Quantitative Aptitude - SPLessons

Last 2 Digits Of A Square Of A Number

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Last 2 Digits Of A Square Of A Number

shape Introduction

Quantitative Aptitude is an important paper in banking exam. One cannot ignore it. So it is the most important to a candidate to improve the math’s skills for competitive exams. Most of the candidates feel that it’s a more time taking paper in exam but by following some guidelines, candidates can easily crack the exam. Competitive exams are setting with time binding. Everyone can do all maths without time binding but the main challenges are came into with in time. So candidates should mainly focus on speed and accuracy. That is possible in their hard working and Dedication. The article provides Quantitative Aptitude Math Shortcut Tricks.


shape Short Cut

1. How to find the last 2 digits of a square of a number (\(a^{2}\))?

Memorize the following table of squares from 1 to 25:

a \(a^{2}\) a \(a^{2}\) a \(a^{2}\) a \(a^{2}\) a \(a^{2}\)
1 01 6 36 11 121 16 256 21 441
2 04 7 49 12 144 17 289 22 484
3 09 8 64 13 169 18 324 23 529
4 16 9 81 14 196 19 361 24 576
5 25 10 100 15 225 20 400 25 625


shape Examples

1) Find the last two digits of \(41^{2}\).

Solution: Here a = 41.

Step 1:
Calculate 50 – a.
So, 50 – 41 = 9.

Step 2:
The last two digits of \(a^{2}\) is equal to last two digits of \((50 – a)^{2}\).
So, the last two digits of \(41^{2}\) is equal to last two digits of \(9^{2}\). The answer is 81.


2) Find the last two digits of \(87^{2}\).

Solution: Here a = 87.

Step 1:
Calculate 100 – a.
So, 100 – 87 = 13.

Step 2:
The last two digits of \(a^{2}\) is equal to last two digits of \((100 – a)^{2}\).
So, the last two digits of \(87^{2}\) is equal to last two digits of \(13^{2}\). The answer is 69.


3) Find the last two digits of \(65^{2}\).

Solution: Here a = 65.

Step 1:
Calculate a – 50.
So, 65 – 50 = 15.

Step 2:
The last two digits of \(a^{2}\) is equal to last two digits of \((a – 50)^{2}\).
So, the last two digits of \(65^{2}\) is equal to last two digits of \(15^{2}\). The answer is 25.


4) Find the last two digits of \(121^{2}\).

Solution: Here a = 121. The last two digits of a is 21. So, the last two digits of \(121^{2}\) is equal to last two digits of \(21^{2}\). The answer is 41.


5) Find the last two digits of \(165^{2}\).

Solution: Here a = 165. The last two digits of a is 65. Calculate 65 – a. So, 65 – 50 = 15. Then, the last two digits of \(165^{2}\) is equal to last two digits of \(15^{2}\). The answer is 25.


6) Find the last two digits of \(1456189^{2}\).

Solution: Here a = 1456165. The last two digits of a is 89. Calculate 100 – 89. So, 65 – 50 = 11. Then, the last two digits of \(1456189^{2}\) is equal to last two digits of \(11^{2}\). The answer is 21.


shape Exercises

1. Find the last two digits of (\(45234^{2}\)).

2. Find the last two digits of (\(99^{2}\)).

3. What are the last two digits of (\(12488899^{2}\))?

4. Find the last two digits of (\(5557^{2}\)).

5. Find the last two digits of (\(478^{2}\)).

Answers:

1. 56

2. 01

3. 01

4. 49

5. 84