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:

Simplify  

1.53 + 4.73 + 3.83 - 3 x 1.5 x 4.7 x 3.81.52 + 4.72 + 3.82 - 1.5 x 4.7 - 4.7 x 3.8 - 1.5 x 3.8

A) 6 B) 8
C) 10 D) 12
 
Answer & Explanation Answer: C) 10

Explanation:

Apply a3 + b3 + c3 - 3abca2 + b2 + c2 - ab - bc - ca = a + b + c

 

Hence the answer is  1.5 + 4.7 + 3.8 = 10.

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34 89823
Q:

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :

A) 35 B) 38
C) 40 D) 42
 
Answer & Explanation Answer: B) 38

Explanation:

Let the number of correct answers be X.

Number of incorrect answers = (60 – X).

4x – (60 – x) = 130

=> 5x = 190 

=> x = 38

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263 86606
Q:

Simplify the following :

373+353+283-3x37x35x28372+352+282-37x35-35x28-37x28 ?

A) 100 B) 1
C) 4 D) 0
 
Answer & Explanation Answer: A) 100

Explanation:

Given 373+353+283-3x37x35x28372+352+282-37x35-35x28-37x28

 

It is in the form of

 a3+b3+c3-3abca2+b2+c2-ab-bc-ca= a + b + c

 

Here a = 37, b = 35 & c = 28 

 

=> a + b + c = 37 + 35 + 28 = 100

 

 

 

Therefore,   = 100

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19 86406
Q:

92613 x 62742241 = ? + 89

Find the value of '?'

A) 166251 B) 166259
C) 166252 D) 166253
 
Answer & Explanation Answer: C) 166252

Explanation:

Given 92613 x 62742241 = ? + 89

 

Using unit digit method,

 

On LHS,

 

1 x 1 x 1 = 1

 

sqrt of last digit 1 => it must end with either 9 or 1

 

so now

 

1 x 1 = 1

 

1 x 9 = 9

 

On RHS,

 

? + 89

 

=> ? = ...1 - 89 = last digit is 11- 9 = 2

 

or

 

=> ? = ...9 - 89 = last digit is 9 - 9 = 0

 

Here in the options last digit 2 is option C.

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22 62635
Q:

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
 
Answer & Explanation Answer: A) 30 birds

Explanation:

Let the no of shots be x. Then, 

Shots fired by A =(5/8)x

Shots fired by B = (3/8)x 

Killing shots 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

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120 53410
Q:

Simplify the following equation.

1943 + 12 + 13 + 11 + 14

A) 43/19 B) 1
C) 38/19 D) None of these
 
Answer & Explanation Answer: D) None of these

Explanation:

After solving we get,

 

62/931.

 

None of the options satisfy.

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23 44858
Q:

If a+b=5 and 3a+2b=20,then (3a+b)will be :

 

A) 20 B) 15
C) 25 D) 30
 
Answer & Explanation Answer: C) 25

Explanation:

a+b=5   ...(1)    and    3a+2b=20 ...(2)

 

Multiplying (1) by 2 and subtracting from (2), we get : a=10.

 

Putting a=10 in (1), we get : b=-5

 

Therefore,   (3a+b) = 3 x 10+(-5)=30-5=25.

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24 43631
Q:

If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?

A) 500 B) 1000
C) 1500 D) 2000
 
Answer & Explanation Answer: B) 1000

Explanation:

Let the cost of a table and that of a chair be Rs. x and Rs, y respectively.

Then, 2x + 3y = 3500 ...(i)

and 3x + 2y = 4000 .....(ii)

solving (i) and (ii) we get x = 1000, y = 500 

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97 43124