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

It is currently 19 Nov 2018, 01:59

INSEAD R1 Results This Week!

First Decision Reported on Decision Tracker  |  Join INSEAD Chat to Calm Your Nerves & Catch the Latest Action


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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

When 15x is divided by 2y, the quotient is x

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

Hide Tags

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

New post 27 Feb 2017, 08:27
3
Top Contributor
6
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

72% (01:55) correct 28% (02:10) wrong based on 275 sessions

HideShow timer Statistics

When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions

_________________

Test confidently with gmatprepnow.com
Image

Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

New post 27 Feb 2017, 08:52
1
2
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions


Hi

We have:

15x = 2y*x + x

14x = 2x*y

y = 7

Answer E
Intern
Intern
avatar
S
Joined: 11 Aug 2016
Posts: 47
Location: India
Concentration: Operations, General Management
Schools: HBS '18, ISB '17, IIMA
GMAT 1: 710 Q49 V38
GPA: 3.95
WE: Design (Manufacturing)
GMAT ToolKit User
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

New post 27 Feb 2017, 10:33
1
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions



When A is divided by B and the quotient is Q and the remainder is R, then
A=B*Q+R ... equation 1

For our case,
A=15x, B=2y , Q=x and R=x

Putting all the values in equation 1, we get
15x=2y*x+x
=>14x=2xy
=> y=7 which is less than 8

Answer E
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1116
When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

New post 27 Feb 2017, 11:23
1
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions


15x=2xy+x
y=7
testing possible values of x,
x=any positive integer≥1
thus, A,B,C and D are false,
and only y<8 is true
E
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

New post 27 Feb 2017, 14:15
1
Top Contributor
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8


There's a nice rule that say, "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

------NOW ONTO THE QUESTION------------------------------

When 15x is divided by 2y, the quotient is x, and the remainder is x.
Applying the above rule, we can write: 15x = (2x)(y) + x
Subtract x from both sides to get: 14x = 2xy
Divide both sides by 2x to get: y = 7

Answer: E
_________________

Test confidently with gmatprepnow.com
Image

Manager
Manager
User avatar
B
Joined: 22 May 2017
Posts: 88
GMAT 1: 580 Q41 V29
GMAT 2: 580 Q43 V27
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

New post 21 Jul 2017, 01:42
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions


Just for curiousity, if we change the question and replaces 15X with only 15 what will the Answer??
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50658
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

New post 21 Jul 2017, 02:10
1
Adityagmatclub wrote:
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions


Just for curiousity, if we change the question and replaces 15X with only 15 what will the Answer??


If it were: when 15 is divided by 2y, the quotient is x, and the remainder is x.

Then, \(15 = 2xy + x = x(2y + 1)\)

In this case, (x, y) can be (1, 7) or (3, 2) only. So, both A and E will be correct.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
B
Joined: 02 Mar 2017
Posts: 79
GMAT 1: 700 Q51 V34
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

New post 21 Jul 2017, 05:13
Bunuel wrote:
Adityagmatclub wrote:
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions


Just for curiousity, if we change the question and replaces 15X with only 15 what will the Answer??


If it were: when 15 is divided by 2y, the quotient is x, and the remainder is x.

Then, \(15 = 2xy + x = x(2y + 1)\)

In this case, (x, y) can be (1, 7) or (3, 2) only. So, both A and E will be correct.


(5,1) also. Right?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50658
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

New post 21 Jul 2017, 05:22
1
pulkitaggi wrote:
Bunuel wrote:
Adityagmatclub wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

Just for curiousity, if we change the question and replaces 15X with only 15 what will the Answer??


If it were: when 15 is divided by 2y, the quotient is x, and the remainder is x.

Then, \(15 = 2xy + x = x(2y + 1)\)

In this case, (x, y) can be (1, 7) or (3, 2) only. So, both A and E will be correct.


(5,1) also. Right?


No, x = 5 and y = 1 does not work. Though these numbers fit the formula they do not satisfy the conditions given in the stem: 15 divided by 2y = 2 gives the quotient 7 and the remainder of 1, not 5 and 5. The point is that the remainder (x= 5 in this case) cannot be more than the divisor (2y = 2 in this case)
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
G
Joined: 18 Jan 2017
Posts: 129
Premium Member CAT Tests
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

New post 21 Jul 2017, 06:25
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions



We know that --> Dividend = Quotient * Divisor + Remainder

we have, 15x = (2x) * y + x
14x = 2x * y
y = 14x/2x
y = 7

y < 8
Therefore, E
_________________

A KUDO = A Thank-you. If this post helped you, please send a KUDO across.

YOU CAN LEARN ANYTHING!
MY GMAT BLOG ---> https://gmatclub.com/forum/a-fitness-mat-some-music-few-books-and-the-gmat-245808.html

Intern
Intern
avatar
B
Joined: 17 Jun 2017
Posts: 28
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

New post 25 Aug 2018, 23:51
1
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions


We can use this formula to get this one , otherwise taking numbers will take too long ,as I tried taking numbers for this one .
Dividend = Divisor * Quotient + Remainder
Then , it comes
15x = 27*x + x
7 = Y
From options E Y < 8 (Y less than 8)
GMAT Club Bot
Re: When 15x is divided by 2y, the quotient is x &nbs [#permalink] 25 Aug 2018, 23:51
Display posts from previous: Sort by

When 15x is divided by 2y, the quotient is x

  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®.