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FUNDAMENTALS
Basic Fundamental Concept
Quantitative aptitude is a very important part to crack any government exam. You need to score good marks in this section. For this, you need to practice a lot of math each and every day. In this chapter, we will discuss few basics of mathematics with few tricks. This will help you to calculate fast.
Square of a Number:
We need to memories the square of 1 to 25. Then we can easily calculate up to 100 square.
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Now for a number which is near about 50 we can calculate the square at that number easily.
For any number which is near about so we need to take base as 25.
Example 1:
Let the number be 47
47 is 3 less than 50.
We need to find the square of 3.
Then we need to subtract 3 from 25.
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Example 2:
Let us take another example 38.
38 is 12 less than 50
We need to take base as 25
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Example 3:
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100 base method when the number is near about 100:
Type – 1 (when the number is less than 100)
Let us take an example,
Example 1:
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95 is less than 100 by 5. We need to find the square of 5. And need to subtract 5 from 95
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Example 2:
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Type – 2 When the number is more than 100.
Example 1:
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Example 2:
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Special Case:
When the last digit at the number is 5:
Example 1:
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[On the right side there will be always , on the left side total digit other than 5 * Next number of that digit]
Example 2:
Let us take another number
Let the number be 145
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Square Roots:
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So,
We can find the last digit 1when squaring 1 or 9.
We can find the last digit 4 when squaring 2 or 8.
We can find the last digit 9 when squaring 3 or 7.
We can find the last digit 6 when squaring 4 or 6.
We can find the last digit 5 when squaring only 5.
# If the last digit at any number is 2, 3, 7, 8 then the number must be no perfect square.
# If the last digit at any number is 1, 4, 9, 6, 5 then the number may be a perfect square.
# If the last digit at any number at zero in the last at any number then the number may be a perfect square.
Example1:
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The last digit is 9.
We can get 9 from either 3 or 7.
So, the last digit of the result will be either 3 or 7.
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So, the first digit will be 5.
Now, 5 * (5 + 1) = 30 > 28
So, it will be 53.
Rules with explanation:
# In unit place we can see that the digit is 9. So, we can get 9 either squaring 3 or 7.
# In answer the unit place digit is either 3 or 7.
# Now first two digits at the question are 28. So we need to take a smaller number whose square is nearest to 28.
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# In this process we can find that the number is either 53 or 57.
# Now we need to multiply the digit in less position with the next number, 5 * 6 = 30
# Now if we compare 30 to 28 then we find that 28 is less than 30.
# Therefore between 53 and 57, the least one is correct. That is 53.
Example 1:
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So, the number is either 84 or 86.
Now, 8 * (8 + 1) = 8 * 9 = 72
73 is greater than 72.
So, In this case, the highest no. is 86. Which one is correct?
Example 2:
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So, the number is either 92 or 98.
Now, 9 * (9 + 1) = 9 * 10 = 90.
96 > 90
Therefore 98, is the answer.
