Simplification Questions

In Simplification Questions, an individual needs to solve the problem by doing complex calculations. Here, on this page we have mentioned Simplification Formulas as well as Simplification Questions & Answers that contains short solutions and can be solved using tricks.

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Simplification Topic comes under Quantitative Aptitude section and is asked in mostly all the competitive exams. So, it’s important for candidates to learn the tricks and tactics of solving Simplification Questions in the given time limit.

Rules of Simplification:

VBODMAS:

• V : Virnaculum or bar
• B : Bracket
• : Of
• D : Division
• M : Multiplication
• A : Addition
• S : Subtraction

Modulus:

Modulus of a real number x is its positive value, denoted by |x|.
Thus, |7| = 7 and |−7| = 7

Simplification Formula:

•  (a + b)² = a² + b² + 2ab
• (a − b)² = a² + b² − 2ab
• (a + b)(a − b) = a² − b²
• (a + b)² − (a − b)² = 4ab
• (a + b)² + (a − b)² = 2 (a² + b²)
• (a + b + c)² = a² + b² + c² + 2 (ab + bc + ac)
• (a³ + b³) = (a + b) (a² − ab + b²)
• (a³ − b³) = (a − b) (a² + ab + b²)
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a − b)³ = a³ − b³ − 3ab(a − b)
• (a³ + b³ + c³ − 3abc) = (a + b + c) (a² + b² + c² − (ab + bc + ca))
• If a + b + c = 0, then a³ + b³ + c³ = 3abc

Simplification Tricks:

• Learn BODMAS.
• Use the concept of digital sum.
• Memorize tables up to 30.
• Memorize cubes and squares of numbers up to 35.
• Learn the concept of percentages.
• Learn tricks to find squares and cubes of numbers greater than 35.
• Learn tricks to find cube roots and square roots of large number.
• Memorize the reciprocals.

Get Here: How to Prepare for Written Exam

Simplification Questions

Simplification Questions and Answers

Question 1) 1035 ÷ [(3/4) of (71 + 65) – 15 ¾] = ?

1. 12
2. 24
3. 18
4. 26
5. None of these

Answer: (1)

Explanation:

1035 ÷ [(3/4)*136 – 63/4] = x

X = 1035 ÷ [102 – (63/4)]

X = 1035 ÷ [(408 – 63)/4]

X = 1035 ÷ (345/4)

X = 1035 *4/345

X = 12

Question 2) √((27 ÷ 5 ×?) ÷ 15) = 5.4 ÷ 6 +0.3

1. 12
2. 4
3. 9
4. 15
5. None of these

Answer: (2)

Explanation:

√((27 /5 )×(x/15)) =0.9+0.3

(3/5) √ x = 1.2

√ x = 6/3 =2

X= 4

Question 3) 36³ × 4096^1/2 × 72 × 18 ÷ (93 × 722) = 4?

1. 8
2. 12
3. 7
4. 5
5. None of these

Answer: (4)

Explanation:

(36*36*36*64*72*18)/(9*9*9*72*72) = 4^x

4*4*4³ = 4^x

4⁵ = 4^x

X = 5

Question 4) (913 + 329 + 522 + 343) ÷ (18 + 24 – ? + 18) = 43

1. 23
2. 11
3. 7
4. 29
5. 15

Answer: (2)

Explanation:

(913 + 329 + 522 + 343) ÷ (18 + 24 – x + 18) = 43

2107 ÷ (60 –x) = 43

(2107/43) = 60 – x

49 = 60 – x

X = 60 – 49 = 11

Question 5) 12¾ % of 2400 + 23 ½ % of 800 + 452 = 1125 ÷ 25 × 4 + ?

1. 658
2. 532
3. 776
4. 614
5. 590

Answer: (3)

Explanation:

(51/400)*2400 + (47/200)*800 + 2025 = (1125/25) + 4x

306 + 818 + 2025 – 45 = 4x

3104 = 4x

X = 3104/4 = 776

Question 6) (4/5) of 11325 + 56 % of 1750 = (?)² + 436

1. 116
2. 72
3. 98
4. 84
5. 102

Answer: (3)

Explanation:

(4/5)*11325 + (56/100)*1750 = x² + 436

9060 + 980 – 436 = x²

10040 – 436 = x²

9604 = x²

X = 98

Question 7) 1.8 × 625 + 5.6 ÷ 0.7 + 415 × 11.8 = (?)² – 211

1. 79
2. 85
3. 92
4. 69
5. 61

Answer: (1)

Explanation:

1.8 × 625 + 5.6 ÷ 0.7 + 415 × 11.8 = (?)² – 211

1125 + 8 + 4897 = x² – 211

6241 = x²

X = 79

Question 8) 586 × 9234 ÷ 48 % of 950 = 36 × 750 ÷ 4 + ? + 4500

1. 25
2. 728
3. 5
4. 75
5. 474

Answer: (3)

Explanation:

586 × [9234 ÷ ((48/100)*950)] = 36 × (750/4) + x + 4500

586*(9234/456) = 6750 + x + 4500

11866.5 – 11250

X = 616.5

Question 9) (28 × 9 + 54 × 3 + 12 × 11) ÷ (142 – √961 + 17) = ?

