GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 08:52 GMAT Club Daily Prep

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

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.  When 10 is divided by the positive integer n, the remainder is n - 4.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58410
When 10 is divided by the positive integer n, the remainder is n - 4.  [#permalink]

Show Tags

1
19 00:00

Difficulty:   5% (low)

Question Stats: 87% (01:20) correct 13% (01:33) wrong based on 777 sessions

HideShow timer Statistics

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

Problem Solving
Question: 164
Category: Algebra Properties of numbers
Page: 84
Difficulty: 600

The Official Guide For GMAT® Quantitative Review, 2ND Edition

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58410
Re: When 10 is divided by the positive integer n, the remainder is n - 4.  [#permalink]

Show Tags

1
6
SOLUTION

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

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.

_________________
General Discussion
Manager  Joined: 26 Feb 2015
Posts: 110
Re: When 10 is divided by the positive integer n, the remainder is n - 4.  [#permalink]

Show Tags

Bunuel wrote:
SOLUTION

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

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.

I simply did it this way:

$$y = 10n + (n - 4)$$

And then I just plugged in values for n. So:
$$10(0) + (0-4) = -4$$
$$10(1) + (1-4) = 7$$ <--my answer

Is this correct reasoning, or simply a lucky coincidence?
Math Expert V
Joined: 02 Aug 2009
Posts: 8005
Re: When 10 is divided by the positive integer n, the remainder is n - 4.  [#permalink]

Show Tags

erikvm wrote:
Bunuel wrote:
SOLUTION

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

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.

I simply did it this way:

$$y = 10n + (n - 4)$$

And then I just plugged in values for n. So:
$$10(0) + (0-4) = -4$$
$$10(1) + (1-4) = 7$$ <--my answer

Is this correct reasoning, or simply a lucky coincidence?

hi erikvm,
here it is a lucky coincidence..
here you have found the value of y and not n...

$$10(1) + (1-4) = 7$$... here n=1 and y=7.... but the question asks us the value of n...
the equation that you have formed is wrong ..
it says when 10 is divided by the positive integer n, the remainder is n-4.. so the equation will be 10=xn+n-4..

what we have to find is that " when 10 is divided by n, the remainder is n-4"
now substitue the values
(A) 3.... 10/3 rem=1, which is not equal to n-4=3-4=-1.... not correct
(B) 4.... 10/4 rem=2, which is not equal to n-4=4-4=0.... not correct
(C) 7.... 10/7 rem=3, which is equal to n-4=7-4=3.... correct
(D) 8.... 10/8 rem=2, which is not equal to n-4=8-4=2.... not correct
(E) 12... 10/12 rem=10, which is not equal to n-4=10-4=6.... not correct

hope it is clear..
_________________
Senior Manager  P
Joined: 10 Apr 2018
Posts: 267
Location: United States (NC)
When 10 is divided by the positive integer n, the remainder is n - 4.  [#permalink]

Show Tags

1
Hi,

Here are my two cents for this question. This solution is same as all others but want to share one important aspect of thinking in case of remainders.

My solution would appear little lengthy, but if you can visualize certain things about remainders, we could solve this question this question in about 33 Secs.

Here we are told that when $$\frac{10}{n}$$ we have remainder in the form (n-4)

So we can write this $$\frac{10}{n}$$ as 10 = nk +(n-4) ------(1)

where 0$$\leq{reminder}$$<n ; where 0$$\leq{n-4}$$<n ( This is the first hint toward rejecting incorrect choice A, B )

which says 4$$\leq{n}$$

here we can have two cases
Case 1: if n>10
then nk =0 and we can re-write the equation (1) as .
10 = n-4
where n =14
This is our second hint for rejecting Answer Choice "E" Consider a case where n = 12 so we have $$\frac{10}{12}$$= 12*0+ 10) here remainder is 10 . But using the equation given to us in the question stem that remainder is n-4 , which in this case would be 12-4 =8 So we can reject answer choice E

Case 2:
If n< 10,
then we have k is a positive integer.
$$\frac{n}{10}$$ = nk +(n-4) ------(1)
and simplifying we get
10+4= nk+n
14=n(k+1)
so we have
14= 7(1+1)
so we have n=7

Hence form given choices we have answer to the question which is choice "C"
_________________
Probus

~You Just Can't beat the person who never gives up~ Babe Ruth When 10 is divided by the positive integer n, the remainder is n - 4.   [#permalink] 13 Apr 2019, 15:54
Display posts from previous: Sort by

When 10 is divided by the positive integer n, the remainder is n - 4.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  