Approximations are the most helpful tool in Data Interpretation questions in most of the competitive examinations. An approximation is anything that is close, but not exactly equal to something else. It is an extremely important technique, which helps a candidate to find the solution quickly in competitive exams by rounding off to the nearest integer, rather than solving for the exact values.
Data Interpretation: Approximations
Let us understand the concept of this technique better with the help of the following examples.
Example 1: Find the approximate value of (13.001)^{3}.
Solution: 13.001 is approximately equal to 13.
So, instead of finding the cube of 13.001 we can simply find the cube of 13 and tick the answer nearest to that value. Now, cube of 13 is 2197 and in options we have 2200, which is nearest to 2197 so the correct answer is option (b).Example 2: What should replace the question mark in the following equation?
55.003 × 54.998 + 5.001 =?Solution: 55.003 is approximately equal to 55 as well as 54.998 is also approximately equal to 55. At the same time, 5.003 is close to 5.
So, the equation reduces to the form 55 × 55 + 5 = 3025 + 5 = 3030. Alternative: Besides, this question can also be solved by the algebraic formula. As you can write 55 × 55 + 5 = (50+5) × (50+5) + 5. => (50+5)^{2} + 5 = (50^{2} + 5^{2} + 2 × 5 × 50) + 5 = (2500 + 25 + 500) + 5 = 3025+5= 3030. Option (d) is the answer.Example 3: What will 50.001% of 99.99 ÷ 49.999 be equal to?
Solution: 50.001 is approximately equal to 50.
99.99 can be written as equivalent to 100 and 49.99 is equivalent to 50. So the equation now becomes 50% of 100 ÷ 50 =? 50% of 100 is 50 and 50 divide by 50 gives answer 1. Hence, option (a) is the answer.Example 4: 999.001 + 899.99 –349.88 =?
Solution: Approximating the above equation, we get, 1000 + 900 - 350 =1550
Option (a) is nearest to our answer. So, the correct answer is 1549.Example 5: 119% of 1190 + 33% of 125 - 97 % of 813 = ?
Solution: Let us split the expression into parts:
To find 119% of 1190; (100 + 19)% of 1190 => 100 % of 1190 + 20 % of 1190 = 1190 + 238 = 1428 Then, 33 % of 125 (33% is equivalent to one-third)=> 125 × 1/3 = 42 approximately. Lastly, 97% of 813 = (100% - 3%) of 813 = 813 - 24 = 789 Now, the final solution will be 1428 + 42 - 789 = 1470 - 789 = 681 Answer nearest to our value is option (e).Data Interpretation-Approximation: Key Learning
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