HackerRank Simplifications and Approximations Quiz- 1

4% of \frac{1}{16} of 0.256 = 0.04 x  \frac{1}{16} x 0.256

=  \frac{1}{400} x 0.256

= 0.00064

Simplify bracket first. Then follow the order of division, multiplication, addition and subtraction.

3+2\div (4-6)x5+2

= 3 + 2 \div (-2) x 5 + 2

= 3 - 1 x 5 + 2

= 3 - 5 + 2

= 3 - 3 = 0

Let chocolate received by each student = n

Then number of students = 20n

Each student is given same number of chocolates

Simplifying ,we get , total Chocolates = 20n x n

 

Number of students is reduced to half

Simplifying, 20n x n chocolates is distributed among 10n students and each gets 6 chocolates

\frac{20n x n}{10n} = 6

So 2n = 6

n = 3

Number of students = 20n = 20 x 3 = 60

12% of x + x% of 56 = 36% of 125 + x% of 8

\frac{12}{100}x +   \frac{x}{100} \times 56 =  \frac{36}{100} \times 125 +  \frac{x}{100} \times 8

0.12x + 0.56 x =  45 + 0.08x

0.6 x =  45

x = 75

30% of one-fifth of 7000 = 0.30 x 0.2 x 7000

= 420

We need to find what percentage of 3726 is 420

So required percentage = \frac{420}{3726} \times 100

= 11.2%

= 11% (approx)

\frac{3}{8} \times  \frac{4}{19} \times \frac{38}{39} \times x = 75

Simplifying, we get

\frac{1}{13} \times x = 75

So x = 13 x 75 = 975

Let x = \sqrt{21+\sqrt{21+\sqrt{21+\sqrt{21......}}}}

Then x^{2} = 21+ \sqrt{21+\sqrt{21+\sqrt{21+\sqrt{21......}}}}

Or  x^{2} = 21 + x

x^{2} - x - 21 = 0

Solving x =  5.1 , -4.1

Taking +ve value of x, x = 5.1

Approximating to nearest integer, x = 5

By approximating, we can write,

(19.92)^{2} + (24.108)^{2} + (22.029)^{2} + (24.89)^{2} = (20)^{2} + (24)^{2} + (22)^{2} + (25)^{2}

= 400 + 576 + 484 + 625

= 2085

a = 48 x 52 = (50 - 2) ( 50 + 2)

= 50^{2} - 2^{2}

= 2500 - 4 = 2496

b = 945 ÷ 35 × 21

=27 × 21

= 567

So a+b = 2496 + 567 = 3063

Let x% be share of one boy

Then x + x + 44 = 100

X = 28

So prize of one boy and one girl is

28% of 2760 + 44% of 2760

= 0.28 x 2760 + 0.44 x 2760

= 1987.2