Simplification Aptitude Questions and Answers – Quantitative Aptitude

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| = Modulus of Real Number

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 = a2+b2+2ab
  • (a-b)2 = a2+b2-2ab
  • a2-b2 = (a+b)(a-b)
  • (a+b)3 = a3+b3+3ab(a+b)
  • (a-b)3 = a3-b3-3ab(a-b)
  • a3+b3 = (a+b)(a2+b2-ab)
  • a3-b3 = (a-b)(a2+b2+ab)
  • (a+b+c)2=a2+b2+c2+2(ab+bc+ca)
  • (a+b+c)3=a3+b3+c3+3(a+b)(b+c)(c+a)

Simplification Aptitude Questions and Answers With Detailed ExplanationQuantitative Aptitude

Simplification

Question 1
If a - b = 3 and a2 + b2 = 29, Find the value of ab.
A
10
B
12
C
15
D
18
Question 1 Explanation: 
Answer: Option A
Explanation:
2ab =(a2 + b2) - (a - b)2
= 29 - 9 = 20
ab = 10
Question 2
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for?
A
160
B
175
C
180
D
195
Question 2 Explanation: 
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
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed.
A
30 birds
B
60 birds
C
72 birds
D
90 birds
Question 3 Explanation: 
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
If 3x + 7 = x2 + p = 7x + 5, what is the value of P?
A
17/2
B
25/3
C
33/4
D
41/5
Question 4 Explanation: 
Answer: Option A
Explanation:
3x + 7 = 7x + 5 => 7x - 3x = 2 =>4x = 2 => x = 2
Now, 3x + 7 = x2 + p = (3/2) + 7 = (1/4) + p p =(17/2)
Question 5
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
A
22
B
23
C
24
D
26
Question 5 Explanation: 
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
Simplify ((31/10) * (3/10) + (7/5)) / 20
A
0
B
1
C
10
D
100
Question 6 Explanation: 
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
How many pieces of 0.85 meters can be cut from a rod 42.5 meters long
A
60
B
30
C
50
D
40
Question 7 Explanation: 
Answer: Option C
Explanation:
We need so simple divide 42.5/0.85
=(4250/85)
Ans = 50
Question 8
Simplify the following equation
A
K = b/a
B
bL = -a
C
KL = 1
D
aK = -b
Question 8 Explanation: 
Answer: Option B
Explanation:
Question 9
A sum of Rs. 1360 has been divided among A, B and C such that A gets (2/3) of what B gets and B gets (1/4) of what C gets. B's share is:
A
Rs. 120
B
Rs. 160
C
Rs. 240
D
Rs. 300
Question 9 Explanation: 
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
What approximate value should come in place of the question mark? 159% of 6531.8 + 5.5 * 1015.2 = ? + 5964.9
A
10,000
B
10,900
C
11,000
D
10,600
Question 10 Explanation: 
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)
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