1. 6
2. 3
3. 5
4. 8
5. 7

Answer: (2)

Explanation:

(28 × 9 + 54 × 3 + 12 × 11) ÷ (14² – √961 + 17) = x

X = (252 + 162 + 132) ÷ (196 – 31 + 17)

X = 546/182

X = 3

Question 10) √13225 + ∛205379 + 52 % of 700 = 408 + ?

1. 156
2. 218
3. 189
4. 130
5. None of these

Answer: (4)

Explanation:

√13225 + ∛205379 + 52 % of 700 = 408 + x

115 + 59 + (52/100)*700 – 408 = x

115 + 59 + 364 – 408 = x

X = 130

Question 11) (7 × 7)³ ÷ (49 × 7)³ × (2401)² = 7^?

1. 7
2. 5
3. 6
4. 8
5. None of these

Answer: (2)

Explanation:

(7 × 7)³ ÷ (49 × 7)³ × (2401)² = 7^x

(7²)³ ÷ (7² × 7)³ × (7⁴)² = 7^x

7⁶ ÷ 7⁹ × 7⁸ = 7^x

7^{6 – 9 + 8} = 7^x

7⁵ = 7^x

X = 5

Question 12) 5 ¾ – 4 1/8 + 7 ½ – 3 3/8 = ?

1. 4 3/7
2. 6 5/6
3. 7 ½
4. 5 ¾
5. None of these

Answer: (4)

Explanation:

5 ¾ – 4 1/8 + 7 ½ – 3 3/8 = x

X = (5 – 4 + 7 – 3) (3/4 – 1/8 + ½ – 3/8)

X = 5 [(6 – 1 + 4 – 3)/8]

X = 5 (6/8) = 5 (3/4)

Question 13) (2 7/9) ÷ (5 1/2) × (693/350) = (1/3) of (5/7) of (147/175) of (?)

1. 12
2. 26
3. 5
4. 18
5. 9

Answer: (3)

Explanation:

(25/9)*(2/11)*(693/350) = (1/3)*(5/7)*(147/175)*x

1 = (x/5)

X = 5

Read Out: Problem on HCF and LCM

Question 14) (3/7) of ? – (2/5) of (13/16) of 2160 = 12 % of 900

1. 2150
2. 1540
3. 1960
4. 1890
5. 2370

Answer: (4)

Explanation:

(3/7)*x – (2/5)*(13/16)*2160 = (12/100)*900

(3x/7) – 702 = 108

(3x/7) = 108 + 702

(3x/7) = 810

X = (810*7/3) = 1890

Question 15) ∛157464 + √8836 – 45 % of 800 =? + (1188 ÷ 9) – 36²

1. 952
2. 816
3. 878
4. 924
5. None of these

Answer: (1)

Explanation:

54 + 94 – (45/100)*800 = x + (1188/9) – 1296

54 + 94 – 360 + 1296 = x + 132

54 + 94 – 360 + 1296 – 132 = x

X = 952

Question 16) (4/5) of 11325 + 56 % of 1750 = (?)² + 436

1. 116
2. 72
3. 98
4. 84
5. 102

Answer: (3)

Explanation:

(4/5)*11325 + (56/100)*1750 = x² + 436

9060 + 980 – 436 = x²

10040 – 436 = x²

9604 = x²

X = 98

Question 17) 18 ¼ % of 17200 + 33 2/3 % of 1860 + 37 2/3 % of 19680 = ?

1. 11178
2. 13456
3. 9824
4. 10242
5. 8454

Answer: (1)

Explanation:

(73/400)*17200 + (101/300)*1860 + (113/300)*19680= x

X = 3139 + 626.2 + 7412.8

X = 11178

Question 18) 1323 ÷ (27 % of 700) = 35 × 7 3/5 of (? ÷ 190)

1. 7
2. 9
3. 4
4. 5
5. 8

Answer: (4)

Explanation:

1323 ÷ [(27/100)*700] = 35 × (38/5)*(x/190)

1323 ÷ 189 = 35 × (38/5)*(x/190)

(7*5*190)/(35*38) = x

X = 5

Question 19) 32450 ÷ 11 + (4/9) of 11520 + 48 % of 7500 = ?² – 430

1. 150
2. 178
3. 110
4. 92
5. None of these

Answer: (3)

Explanation:

(32450/11) + (4/9)*11520 + (48/100)*7500 = x² – 430

2950 + 5120 + 3600 + 430 = x²

X² = 12100

X = 110

Solve Here: Discount Questions and Answers

Question 20) 49² ÷ 14 × 8 + 582 = 4 × ? – 15 % of 2480

1. 1489
2. 1277
3. 1645
4. 1823
5. None of these

Answer: (2)

Explanation:

(49*49*8)/14 + 58² = 4x – (15/100)*2480

1372 + 3364 = 4x – 372

1372 + 3364 + 372 = 4x

5108 = 4x

X = 5108/4 = 1277

Candidates must go through Simplification Questions & Answers given on this page of recruitmentresult.com and can practice from it to score good marks in the examination.