1499+ Simplification Questions and Answers With Explanation

Q:

Simplify

$\frac{1 . 5^{3} + 4 . 7^{3} + 3 . 8^{3} - 3 x 1.5 x 4.7 x 3.8}{1 . 5^{2} + 4 . 7^{2} + 3 . 8^{2} - 1.5 x 4.7 - 4.7 x 3.8 - 1.5 x 3.8}$

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

Answer & Explanation Answer: C) 10

Explanation:

Apply $\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a^{2} + b^{2} + c^{2} - a b - b c - c a} = a + b + c$

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

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34 108754

Q:

Simplify the following :

$\frac{37^{3} + 35^{3} + 28^{3} - 3 x 37 x 35 x 28}{37^{2} + 35^{2} + 28^{2} - 37 x 35 - 35 x 28 - 37 x 28}$ ?

A) 100	B) 1
C) 4	D) 0

Answer & Explanation Answer: A) 100

Explanation:

Given $\frac{37^{3} + 35^{3} + 28^{3} - 3 x 37 x 35 x 28}{37^{2} + 35^{2} + 28^{2} - 37 x 35 - 35 x 28 - 37 x 28}$

It is in the form of

$\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a^{2} + b^{2} + c^{2} - a b - b c - c a}$ = a + b + c

Here a = 37, b = 35 & c = 28

=> a + b + c = 37 + 35 + 28 = 100

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

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19 106448

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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265 87022

Q:

$\sqrt[3]{9261} x \sqrt{62742241} = ? + 89$

Find the value of '?'

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

Answer & Explanation Answer: C) 166252

Explanation:

Given $\sqrt[3]{9261} x \sqrt{62742241} = ? + 89$

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 77344

Q:

The radius of base of a right circular cone is 6cm and its slant height is 10cm. Then its volume is

$(u s e π = \frac{22}{7})$

A) 301.71 cm3	B) 310.71 cm3
C) 301.17 cm3	D) 310.17 cm3

Answer & Explanation Answer: A) 301.71 cm3

Explanation:

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Q:

Simplify the following equation.

$\frac{19}{43} + \frac{1}{(2 + \frac{1}{3 + \frac{1}{1 + \frac{1}{4}}})}$

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 56329

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 $\Rightarrow$ x =144

Birds killed by A = (5/24)x = (5/24)*144 = 30

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120 54486

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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