Basics of Simplification for Rajasthan State Exams

By Mayank Yadav|Updated : May 14th, 2021

We all know the importance of fast and speedy calculation in state exams. Simplification is one of the topics in the quant section that requires a speedy calculation to solve maximum questions on it in less time. It is one of the most widely asked topics in competitive exams, especially in prelims stage. So today, we are discussing some key points to deal with Simplification topics to score well in this section.

Simplification generally means to find an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus.

Simplification questions are asked in the exam to check the ability of an aspirant to deal with numbers which can be in one of the following two types.

  • Sometimes, a calculation is given and one of the numbers is missing from the calculation. To find out the missing number, we have to approximate the given numbers or do the basic operations.
  • Sometimes all the numbers are given with some operations between them & we have to simplify the calculation.

 

Rules related to Simplification

Rule-(I) Replace ‘of’ by ‘Multiplication’ & ‘/’ by ‘Division’.

Explanation: Whenever we find ‘of’ in a simplification problem, we can replace that by ‘multiplication(*)’. Similarly ‘/’ can be replaced by ‘÷’.

Example: Find ¼ of 20

Solution: (¼) x 20 = 20÷4 = 5

Rule-(II) Always keep in mind the “BODMAS” rule. These operations have priorities in the same order as mentioned.

Explanation: Whenever we have more than one operation in the given calculation, we have to do the operations according to the priority specified by ‘BODMAS’

  • B-Bracket
  • O-Of (means multiplication)
  • D-Division
  • M-Multiplication
  • A-Addition
  • S-Subtraction

Example: Simplify: (2+3)*30

Solution: In this question, we have two things-Bracket & Multiplication. According to the BODMAS rule, we have to solve bracket first and not multiplication. So now coming to bracket, we have only one operation-Addition, so we will do addition.

(2+3)*30 = 5*30

Now we have only one operation to do – Multiplication

5*30 = 150

Example: Simplify: (2+5) of 80

Solution: In this question, we have three things – bracket, addition & of. Replacing ‘of’ by ‘multiplication’.

(2+5) of 30 = (2+5)*80

Now we have three things – bracket, addition & Multiplication. According to the BODMAS rule, we have to solve bracket first and not multiplication. So now coming to bracket, we have only one operation-Addition, we will do addition.

(2+5)*80 = 7*80

Now we will do multiplication.

7*80 = 560

Rule-(III) Multiplication & Division have the same priority(Do that operation first which is on left)

Explanation: Though division has more priority than multiplication according to ‘BODMAS’ but we can perform any of the two operations first if multiplication is on left.

Example:  8*30/15

                8*30 ÷ 15

Solution: In this question, we have two things – Multiplication & Division. Multiplication is on left So we can perform that first.

Doing Multiplication first:

                240 ÷ 15

                16

Doing division first:

                8*2

                16

Rule-(IV) Addition & Subtraction have the same priority.

Explanation: Though addition has more priority than division according to ‘BODMAS’ but we can perform any of the two operations first.

Example:  30+40-15

Solution: In this question, we have two things – Addition & Subtraction. So we can perform any operation first as they have same priority.

Doing Addition first:

                70 – 15

                55

Doing Subtraction first:

                30 + 25

                55

Rule-(V) Don’t hesitate in rounding the numbers to nearest integers.

Explanation: Most of the times the numbers are given in such a way that you can round them quickly and get the answer (Rounding should be done or not, It can be realised by looking at the given options).

Example: (324.5*15)/(5.01*24.98)

Solution: (325*15)/(5*25)

   =13*3

   =39

Now let us see some of the previous year questions asked from 'Simplification' & try to apply the rules learnt so far.

Q. 1) (17 -13)4 - 174 – 134 – [- 52(17)3 – 68(133)] = (?)*221

Using formula: (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3+ b4
⇒ (a – b)4 - a4 + 4a3b + 4ab3 - b4 = + 6a2b2 
(17 -13)4 - 174 – 134 – [- 52(17)3 – 68(133)] = (?)*221 
Here, a = 17 and b = 13 
⇒ (?)= (6 (17)2 (13)2)/221 
⇒ (?) = (6 × 289 × 169)/221 
⇒ (?) = 1326

Q.2) Simplify: 127.001 * 7.998 + 6.05 * 4.001

  1. 1000
  2. 1020
  3. 1040
  4. 1080
  5. None of these

       Solution: Using the rounding concept

                127 * 8 + 6 * 4

       Using the BODMAS rule

                1016 + 24

                1040 (Option 3)

Q.3) What will come at place of ?: 9876 ÷ 24.96 + 215.005 - ? = 309.99

  1. 270
  2. 280
  3. 290
  4. 300
  5. 310

       Solution: Using the rounding concept

                 9875 ÷ 25 + 215 - ? = 310

      Using the BODMAS rule

                395 + 215 - ? = 310

                610 - ? = 310

                ? = 300 (Option 4)

Q.4) What will come at place of a: (128 ÷ 16 x a – 7*2)/(72-8*6+a2) = 1

  1. 1
  2. 5
  3. 9
  4. 13
  5. 17

    Solution: Using the BODMAS rule

                (8*a – 14)/(49-48+a2) = 1

                (8*a – 14)/(1 + a2) = 1

                8a – 14 = 1 + a2

                a2 – 8a + 15 = 0

                a=3 or 5 (Option 2)

Q.5) What will come at place of ?: 85.147 + 34.192*6.2 + ? = 802.293

  1. 400
  2. 450
  3. 550
  4. 600
  5. 500

    Solution: Using the rounding concept

                85 + 35*6 + ? = 803

    Using the BODMAS rule

                85 + 210 + ? = 803

                295 + ? = 803

                ? = 508 [approx. = 500] (Option 5)

Q.6) What will come at place of ? : (3/8 of 168)*15 ÷ 5 + ? = 549 ÷ 9 + 235

  1. 189
  2. 107
  3. 174
  4. 296
  5. None of these

Solution: Using the BODMAS rule

                (3*168÷8)*15 ÷ 5 + ? = 549 ÷ 9 + 235

                (504÷8)*3 + ? = 61 + 235

                63*3 + ? = 296

                189 + ? = 296

                ? = 107 (Option 2)

Key points to remember while solving Simplification Question:

  • Replace ‘of’ by ‘Multiplication’
  • Replace ‘/’ by ‘Division’
  • Always do the operations in priority according to ‘BODMAS’
  • Division & Multiplication have the same priority (Start from left)
  • Addition & Subtraction have the same priority
  • Rounding can be done to simplify problems
  • When the given options are very close then rounding doesn’t help much
  • Always look at the options before doing simplification that can help in the elimination of options.

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Mayank YadavMayank YadavMember since Mar 2021
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