Problem Solving

1.Before being simplified,the instructions for computing income tax in Country Rwere to add 2 percent of one's annual income to the average(arithmetic mean)of 100units of Country R's currency and 1 percent of one's annual income.Which of the following represents the cimplified formula for computing the income tax,in Country R's currency,for a person in that country whoses annual income is I?

A 50+I/200 B 50+3I/100 C 50+I/40 D 100+I/50 E100+3I/100

answer is C
2.For every positive even integer n,the function h(n) is defined to be the product of all the even integers from 2 to n.If p is the smallest prime factor of h(100)+1,then p is ?


A between 2 and 10 B between 10 and 20 C between 20 and 30 D between 30 and 40 E greater than 40

Answer is E

Second is an easy one

h(100) will be 2 * 4 * 6 * 8 .... 100

= 2^50 (1 * 2 * 3 ... 50)

= 2^50 * 50!

This h(100) will be divisible by all numbers from 1 to 50

adding 1
h(100) + 1 will not be divisible by any number from 1 to 50

hence smallest prime factor will be greater than 50
so answer is E

Do let me know if you need detailed explanation

First question has tricky language.
Read it carefully it will be a cakewalk

Lets try.
Total income is I.

1.Before being simplified,the instructions for computing income tax in Country Rwere to add 2 percent of one's annual income

2% of income will be 2I/100 = I/50

we need to add next part to this

to the average(arithmetic mean)of

We need to take average of

100units of Country R's currency

100 and

and 1 percent of one's annual income.

1% of income
which shall be I/100

now average will be

(100 + I/100) / 2

50 + I/200

Now the result will be

I/50 + 50 + I/200
=50 + 5I/200
=50 + I/40

Hope its clear now

I have no idea that questions can be solved this simple. Thanks!

real simple when read closely !