Live Chat with Former Admission Directors of INSEAD | Join Chat Room to Participate
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 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:
A number when divided by a divisor leaves a remainder of 24. [#permalink]
07 Apr 2007, 22:45
1
This post received KUDOS
8
This post was BOOKMARKED
00:00
A
B
C
D
E
Difficulty:
35% (medium)
Question Stats:
72% (02:36) correct
28% (01:34) wrong based on 347 sessions
A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
A) 12 B) 13 C) 35 D) 37 E) 59
I'm already familiar with the textbook method. I'm trying to discover what's wrong with the below method.
I am sorry, but described steps have mistakes in it.
My quick way of solving this would be:
1) a= d+24
2) 2a=kd+11
3) multiply step 1 by 2 and subtruct 1 from 2
4) 0=d(k-2)-37
5) because 37 is prime number, eq would make sense if k=3, hence answer would be 37 (D)
I am sorry, but described steps have mistakes in it. My quick way of solving this would be:
1) a= d+24 2) 2a=kd+11 3) multiply step 1 by 2 and subtruct 1 from 2 4) 0=d(k-2)-37 5) because 37 is prime number, eq would make sense if k=3, hence answer would be 37 (D)
Hi, Thanks. I know. Hence the answer. Will you let me know what mistakes you found.
Also, how does a = d+24 when the prob says "a number when divided by a divisor leaves a remainder of 24"? Is this some sort of shortcut?
A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
A) 13 B) 59 C) 35 D) 37 E) 12
I'm already familiar with the textbook method. I'm trying to discover what's wrong with the below method.
A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor? A. 6 B. 7 C. 5 D. 8 E. 18
We know that: . The excess remainder is a multiple of the divisor. . The divisor is greater than the greatest remainder (which is 24).
The only multiple of 37 greater than 24 is 37. Therefore, the divisor is 37.
Lets illustrate this by picking numbers: a=24 remainder equation: a/d=k+r/d -a. 24/37=0+24/37 ->remainder is 24 -ax2. 48/37=1+11/37 ->remainder is 11
Another way to see it is through algebra: -a. a/d=k+24/d -> a=dk+24 -ax2. 2a/d=q+11/d -> a=(dq+11)/2 -> 2dk+48=dq+11 Keep in mind that dq = 2dk + "excess remainder" -> 2dk + 48 = 2dk + "excess remainder" + 11 -> "excess remainder" = 37
Sorry if this is not clear enough. Can't think of another way to explain it.
You may want to refer to the Man NP guide for looking into arithmetic with remainders (pg128).
n = da + 24 (1) and 2n = db +11 (2) subtract (1) form (2) you get n = d(b-a) - 13 (3) subtract (1) from (3), you get 0 = d(b-a-a) - 37 it is a prime so lowest d is 37
divisibility and remainders [#permalink]
12 Jul 2011, 08:42
A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
A. 13 B. 59 C. 35 D. 37 E. 12.
I solve till a = fx + 24 2a = fx + 11
After this step I'm lost.
Can someone please explain me the solution, I read the solution but was not totally convinced.
Re: divisibility and remainders [#permalink]
12 Jul 2011, 08:48
1
This post received KUDOS
mustu wrote:
A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
A. 13 B. 59 C. 35 D. 37 E. 12.
I solve till a = fx + 24 2a = fx + 11
After this step I'm lost.
Can someone please explain me the solution, I read the solution but was not totally convinced.
Regards, Mustu
Looking at the options i know A and E are out ...
so it has to be B ,C or D
59/35 = 24 R 118/35 = 13 R...............wrong
37+24 = 61 61/37 = 24 R 122/37 = 11 R............. right
Re: divisibility and remainders [#permalink]
13 Jul 2011, 12:58
I used N=DQ+24, 2N=DQ+11. Multiplied the first equation by 2 to get 2N on both sides, then set the equations equal to each other. 2DQ+48=DQ+11. Ended up with DQ=-37. Picked D, got it right. Can anyone explain what was wrong with that approach?
gmatclubot
Re: divisibility and remainders
[#permalink]
13 Jul 2011, 12:58
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Wow! MBA life is hectic indeed. Time flies by. It is hard to keep track of the time. Last week was high intense training Yeah, Finance, Accounting, Marketing, Economics...