Simplification Questions

FACTS  AND  FORMULAE  FOR  SIMPLIFICATION  QUESTIONS

 

 

1. BODMAS Rule: This rule depicts the correct sequence in which the operations are to be executed,so as to find out the value of a given expression. Here, 'B' stands for bracket , 'O' for of , 'D' for division and 'M' for multiplication, 'A' for addition and 'S' for subtraction.

Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order(), {} and [].

After removing the brackets, we must use the following operations strictly in the order:

(1) of    (2)division   (3) multiplication   (4)addition   (5)subtraction.

 Modulus of a real number : Modulus of a real number a is defined as |a| = aif a>0-aif a<0

 

2. Virnaculum (or bar) : When an expression contains Virnaculum, before applying the ‘BODMAS’ rule, we simplify the expression under the Virnaculum.

Q:

How many  18' s are there in  3712?

A) 300 B) 400
C) 500 D) 600
 
Answer & Explanation Answer: A) 300

Explanation:

3712 = 752

Required number =  75218 = 75 x 4 = 300

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23 11061
Q:

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
 
Answer & Explanation Answer: A) 17/2

Explanation:

 

 

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

 

Now, 3x+7=x2+p=32+7=14+p=>p=172

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11 10947
Q:

What should come in place of question mark (?) in the following question?

115 ÷ 5 + 12 × 6 = ? + 64 ÷ 4 - 35

A) 95 B) 136
C) 102 D) 74
 
Answer & Explanation Answer:

Explanation:

 As per the BODMAS rule, the priority in which the operations should be done is:

Priority wise operations Symbol
B-Bracket ()
O-of of
D-Division /,÷
M-Multiplication *,x
A-Addition +
S-Subtraction -

Note: Addition and subtraction can be treated on same priority (from left to right) when they are in consecutive order.

(115/5) + 12 × 6 = ? + (64/4) – 35 23 + 72 = ? + 16 – 35 95 = ? - 19 95+19 = ? ? = 114

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1 10890
Q:

Suppose 0 < θ < 90, then for every θ 4 sin2 θ + 1 is greater than or equal to ?

 

A) 2 B) 4 sin θ 
C) 4 cos θ  D) 4 tan θ
 
Answer & Explanation Answer: B) 4 sin θ 

Explanation:
We know that,
Arithmetic mean ≥ Geometric mean
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5 10731
Q:

If a - b = 3,  a2+b2=29, find the value of ab.

A) 10 B) 12
C) 15 D) 18
 
Answer & Explanation Answer: A) 10

Explanation:

2ab=a2+b2-a2-b2

 

29-9=20

=>ab=10

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8 10139
Q:

Twenty times a positive integer is less than its square by 96. What is the integer ?

A) 42 B) 36
C) 48 D) 24
 
Answer & Explanation Answer: D) 24

Explanation:

Let the integer be x. Then,

x2 - 20x = 96

(x + 4)(x - 24) = 0

x = 24

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11 9981
Q:

217 x 217 + 183 x 183 = ?

A) 84521 B) 87487
C) 80578 D) 78458
 
Answer & Explanation Answer: C) 80578

Explanation:

2172+1832

 

= 200+172+200-172

 

It is in the form of a+b2+a-b2=2a2+b2

 

= 2(40000 + 289) = 80578.

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18 9748
Q:

If 3x-y=273x+y=243 then find the x value

A) 2 B) 8
C) 4 D) 1
 
Answer & Explanation Answer: C) 4

Explanation:

Given that 3x-y=273x+y=243

3x-y =33 , 3x+y=35

 => x-y=3, x+y=5

 => x = 4

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15 9647