Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 01 Jan 2016
Posts: 57
GPA: 3.75
WE: Engineering (Energy and Utilities)

If a and b are positive integers so that the remainder, when dividing [#permalink]
Show Tags
06 Feb 2018, 10:30
1
This post received KUDOS
5
This post was BOOKMARKED
Question Stats:
44% (01:27) correct 56% (01:42) wrong based on 88 sessions
HideShow timer Statistics
If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b? a)3/4 b) 1/3 c) 5/8 d) 5/7 e) 7/8 Source: ExamPALKudos for detailed explanation!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
If you like it, give kudos. Thanks
The price of success is hard work, dedication to the job at hand, and the determination that whether we win or lose, we have applied the best of ourselves to the task at hand. ~Vince Lombardi



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2454
Location: India
GPA: 3.12

If a and b are positive integers so that the remainder, when dividing [#permalink]
Show Tags
06 Feb 2018, 12:37
1
This post received KUDOS
Teerex wrote: If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b? a)3/4 b) 1/3 c) 5/8 d) 5/7 e) 7/8 Source: ExamPALKudos for detailed explanation! This is the method that I used to solve this problem We need the fraction a/b such that we get remainder as 4. Evaluate the various answer options available a) 3x/4x When x=1, remainder of 3 When x=2, remainder of 6 When x=3, remainder of 9 When x=4, remainder of 12 b) x/3x When x=1, remainder of 1 When x=2, remainder of 2 When x=3, remainder of 3 When x=4, remainder of 4Hence, Option B(1/3) could be the value of the expression (a/b)
_________________
Stay hungry, Stay foolish
20172018 MBA Deadlines
Class of 2020: Rotman Thread  Schulich Thread Class of 2019: Sauder Thread



Manager
Joined: 01 Jan 2016
Posts: 57
GPA: 3.75
WE: Engineering (Energy and Utilities)

Re: If a and b are positive integers so that the remainder, when dividing [#permalink]
Show Tags
06 Feb 2018, 23:42
1
This post received KUDOS
pushpitkc wrote: Teerex wrote: If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b? a)3/4 b) 1/3 c) 5/8 d) 5/7 e) 7/8 Source: ExamPALKudos for detailed explanation! This is ExamPAL's solution: Since all the answers are smaller than 1, a must be smaller than b. So a must be the remainder itself. so, 4/b=fraction such that b is an integer. Checking this: Option A: 4/b=3/4 => b=16/3 (incorrect as b is not an integer) Option B: 4/b=1/3 =>b=12 (Correct as b is an integer) So, B is the correct answer! I thought the solution is really cool coz I didn't think like that at all! Hope you like it :D
_________________
If you like it, give kudos. Thanks
The price of success is hard work, dedication to the job at hand, and the determination that whether we win or lose, we have applied the best of ourselves to the task at hand. ~Vince Lombardi



Senior Manager
Joined: 31 Jul 2017
Posts: 332
Location: Malaysia
WE: Consulting (Energy and Utilities)

Re: If a and b are positive integers so that the remainder, when dividing [#permalink]
Show Tags
07 Feb 2018, 04:37
Teerex wrote: If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b? a)3/4 b) 1/3 c) 5/8 d) 5/7 e) 7/8 Source: ExamPALKudos for detailed explanation! As per the question  \(a  4 = bq\), which means as a & b are positive integers, a value will always be greater than or equal to 4. Lets take \(a = 5, bq = 1 (a>b)\) \(a = 6, bq = 2 (a > b).\) But as per the options a < b. So, the only value possible for \(a = 4, bq = 0\) (here, \(q = 0\) as b is positive integer) As \(a = 4\), to make \(a < b, b = 4k\) (Where \(k = 2,3,4,5,6,7,8.....\) etc). Only Option is \(\frac{4}{12} = \frac{1}{3}\)
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Director
Joined: 07 Dec 2014
Posts: 967

If a and b are positive integers so that the remainder, when dividing [#permalink]
Show Tags
Updated on: 11 Mar 2018, 18:21
Teerex wrote: If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b?
a)3/4
b) 1/3
c) 5/8
d) 5/7
e) 7/8 let q=quotient a=bq+4 assume b>a then q=0 and a=4 only 4/b=1/3 makes b an integer 4/12=1/3 B
Originally posted by gracie on 07 Feb 2018, 14:05.
Last edited by gracie on 11 Mar 2018, 18:21, edited 1 time in total.



Math Expert
Joined: 02 Aug 2009
Posts: 5777

If a and b are positive integers so that the remainder, when dividing [#permalink]
Show Tags
07 Feb 2018, 20:25
Teerex wrote: If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b? a)3/4 b) 1/3 c) 5/8 d) 5/7 e) 7/8 Source: ExamPALKudos for detailed explanation! Hi.... All the choices are in simplest form with denominator>numerator.. So the REMAINDER will be MULTIPLE of numerator.. All other except A and B have a numerator>4, so none of the C, D and E can have a Remainder of 4.. A has 3 in numerator so the Remainder will be 3,6,9... 4 is not a MULTIPLE of 3, so A out Ans B. and a and b are 4 and 12.. Note: choices should have been in increasing/decreasing order.
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2297

Re: If a and b are positive integers so that the remainder, when dividing [#permalink]
Show Tags
09 Feb 2018, 10:56
Teerex wrote: If a and b are positive integers so that the remainder, when dividing a by b is 4. Which of the following could be the value of a/b?
a)3/4
b) 1/3
c) 5/8
d) 5/7
e) 7/8
Scanning the answer choices, we observe that all the choices are proper fractions. This means that b is greater than a, which in turn implies that the remainder from the division of a by b is in fact a. Therefore, a = 4. We note that for any answer choice besides 1/3, it is not possible to obtain an equivalent fraction where the numerator is 4. Since 1/3 = 4/12, the remainder when dividing 4 by 12 is 4. Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 04 Feb 2016
Posts: 36
Location: India
Concentration: Technology, Marketing
GPA: 3.7
WE: Sales (Computer Software)

Re: If a and b are positive integers so that the remainder, when dividing [#permalink]
Show Tags
12 Mar 2018, 08:50
Mathematically, a=kb+4 where k=0,1,2,.....
so, a/b = k+4/b .. hence a/b has to be greater than 1 for all values of k except 0. For k=0, a=4. Hence the numerator must be a multiple of 4. Hence, B.
Hope this makes sense.
Tx.




Re: If a and b are positive integers so that the remainder, when dividing
[#permalink]
12 Mar 2018, 08:50






