Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

fresinha12 - I did the same way as you had described. But is it safe to assume that K=1?

well, since we can never have the denominator to be zero, otherwise the fraction will be undefined. so it makes sense to start off with k=1. If that doesn't work, then you just have to keep increasing the value of k until you can match your answer with the correct answer choice.

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

Show Tags

18 Jun 2010, 00:56

As per my approach, it is easy to reach the solution by going thorough each one of the options. You can eliminate 12,8,4 and 3 at one look. Then you just need to check for 7. It took me less than 1 minute to get to the answer. So that should be fine I guess.

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

My strategy was to create lists below: n = 3, 4, 7, 8, 12 n-4 = -1(becomes 9), 0, 3, 4, 8 n/10 = R? = 3, 4, 7, 8, 4

There is no match between n-4 and n/10's R.

The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?

Algebraic approach:

THEORY: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

Original question says that when 10 is divided by the positive integer n, the remainder is n-4, so \(10=nq+(n-4)\) and also \(n-4\geq{0}\) or \(n\geq{4}\) (remainder must be non-negative).

\(10=nq+n-4\) --> \(14=n(q+1)\) --> as \(14=1*14=2*7\) and \(\geq{4}\) then --> \(n\) can be 7 or 14.

It says that the remainder when you divide 10 by n is n-4

This basically can be translated into the following statement algebraically:

\(10 = kn + (n-4)\)

This is simplified as follows:

\(10 = kn + n -4 = n *(k+1) - 4\)

Further simplifying:

\(10 + 4 = n*(k+1)

14 = n*(k+1)

7*2 = n*(k+1)\)

So n can be 7 or 2.

Only 7 is listed as an option here, so the answer is C. Hope this helps!

\(n\) cannot be 2 as in this case \(remainder =n-4=-2<0\) and remainder is always non-negative (also notice that 10/2 has no remainder and n-4=-2, though n can also be 14 --> 10=14*0+(14-4)).

If \(a\) and \(d\) are positive integers, there exists unique integers \(q\) and \(r\), such that \(a = qd + r\) and \(0\leq{r}<d\). \(q\) is called a quotient and \(r\) is called a remainder.

Also EVERY GMAT divisibility question will tell you in advance that any unknowns represent positive integers.

So trust me: remainder is always non-negative and less than divisor for GMAT - \(0\leq{r}<d\). _________________

If division by n leaves reminder. Then i.e. Dividend - Remainder is a multiple of divider. Here 10 -(n-4) must be a multiple of n.

Or Is [10 - (n-4)] / n = integer?

Now plug in the values of n from the options.

A - n-4 will give negative remainder. Illogical B - (10-0)/4 is not integer C - (10-3)/7 is integer D - (10-4)/8 is not integer E - (10-8)/12 is not integer

Answer C.

Baten80 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 ?

Factors of 14; n*(Q+1) 1*14; n=1, Q=13; Not possible because 1 won't leave any remainder with 10 2*7; n=2, Q=6; Not possible because 2 won't leave any remainder with 10 7*2; n=7, Q=1; Possible 14*1; n=14, Q=0; Possible

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

Show Tags

06 Mar 2011, 15:04

Nice explanation there Bunuel.

Bunuel wrote:

jpr200012 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

My strategy was to create lists below: n = 3, 4, 7, 8, 12 n-4 = -1(becomes 9), 0, 3, 4, 8 n/10 = R? = 3, 4, 7, 8, 4

There is no match between n-4 and n/10's R.

The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?

Algebraic approach:

THEORY: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

Original question says that when 10 is divided by the positive integer n, the remainder is n-4, so \(10=nq+(n-4)\) and also \(n-4\geq{0}\) or \(n\geq{4}\) (remainder must be non-negative).

\(10=nq+n-4\) --> \(14=n(q+1)\) --> \(n\) is an factor of 14 and \(\geq{4}\) --> \(n\) can be 7 or 14.

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

Show Tags

06 Mar 2011, 16:41

Bunuel,

I know in this case we don't have to make any assumption, because the question clearly states these are two positive integers.

i was referring more to scenarios like negative number division

-25 /7

-25 = 7(-3)+(-4)

Here remainder is -4 which is negative.

so lets say if question is like x,y are integers x/y . we cannot generalize and say remainder >=0 ,unless we assume that we are only talking about positive integers.

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...