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

Last Updated : 15 Sep, 2017

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

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