1499+ Simplification Questions and Answers With Explanation

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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261 85657

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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33 69047

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 62663

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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113 51382

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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21 47394

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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97 40220

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

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

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48 35725

Q:

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

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

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