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

It is currently 17 Jan 2019, 10:15

Close

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • The winning strategy for a high GRE score

     January 17, 2019

     January 17, 2019

     08:00 AM PST

     09:00 AM PST

    Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

If a and b are positive integers so that the remainder, when dividing

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

Hide Tags

 
Manager
Manager
User avatar
B
Joined: 01 Jan 2016
Posts: 53
GPA: 3.75
WE: Engineering (Energy and Utilities)
If a and b are positive integers so that the remainder, when dividing  [#permalink]

Show Tags

New post 06 Feb 2018, 09:30
1
7
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

47% (01:35) correct 53% (01:52) wrong based on 152 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: ExamPAL

Kudos for detailed explanation!

_________________


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 PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
Premium Member CAT Tests
If a and b are positive integers so that the remainder, when dividing  [#permalink]

Show Tags

New post 06 Feb 2018, 11:37
1
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: ExamPAL

Kudos 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 4

Hence, Option B(1/3) could be the value of the expression (a/b)
_________________

You've got what it takes, but it will take everything you've got

Manager
Manager
User avatar
B
Joined: 01 Jan 2016
Posts: 53
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

New post 06 Feb 2018, 22:42
1
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: ExamPAL

Kudos 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

Director
Director
avatar
P
Joined: 31 Jul 2017
Posts: 517
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If a and b are positive integers so that the remainder, when dividing  [#permalink]

Show Tags

New post 07 Feb 2018, 03:37
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: ExamPAL

Kudos 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.. !!

VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1151
If a and b are positive integers so that the remainder, when dividing  [#permalink]

Show Tags

New post Updated on: 11 Mar 2018, 17:21
1
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, 13:05.
Last edited by gracie on 11 Mar 2018, 17:21, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7198
If a and b are positive integers so that the remainder, when dividing  [#permalink]

Show Tags

New post 07 Feb 2018, 19:25
1
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: ExamPAL

Kudos 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.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If a and b are positive integers so that the remainder, when dividing  [#permalink]

Show Tags

New post 09 Feb 2018, 09:56
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 Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Manager
avatar
B
Joined: 03 Feb 2016
Posts: 68
Location: India
Concentration: Technology, Marketing
GMAT 1: 650 Q48 V32
GPA: 4
WE: Sales (Computer Software)
CAT Tests
Re: If a and b are positive integers so that the remainder, when dividing  [#permalink]

Show Tags

New post 12 Mar 2018, 07:50
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.
_________________

GMAT1 650 Q48 V32.

Manager
Manager
avatar
G
Joined: 10 Oct 2018
Posts: 114
Location: United States
Schools: Sloan (MIT)
GPA: 4
If a and b are positive integers so that the remainder, when dividing  [#permalink]

Show Tags

New post 11 Dec 2018, 05:44
I have a doubt (marked in red). I have seen such calculations in this forum but never really understand it. I know the doubt might be silly but someone pls explain it to me?

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: ExamPAL

Kudos 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 4

Hence, Option B(1/3) could be the value of the expression (a/b)


when x is 1, 3/4 after doing long division would give quotient=0.7 and remainder=2
similarly, when x=2, 6/8 would give quotient=0.7 and remainder=4 and likewise for the rest. quotient will be in decimals as the numerator<denominator.

after using the same method, (2) was solved and yes, the remainders are correct like 1/3 gives quotient=0.3 and remainder=1.
Where am I going wrong?
_________________

Kudos OK Please!!

GMAT Club Bot
If a and b are positive integers so that the remainder, when dividing &nbs [#permalink] 11 Dec 2018, 05:44
Display posts from previous: Sort by

If a and b are positive integers so that the remainder, when dividing

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.