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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:

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 10289
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 10104
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 10099
Q:

Which of the following statement(s) is/are true?

I. (65)1/6 > (17)1/4 > (12)1/3  II. (17)1/4 > (65)1/6 > (12)1/3   III. (12)1/3 > (17)1/4 > (65)1/6

A) Only I B) Only III
C) Only II D) None of these
 
Answer & Explanation Answer: B) Only III

Explanation:
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0 9792
Q:

If 3x-y=27, 3x+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=27, 3x+y=243

⇒3x-y =33 , 3x+y=35

 => x-y=3, x+y=5

 => x = 4

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15 9738
Q:

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

1234 + 2345 – 3456 + 4567 = ?

A) 4590 B) 4680
C) 4670 D) 4690
 
Answer & Explanation Answer: D) 4690

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. ? = 1234 + 2345 – 3456 + 4567 ? = 3579 - 3456 + 4567 ? = 123 + 4567 ? = 4690

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0 9697
Q:

38% of 7500 +  ?% of 375 = 50% of 6000

A) 50 B) 40
C) 60 D) 45
 
Answer & Explanation Answer: B) 40

Explanation:

Let ? = p

38 x 7500/100  + p x 375/100 = 50 x 6000/100

=> 38 x 75 + 3.75p = 3000

=> 3.75p = 3000 - 2850

=> p = 150/3.75 

=> p = ? = 40

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11 9533
Q:

By how much is three-fifth of 350  greater than four-seventh of 210 ?

A) 90 B) 100
C) 110 D) 120
 
Answer & Explanation Answer: A) 90

Explanation:

3/5 of  350 - 4/7 of 210 = 210 - 120 = 90.

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16 9362