 17  Step 3: 8^2 = 1764  Final Result: From step 2 and step 3 : 42^2 = 1764

This article is contributed by Ankit Jain. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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