MaxWong

\(\underbrace{something something}_{No\; solution}\)? I don't know what you mean but I am trying to solve this.

$90000 per year(per annum) = $(90000/12) per month = $ 7500 per month!!

Which is same as Guest number 1's answer.

(Method 1)There are 10 multiples of 3 in 1- 30, So there are 10 multiples of 3 in 50 - 80. Then we count from 81.

81, 84, 87, 90, 93, 96, 99.

There are 17 multiples of 3 between 50 and 100.

Then we have 99 is not an even number.

51, 54, 57, 60..... , 96 <---- 16 numbers there.

Then we divide 16 by 2 which is 8

There are 8 even multiples of 3 between 50 and 100.

(Method 2) Even multiples of 3 must be divisible by 6 because those multiples of 3 are divisible by 2 and 3.

Starting from 54, we have

54, 60, 66, 72, 78, 84, 90, 96 Which is 8 numbers.

72 is not divisible by 7.

Therefore answer is C.

\((40,000-3000-(-18,000+10000))\times1-0.4\\ = 40000 - 3000 + 18000 - 10000-0.4\\ =45000 - 0.4\\ = 44999.6\\ \text{It doesn't equal 25400}\)

\(\dfrac{4\pi r^3}{3}=3000\\ 4\pi r^3 = 9000\\ \pi r^3 = 2250 \\r=\sqrt[3]{\dfrac{2250}{\pi}}\)

r is the radius of the sphere.

\(\text{Surface area}\\ =4 \pi r^2\\ = 4(\dfrac{2250}{\pi})^{\frac{2}{3}}\\ \approx 320.195399866\;\;\text{cm}^2\)

This is a approximate value of pi. But starting from ..... 897932 ....... it's not so accurate. The previous digits are correct though......

\(f(x)=\dfrac{x^2-1}{\ln x}+x-1\\ f(0.0001)=\dfrac{(0.0001)^2-1}{\ln (0.0001)}+0.0001-1\)

= -0.8913263806099232

\(\text{The question means:}\\ \text{How many values give } \dfrac{n}{g(n)}\text{ is not an integer?}\)

n=2, g(n)= 1 , 2/1 is an integer

n=3, g(n)= 1, 3/1 is an integer.

Looks like prime numbers does give n/g(n) = (some integer.)

Prime numbers between 2 and 50:

2, 3, 5, 7 , 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Total 15 numbers.

also n = 6 does give n/g(n) = integer.

Total 16 numbers now.

Answer = (Number of integers between 2 and 50) - 16

= 50 - 2 + 1 - 16

= 33

33 values of n does n not divide g(n). 

Finish!!