Thursday, 11 May 2017

Simplification I - Simplification Tricks to Solve Simplification Problems

In this post, we will solve simplification problems using simplification tricks to save time in IBPS PO and SSC CGL Exam.
Simplification Problems
Sums that have only two numbers and a single operation to perform such as addition, subtraction, multiplication or division, are easy to solve. But what if, you have several numbers and multiple operations to perform? In SBI PO, IBPS PO and SSC CGL Exam where limited time is allotted for simplification problems, it becomes difficult to calculate several numbers with several operations in given time.

Well, don't worry! There is a simple rule that you need to follow while solving simplification problems in a systematic order. This rule is called as " BODMAS." BODMAS will help you to perform the operations in a systematical order and it will make it easy for you to reach the solution of simplification problems in minimum time.

Order of BODMAS
Simplification Problems

First - Start simplifying the numbers present inside the brackets- from left to right.

Second - Then simplify the numbers which involve power or finding a square root of the number- from left to right.

Third - Once you are done with simplifying the numbers that involve brackets or orders, then move on to division or multiplication. Division and multiplication rank equally, you can start performing the operation from left to right- as they appear in the order.

Fourth- This is the final step in which you perform addition and subtraction. Addition and subtraction are also ranked equally, you can perform any of the operation that appears in the order- from left to right.

Example 1: Simplification Problems Solved using Simplification Tricks

Question: 38.734 + 8.638 - 5.19 = ?
1) 41.971    2) 42.197    3) 43.072    4) 42.182    5) None of these

Solution:
Step 1:
First, balance the numbers by adding zero after the decimal place.
38.734 + 8.638 - 5.190

Step 2:
By using the smart method of calculation, we start calculating from right to left
4 + 8 - 0 = 2
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3 + 3 - 9 = 8
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7 + 6 - 1 = 1
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8 + 6 - 5 = 2
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3 + 0 - 0 = 4

Step 3:
By merging all the numbers together we get 42.182

Therefore, 38.734 + 8.638 - 5.190 = 42.182
Simplification Problems
Example 2: Simplification Problems Solved using Simplification Tricks

Question: -676.76 + 1237.87 + 897.34 - ? = 1294.25
1) 168.2    2) 164.2    3)154.2    4) 164.8    5) None of these

Solution:
Step 1:
As there are numbers on the left side and the right side, we shift the numbers to one side in order to make simplification easier. So we shift 1294.4 to the left side and shift the unknown value to the right side. 
Simplification Problems

Step 2:
We will get the equation as- 
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Step 3:
Now using the simplification trick to solve this simplification problem, start calculating from the rightmost digit  as given below-
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Simplification Problems

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Simplification Problems

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Step 4: Now, by putting all the digits we get-
164.2

Therefore the answer is option 2: 164.2

Example 3: Simplification Problems Solved using Simplification Tricks

Question: 3(2/5) + 1(2/9) = 4(4/5)- ?
1.8/45    2) 7/47    3)4/45     4)5/81    5)None of these

Conventional Method:
Solution:
Step 1:
First let's arrange the values in order- 
? = 4(4/5) -3(2/5) - 1(2/9)

Step 2:
Then convert mixed fraction into an improper fraction-
? = 2(4/5) - 1(7/5) - 1(1/9)

Step 3:
To simplify the question, take the LCM of the denominator to balance the numbers-  
LCM of 5, 5 and 9 is 45.
= [(24 x 9) - (12 x 9) - (5 x 11) / 45]
(63 - 55) / 45 = 8/45

Therefore,  the answer is option A: 8/45

While Solving the problem like this, you don't realise that you have wasted a lot of time. Though this method appears easy but is not time effective in IBPS PO and SSC CGL Exam. So, let's solve simplification problems in a smart way.

Smart Method
Step 1:
First let's arrange the values in order- 
? = 4(4/5) -3 (2/5) - 1(2/9)

Step 2:
Then split integer and fraction in the way given below-
? = 4 + 4/5 - 3 - 2/5 -1 - 2/9

Step 3:
Then perform the calculation on the integers-
4 - 3 - 1 = 0

Step 4:
Then simplify the fraction-
4/5 - 2/5 -2/9 = (36 - 18 - 10) / 45 = 8/45

Therefore,  the answer is option A: 8/45

Though this method appears to be lengthy, it isn't! Half of the calculations are done in mind without the use of pen and paper and other calculations are made simple, which help in improving your speed while solving simplification problems.

So, this shouldn't take much time! Quickly try to solve these simple simplification problems by using simplification tricks we have discussed- 

1)  -84 x 29 + 365 = ?

1)  2436      2) 2801     3) -2801    4) -2071     5)None of these

2) ?  25  12 = 248.56

1) 74628     2)497.52   3) 305867    4)389017    5)None of these

Do write in the comment section, how much time did you take to solve these simplification problems.

Stay tuned for more on Simplification Problems.
Simplification Problems
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