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 Simplification Questions

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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:

1422 ÷ 1260.25 = ?

A) 586 B) 578
C) 568 D) 566
 
Answer & Explanation Answer: C) 568

Explanation:

142 x 142 x 11260.25

 

=> 142 x 142 x 135.5  = 568

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4 4554
Q:

A secret can be told to only 3 persons in 3 minutes. Each person in turn tells 3 other persons in the next 3 minutes and the processes continues accordingly. In 30 minutes how many persons can be told this secret in this way ?

A) 88572 B) 77854
C) 99584 D) 55654
 
Answer & Explanation Answer: A) 88572

Explanation:

Given a secret is told to 3 persons in 3 minutes.
And if the process continues with each person saying 3 other persons,
In 30 minutes => the rocess for 10 times because each person time is 3 minutes.
Required number of persons = 3 + 32 + 33 + .... + 39 + 310

 

Now it forms a geometric progression,

 

Sum to n terms is S = arn - 1r - 1

 

Here a = 3, r = 3

 
=> 59048 x 3 /2

 

= 88572.

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5 4489
Q:

In a slip test, K got the 15th rank and he was 44th from the bottom of the list of passed students. 4 students did not take up the slip test and 3 students were failed. What is the total strenght of the class ?

A) 63 B) 62
C) 64 D) 65
 
Answer & Explanation Answer: D) 65

Explanation:

Total strength of the class is given by

15 + 44 + 4 + 3 - 1 = 65

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9 4472
Q:

Solve this inequality 3b - 7 < 32?

A) b = 13 B) b < 13
C) b > = 13 D) b < = 13
 
Answer & Explanation Answer: B) b < 13

Explanation:

The given 3b - 7 < 32 can be solved as

3b - 7 < 32

3b < 39

b < 13.

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12 4421
Q:

When 721+722+723+724 is divided by 25 the remainder is:

A) 5 B) 17
C) 7 D) 0
 
Answer & Explanation Answer: D) 0

Explanation:

Given,721+722+723+724

721(1 + 7 + 49 + 343)
721(400)

Now, 400 is divisible by 25. The remainder will be 0

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2 4375
Q:

In an examination, a student scores 4 marks for every correct answer and loses I mark for every wrong answer. If he attempts in all 60 questions and secures 130 marks, the number 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).

Therefore, 4x – (60 – x) = 130 

=> 5x = 190  => x = 38

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2 4317
Q:

78 of 448 + 67 of 3374 = ?

A) 3084 B) 3184
C) 3584 D) None of these
 
Answer & Explanation Answer: D) None of these

Explanation:

78 x 448 + 67 x 3374 => 392 + 2892=> 3284

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3 4248
Q:

The average temperature of Monday to Wednesday was 37 C and of Tuesday to Thursday was 34 C. If the temperature on Thursday was 4/5 th of that of Monday, the temperature on Thursday was ?

A) 35 c B) 36 c
C) 34 c D) 32 c
 
Answer & Explanation Answer: B) 36 c

Explanation:

Monday + Tuesday + Wednesday = 37 x 3 -----------(1)
Tuesday + Wednesday + Thursday = 34 x 3---------(2)
Thursday = 4/5 of Monday ------------------(3)
subtract eqn (1) from (2) we get,
Thursday - Monday = -9
=> Monday - Thursday = 9.......(4)
From (3) & (4), we get

So,Thursday = 36 C

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3 4040