# 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| =

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

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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245 81027
Q:

Simplify

 A) 6 B) 8 C) 10 D) 12

Answer & Explanation Answer: C) 10

Explanation:

Apply

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

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25 55154
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, $\inline \fn_jvn \frac{(37)^{3}+(35)^{3}+(28)^{3}-3x37x35x28}{(37)^{2}+(35)^{2}+(28)^{2}-37x35-35x28-37x28}$  = 100

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15 52897
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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102 45730
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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92 36196
Q:

Find the value of '?'

 A) 166251 B) 166259 C) 166252 D) 166253

Answer & Explanation Answer: C) 166252

Explanation:

Given

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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18 34254
Q:

To fill a tank, 25 buckets of water is required.  How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ?

 A) 52.5 B) 62.5 C) 72.5 D) 82.5

Answer & Explanation Answer: B) 62.5

Explanation:

Let the capacity of 1 bucket = x.

Then, capacity of tank = 25x.

New capacity of bucket  = (2/5)x

$\inline \therefore$Required no of buckets = 25x/(2x/5)  = 62.5

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42 31137
Q:

If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3  is equal to :

 A) 22 B) 23 C) 24 D) 25

Answer & Explanation Answer: A) 22

Explanation:

3 * 5 + 5 * 3 = (2 * 3 - 3 * 5 + 3 * 5) + ( 2 * 5 - 3 * 3 + 5 * 3)

= (6 + 10 - 9 + 15) = 22.

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75 29400