**Simplification** Aptitude Questions and Answers – Formulas & Tricks

**Simplification****Rule**

To solve simplification questions, it is important to be aware of **BODMAS** which is the basic rule

- B – Bracket
- O – Order (Indicate Square Root , Power)
- D – Division
- M – Multiplication
- A – Addition
- S – Subtraction

According to this rule, first simplify all the brackets in order (), {}, and ||

After solving the brackets, we Solve the simplification in the following order (i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction

**Modulus of Real Number**

Modulus of a real number a is defined as

|a| =

Thus, |5|= 5 and |-5| = -(-5) = 5

**Virnaculum (or Bar)**

If the given expression contains a Virnaculum (Bar), then first simplify the given expression under Virnaculum and the BODMAS Rule.

**Basic Important Formulas**

- (a+b)
^{2}= a^{2}+b^{2}+2ab - (a-b)
^{2}= a^{2}+b^{2}-2ab - a
^{2}-b^{2}= (a+b)(a-b) - (a+b)
^{3}= a^{3}+b^{3}+3ab(a+b) - (a-b)
^{3}= a^{3}-b^{3}-3ab(a-b) - a
^{3}+b^{3}= (a+b)(a^{2}+b^{2}-ab) - a
^{3}-b^{3}= (a-b)(a^{2}+b^{2}+ab) - (a+b+c)
^{2}=a^{2}+b^{2}+c^{2}+2(ab+bc+ca) - (a+b+c)
^{3}=a^{3}+b^{3}+c^{3}+3(a+b)(b+c)(c+a)

Simplification Aptitude Questions and Answers **With Detailed Explanation** – Quantitative Aptitude

## Simplification

Question 1 |

^{2}+ b

^{2}= 29, Find the value of ab.

10 | |

12 | |

15 | |

18 |

**Answer: Option A**

__Explanation:__

2ab =(a

^{2}+ b

^{2}) - (a - b)

^{2}

= 29 - 9 = 20

ab = 10

Question 2 |

160 | |

175 | |

180 | |

195 |

**Answer: Option B**

__Explanation:__

Suppose the man works overtime for x hours

Now, Working hours is 4 weeks = (5 * 8 * 4) = 160

Therefore, 160 * 2.40 + x * 3.20 = 432

=>3.20x = 432 - 384 = 48

x = 15

Hence, total hours of work = (160 + 15) = 175

Question 3 |

30 birds | |

60 birds | |

72 birds | |

90 birds |

**Answer: Option A**

__Explanation:__

Let the no of shots be x. Yhen,

Shorts fired by A =(5/8)x

Shots fired b b B = (3/8)x

Killing shorts by A = (1/3) of (5/8)x = (5/24)x

Shots missed by B = (1/2) of (3/8)x = (3/16)x

(3/16)x = 27 =>x = 144

Birds Killed by A =(5/24)x = (5/24)*144 = 30

Question 4 |

^{2}+ p = 7x + 5, what is the value of P?

17/2 | |

25/3 | |

33/4 | |

41/5 |

**Answer: Option A**

__Explanation:__

3x + 7 = 7x + 5 => 7x - 3x = 2 =>4x = 2 => x = 2

Now, 3x + 7 = x

^{2}+ p = (3/2) + 7 = (1/4) + p p =(17/2)

Question 5 |

22 | |

23 | |

24 | |

26 |

**Answer: Option D**

__Explanation:__

Let the number of hens be x and the number of cows be y

Then, x + y = 48..........(1)

and 2x + 4y = 140

x + 2y = 70 ..............(2)

Solving (1) and (2) we get: x = 26, y = 22

Therefore, the required answer = 26

Question 6 |

0 | |

1 | |

10 | |

100 |

**Answer: Option B**

__Explanation:__

((31/10) * (3/10) + (7/5)) / 20

=(3.1 * 0.3 * 1.4 ) / 20

=0.93 + 0.07

**Ans = 1**

Question 7 |

60 | |

30 | |

50 | |

40 |

**Answer: Option C**

__Explanation:__

We need so simple divide 42.5/0.85

=(4250/85)

**Ans = 50**

Question 8 |

K = b/a | |

bL = -a | |

KL = 1 | |

aK = -b |

**Answer: Option B**

__Explanation:__

Question 9 |

Rs. 120 | |

Rs. 160 | |

Rs. 240 | |

Rs. 300 |

**Answer: Option C**

__Explanation:__

Let C's share = Rs. x

Then, B's share = Rs (x/4), A's share = Rs. ((2/3) * (x/4)) = Rs. (x/6)

Therefore ((x+6) + (x+4) + x) = 1360

=> (17x/12) = 1360

=>x = (1360 * 12) / 17 = Rs. 960

Hence, B' share = Rs. (960/4) = Rs. 240

Question 10 |

10,000 | |

10,900 | |

11,000 | |

10,600 |

**Answer: Option A**

__Explanation:__

159% of 6531.8 + 5.5 * 1015.2 = ? + 5964.9

(159/00) * 6531.8 + 5.5 * 1015.2 - 5964.9 = ?

? = 10385.562 + 5583.6 - 5964.9

10004.262 = 10,000 (approx)