Instructions

The pages of a book are numbered 0, 1, 2 . upto M, M>0. There are four categories of instructions that direct a person in positioning the book at a page. The instruction types and their meanings are :
1. OPEN : Position the book at page No. 1
2. CLOSE : Position the book at page No. 0
3. FORWARD, n :From the current page move forward by n pages; if, in this process, page number M is reached, stop at M.
4. BACKWARD, n : From the current page, move backward by n pages; if in this process, page number 0 is reached, stop at page number 0.
In each of the following questions, you will find a sequence of instructions formed from the above categories. In each case, let n1 be the page number before the instructions are executed and n2 be the page number at which the book is positioned after the instructions are executed.

Question 43

# FORWARD, 10; FORWARD, 10. Which of the following statements about the above instructions is true?

Solution

Let's consider each statement one by one

A) Suppose M=50, $$n_1$$=5

In this case, $$n_2$$ = 5 + 10 + 10 = 25. Hence, $$n_2 - n_1 = 20$$ even though $$n_1 \neq 0$$. Hence, statement A is false.

B) Suppose M=21 and $$n_1$$=1

In this case, $$n_2$$ = 1 + 10 + 10 = 21. Hence, $$n_2 - n_1 = 20$$. Thus, if M>20 then this statement is true.

If M = 19

In this case, the process stops when M is reached. Hence, $$n_2$$=19 and $$n_2 - n_1 = 18$$. Hence, option B is true.

C) As we have seen earlier, $$n_2 - n_1 = 20$$ in this case. Hence, option C is false.

D) Suppose $$n_1=M$$. In this case, $$n_2 = n_1$$. Hence, option D is false.