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

It is currently 16 Nov 2018, 22:58

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
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 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.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

x and y are positive integers. When 16x is divided by y,

  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
x and y are positive integers. When 16x is divided by y,  [#permalink]

Show Tags

New post Updated on: 27 Feb 2017, 09:21
6
Top Contributor
8
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

66% (03:00) correct 34% (02:09) wrong based on 217 sessions

HideShow timer Statistics

x and y are positive integers. When 16x is divided by y, the quotient is x, and the remainder is 4. What is the sum of all possible y-values?

A) 7
B) 12
C) 19
D) 26
E) 41

*Kudos for all correct solutions

EDIT: Changed answer choice E

_________________

Test confidently with gmatprepnow.com
Image


Originally posted by GMATPrepNow on 27 Feb 2017, 08:34.
Last edited by GMATPrepNow on 27 Feb 2017, 09:21, edited 1 time in total.
VP
VP
User avatar
P
Joined: 05 Mar 2015
Posts: 1000
Re: x and y are positive integers. When 16x is divided by y,  [#permalink]

Show Tags

New post 27 Feb 2017, 09:17
1
GMATPrepNow wrote:
x and y are positive integers. When 16x is divided by y, the quotient is x, and the remainder is 4. What is the sum of all possible y-values?

A) 7
B) 12
C) 19
D) 26
E) 39

*Kudos for all correct solutions



16x = yx+4
y=(16x-4)/x

if x=1 then y =12
if x= 2 then y= 14
if x=3 y is no longer integer
if x=4 then y = 15

upto here y = 12+14+15 = 41...
but i m not finding any such option.....

can any one explain!!!!!

thanks
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
Re: x and y are positive integers. When 16x is divided by y,  [#permalink]

Show Tags

New post 27 Feb 2017, 09:23
Top Contributor
Yeesh, I added those values several times and got 39 each time.
I've changed answer choice E to the correct value.

Cheers and thanks,
Brent
_________________

Test confidently with gmatprepnow.com
Image

Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: x and y are positive integers. When 16x is divided by y,  [#permalink]

Show Tags

New post 27 Feb 2017, 09:27
1
1
GMATPrepNow wrote:
x and y are positive integers. When 16x is divided by y, the quotient is x, and the remainder is 4. What is the sum of all possible y-values?

A) 7
B) 12
C) 19
D) 26
E) 39

*Kudos for all correct solutions


Hi

It seems I've missed something.

16x = yx + 4

16x - yx = 4

x(16 - y) = 4 (1*4), (2*2) and (4*1). I'm discarding negativ values because our x an y are >0.

x=1, 16 - y = 4 ---> y=12, check: 16*1 = 12*1 + 4

x = 2, 16 - y = 2 -----> y = 14, check: 32 = 14*2 + 4

x = 4, 16 - y = 1 -------> y=15, chek: 64 = 15*4 + 4

4<y<16

12+14+15 = 41

I'm not getting 39. Please correct me.
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
Re: x and y are positive integers. When 16x is divided by y,  [#permalink]

Show Tags

New post 27 Feb 2017, 09:37
Top Contributor
You're correct, vitaliyGMAT

It seems I have not yet mastered addition. :oops:

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: x and y are positive integers. When 16x is divided by y,  [#permalink]

Show Tags

New post 27 Feb 2017, 09:56
GMATPrepNow wrote:
You're correct, vitaliyGMAT

It seems I have not yet mastered addition. :oops:

Cheers,
Brent


Thanks

Your questions are really good! Please keep posting, just don't hurry next time :-D
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
Re: x and y are positive integers. When 16x is divided by y,  [#permalink]

Show Tags

New post 27 Feb 2017, 14:21
1
Top Contributor
3
GMATPrepNow wrote:
x and y are positive integers. When 16x is divided by y, the quotient is x, and the remainder is 4. What is the sum of all possible y-values?

A) 7
B) 12
C) 19
D) 26
E) 41


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 16x is divided by y, the quotient is x, and the remainder is 4.
Applying the above rule, we can write: 16x = (y)(x) + 4
Subtract xy from both sides: 16x - xy = 4
Factor: x(16 - y) = 4

Since x and (16 - y) are both positive integers, there are 3 possible solutions:
#1: x = 1 and (16 - y) = 4, in which case y = 12
#2: x = 2 and (16 - y) = 2, in which case y = 14
#3: x = 4 and (16 - y) = 1, in which case y = 15

What is the sum of all possible y-values?
SUM = 12 + 14 + 15
= 41

Answer: E

RELATED VIDEO FROM OUR COURSE

_________________

Test confidently with gmatprepnow.com
Image

Intern
Intern
avatar
S
Joined: 11 Mar 2015
Posts: 44
Schools: Haas '20
GPA: 2.99
WE: Corporate Finance (Aerospace and Defense)
GMAT ToolKit User
Re: x and y are positive integers. When 16x is divided by y,  [#permalink]

Show Tags

New post 27 Feb 2017, 15:19
2
Great question! I solved it a very similar way to you all.
(16x)/y = x + 4
--> 16x = xy + 4 --> y = (16x - 4)/x ---> y = 16 - 4/x.

We know from the prompt that Y is an integer, therefore, the only values of X that will make Y and integer is 0, 1, 2, 4. However, the prompt says that X & Y are positive integers. Therefore we can't use 0. So plugging in the values of 1, 2, and 4 into the equation, you're left with 15 + 14 + 12 = 41.
Intern
Intern
avatar
B
Joined: 09 Oct 2017
Posts: 13
Location: India
Re: x and y are positive integers. When 16x is divided by y,  [#permalink]

Show Tags

New post 06 Oct 2018, 08:15
X and y are positiv integers
GMAT Club Bot
Re: x and y are positive integers. When 16x is divided by y, &nbs [#permalink] 06 Oct 2018, 08:15
Display posts from previous: Sort by

x and y are positive integers. When 16x is divided by y,

  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®.