Question

FORWARD, 25 ; BACKWARD, 10 — Which of the following statements is true?

• A. $n_1 = n_2$ if $M = 10$ and $n_1 = 0$
• B. $M = 20$ provided $n_1>0$
• C. $n_1>30$ provided $M = 900$
• D. $n_1 = 37$ provided $M = 25$
• A. $n_1 = n_2$ provided $n_1 \ge 5$
• B. $n_1 = n_2$ provided $n_1>0$
• C. $n_2 = 5$ provided $M>0$
• D. $n_1>n_2$ provided $M>0$
• A. $n_2 = n_1 = 20$ only if $n_1 = 0$
• B. $n_2 - n_1 = 20$ if $M>20$ and $n_1 = 1$
• C. $n_2 - n_1 = 10$ if $M = 21$ and $n_1 = 0$
• D. $n_2>n_1$ if $M>0$
• A. $n_2 = n_1 + 4$ provided $1<n_1<7$
• B. $n_2 = n_1$ provided $M<6$
• C. $n_2 = n_1 + M - n_1 - 5$
• D. $n_2 = n_1<0$ provided $M>0$

Answer 1

The Correct Option is D

We start at page $n_1$.
Instruction 1: FORWARD, 25 means move forward by 25 pages from the current page.
If during this move we cross or reach $M$, we stop exactly at $M$.
If $M = 25$ and $n_1 = 37$, then $n_1 + 25 = 62$ which is greater than $M$.
So, according to the rule, we stop at page $M = 25$.
Now we apply Instruction 2: BACKWARD, 10 means move backward by 10 pages from the current page.
From page 25, going back 10 pages puts us at page $25 - 10 = 15$.
There is no stopping at 0 in this case because the move does not take us below page 0.
Thus, the statement “$n_1 = 37$ provided $M = 25$” correctly describes a case matching the given sequence.

Answer 2

We start at page $n_1$.
Instruction 1: BACKWARD, 5 means move backward by 5 pages.
If $n_1 \ge 5$, then after moving backward we are at page $n_1 - 5$.
There is no stopping at 0 in this case because the move does not take us below page 0.
Instruction 2: FORWARD, 5 means move forward by 5 pages from the current page.
From page $n_1 - 5$, adding 5 returns us to $n_1$.
Thus, $n_2 = n_1$ provided $n_1 \ge 5$.
If $n_1<5$, then the first move would stop at page 0, and the second move would take us to page 5, so $n_2 \neq n_1$.

Answer 3

We start at page $n_1$.
Instruction 1: FORWARD, 10 means move forward by 10 pages.
If $n_1 + 10 \le M$, then we simply go to page $n_1 + 10$.
If $n_1 + 10>M$, we stop at page $M$.
Instruction 2: FORWARD, 10 means move forward by 10 pages again from the new position.
If $n_1<M$, each FORWARD move increases the page number or leaves it at $M$ if the limit is reached.
Thus, if $M>0$ and $n_1<M$, $n_2$ will always be greater than $n_1$.
Only if $n_1 = M$ will $n_2 = n_1$, but the statement says “if $M>0$” which allows $n_1<M$ — making $n_2>n_1$ true.

Answer 4

We start at page $n_1$.
Instruction 1: FORWARD, 5 means move forward by 5 pages.
If $n_1 + 5 \le M$, then we go to page $n_1 + 5$.
Instruction 2: BACKWARD, 4 means move backward by 4 pages from the new position.
From page $n_1 + 5$, going back 4 pages puts us at $n_1 + 1$.
This seems to contradict the “$n_1 + 4$” in the option, so let’s check boundary effects.
If $1<n_1<7$, the first move will not hit $M$ or 0, and the second move will not hit 0 either.
Thus, net change = $+5$ then $-4$, so overall $+1$.
It appears the given option “$n_1 + 4$” may be a misprint, and the correct net result should be $n_1 + 1$.