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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:

5 + 2 x 10/2 = ?

A) 15 B) 35
C) 10 D) 20
 
Answer & Explanation Answer: A) 15

Explanation:

Using BODMAS Rule,

First solve division, mutiplication and Addition

So here 10/2 = 5

Then 2 x 5 =  10

Now, 5 + 10 = 15.

 

Hence, 5 + 2 x 10/2 = 15.

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5 3589
Q:

5 + 2 x 10 =

A) 70 B) 20
C) 25 D) 52
 
Answer & Explanation Answer: C) 25

Explanation:

According to BODMAS rule,

After multiplication only, addition is done.

Hence,

5 + 2 x 10 = 5 + 20 = 25.

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4 3439
Q:

If a/(a+b) = 15/21, what is (a+b)/(a-b) is equal to?

A) 13/9 B) 23/11
C) 14/5 D) 21/9
 
Answer & Explanation Answer: D) 21/9

Explanation:

a/(a + b) = 15/21 → a = 15, a + b = 21

→ b = 21– 15 = 6
⇒ a – b =15 – 6 = 9
⇒ (a + b)/(a – b) = 21/9

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0 3354
Q:

[15% of 300% of 560] × 2 ÷ 5 =

A) 100 B) 90
C) 85 D) 105
 
Answer & Explanation Answer: A) 100

Explanation:

[15% of 300% of 560] × 2 ÷ 5

= (15 x 300 x 560 x 2)/100 x 100 x 5

~= 100 

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4 3333
Q:

If a3+ b3 = 341 and ab = 30, then what is the value of a + b?

A) 1 B) 9
C) 7 D) 11
 
Answer & Explanation Answer: D) 11

Explanation:
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6 3279
Q:

If the mean of m observations out of n observations is n and the mean of remaining observations is m, then what is the mean of all n observations?

A) 2m –m^2/n B) 2m –m/n
C) 2m D) 2m –m
 
Answer & Explanation Answer: A) 2m –m^2/n

Explanation:

Mean of m observations is n

Mean of n-m observations is m

So total = nm+ (n-m)m

Total observations = n

Mean = Total / Total observations = (2mn-m^2)/n = 2m –m^2/n

 

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0 3097
Q:

If a + b + c = 7/12, 3a – 4b + 5c = 3/4 and 7a – 11b – 13c = – 7/12, then what is the value of a + c?

A) 1/2 B) 5/12
C) 3/4 D) 1/4
 
Answer & Explanation Answer: B) 5/12

Explanation:
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2 3061
Q:

If 9 * 6 = 45, 7 * 4 = 33, and 6 * 4 = 20, then what is the value of 5 * 3?

A) 24 B) 16
C) 13 D) 10
 
Answer & Explanation Answer: A) 24

Explanation:
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