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.
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:
Attend the upcoming GMAT Strategy masterclass to get your personalized study plan that defines the exact metrics you need to hit to score GMAT 760 ‘effectively’.
Join us for a GMAT Verbal webinar on Modifiers. This live session will be hosted by Marty Murray, Chief Curriculum and Content Architect at Target Test Prep. A test prep veteran who has scored 800 on the GMAT, Marty is known worldwide.
Re: When 10 is divided by the positive integer n, the remainder is n - 4.
[#permalink]
16 Mar 2014, 04:55
5
Kudos
19
Bookmarks
Expert Reply
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.
Re: When 10 is divided by the positive integer n, the remainder is n - 4.
[#permalink]
14 Mar 2015, 06:39
1
Kudos
2
Bookmarks
Expert Reply
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.
Answer: C.
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
We can always plug in one by one and test which works. (A) The remainder is 3 - 4 = -1 which doesn't make sense. (B) 10/4 gives a remainder of 2, n - 4 = 4 - 4 = 0 however so not B. (C) 10/7 gives a remainder of 3. n - 4 = 7 - 4 = 3. Bingo.
Ans: C _________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
When 10 is divided by the positive integer n, the remainder is n - 4.
[#permalink]
Updated on: 17 May 2021, 07:33
1
Kudos
1
Bookmarks
Expert Reply
Top Contributor
Bunuel 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
APPROACH #1: I'd say that the fastest approach is to simply test answer choices
(A) 3 The question tells us that we get a remainder of n - 4 So, if n = 3, then the remainder = 3 - 4 = -1, which makes no sense (the remainder must always be greater than or equal to 0) Eliminate A
(B) 4 Plug n = 4 into the given information to get: When 10 is divided by 4, the remainder is 4 - 4 (aka 0) This is not true. When we divide 10 by 4, we get reminder 2 Eliminate B
(C) 7 Plug n = 7 into the given information to get: When 10 is divided by 7, the remainder is 7 - 4 (aka 3) WORKS!
Answer: C -------------------------
APPROACH #2: Apply the rule for rebuilding the dividend
There's a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
Given: When 10 is divided by the positive integer n, the remainder is n - 4 Since we're not told what the quotient is, let's just say that it's q. In other words: When 10 is divided by the positive integer n, the quotient is q, and the remainder remainder is n - 4
When we apply the above rule we get: 10 = nq + (n-4) Add 4 to both sides of the equation to get: 14 = nq + n Factor to get: 14 = n(q + 1)
Importance: Since n and (q + 1) are INTEGERS, n must be a FACTOR of 14.
Check the answer choices.... only answer choice C (7) is a factor of 14
Re: When 10 is divided by the positive integer n, the remainder is n - 4.
[#permalink]
14 Mar 2015, 06:08
1
Bookmarks
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.
Answer: C.
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?
Re: When 10 is divided by the positive integer n, the remainder is n - 4.
[#permalink]
13 Apr 2019, 14:54
2
Bookmarks
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
Re: When 10 is divided by the positive integer n, the remainder is n - 4.
[#permalink]
06 Jan 2022, 01:02
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
One of the fastest-growing graduate business schools in Southern California, shaping the future by developing leading thinkers who will stand at the forefront of business growth. MBA Landing | School of Business (ucr.edu)