Problem Solving

When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

a. 3
b. 4
c. 7
d. 8
e. 12

Answer is C

10/n = k.n +(n-4)
if we take n=7 then 10/7 = k.7 +(7-4)
if k=1 , 7+3 is 10
the other values of n don't satisfy.

Am I correct? any expert comment?

Brent Hanneson wrote:

480ocean wrote:When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

a. 3
b. 4
c. 7
d. 8
e. 12

Answer is C

There is a rule that says "If a/b = c with remainder d, then bc + d = a
In other words, we can "build/recreate" a with the other information.
For example: 17/5 = 3 with remainder 2
We can build/recreate 17 as follows: (3)(5) + 2 = 17

Here we are told that 10/n = k (some integer) with remainder n-4
We can "build/recreate" 10 as follows: nk + (n-4) = 10
Simplify: nk + n = 14
or n(k+1)=14
Since n and k+1 are both positive integers, then n must equal 1, 2, 7, or 14Only 1 of those (7) appears in the answer choices.

In this case since n-4 is a remainder n-4 must be non-negative.
So n>=4. So n must be 7 or 14. Is this correct or not?

ven4gmat wrote:

Brent Hanneson wrote:

480ocean wrote:When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

a. 3
b. 4
c. 7
d. 8
e. 12

Answer is C

There is a rule that says "If a/b = c with remainder d, then bc + d = a
In other words, we can "build/recreate" a with the other information.
For example: 17/5 = 3 with remainder 2
We can build/recreate 17 as follows: (3)(5) + 2 = 17

Here we are told that 10/n = k (some integer) with remainder n-4
We can "build/recreate" 10 as follows: nk + (n-4) = 10
Simplify: nk + n = 14
or n(k+1)=14
Since n and k+1 are both positive integers, then n must equal 1, 2, 7, or 14Only 1 of those (7) appears in the answer choices.

In this case since n-4 is a remainder n-4 must be non-negative.
So n>=4. So n must be 7 or 14. Is this correct or not?

Yes, what you said is definitely true. For those of you who want to solve this with the options given, you can eliminate the first option straight away as n>=4.

Let's look at another way of doing this

Since (n-4) is remainder when 10 is divided byt n, 10-(n-4) must be divisible by n.

i.e 14-n must be divisible by n

i.e 14 must be divisible by n.

So n (>=4) is a factor of 14. So n must be 7 or 14.

480ocean wrote:When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

a. 3
b. 4
c. 7
d. 8
e. 12

Answer is C

I feel for such questions, we should simply plug-in to quickly identify the right choice. As mentioned by others, choice a can be ruled out as the reminder can never be a negative number.

When using the plug-in strategy, ensure you are starting with option C. This will tell you which options to look for next (either the 2 options above or below).

In this case, option C gives you the answer straight away. If n=7, then dividing 10/7 gives reminder 3. This is the same value that you get when substituting 7 in n-4 (i.e. 7-4=3).

Hope that helps.

I always use backsolving on these problems. Starting with B and then jumping to D choice. It's the quickest way for me

I perfectly agree with our friends that going with the options is the quickest way to answer this. But when it comes to learning the subject (while practicing) it will help if you can solve without using the options.

For example, if the question is something like "How many values of n satisfy the given condition?" then definitely learning the above concepts will help to answer this quickly.

Anyway folks, nice discussion...

Thanks you guys! You're the best!