Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Jul 2015, 22:56
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If 4 is divided into the positive integer x, it leaves a rem

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 18 Aug 2009
Posts: 437
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
Followers: 6

Kudos [?]: 75 [0], given: 16

If 4 is divided into the positive integer x, it leaves a rem [#permalink] New post 23 Jun 2010, 13:40
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

70% (02:50) correct 30% (02:38) wrong based on 37 sessions
If 4 is divided into the positive integer x, it leaves a remainder of 3. If 9 is divided into x, it leaves a remainder of 4. If y is a positive integer such that x + y is divisible by 36, what is the smallest possible value of y?

(A) 4
(B) 5
(C) 7
(D) 33
(E) 36

I do not know how to solve it although I know OA for the test. Can somebody show how to do the problem algebraically?
Thank you
[Reveal] Spoiler: OA

_________________

Never give up,,,

1 KUDOS received
Current Student
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2799
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 198

Kudos [?]: 1183 [1] , given: 235

Reviews Badge
Re: KNEWTON TEST [#permalink] New post 23 Jun 2010, 13:54
1
This post received
KUDOS
x = 4a+3 and x = 9b+4 => 4a=9b+1 this will be possible when 4a=9b+1 = 28 as a and b are both integers.

if 4a=28 => a=7 => x = 4*7+3 = 31

for x+y to be divisible by 36, 31+y should be divisible by 36

for smallest value 31+y = 36 => y=5
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Manager
Manager
User avatar
Joined: 12 Jun 2007
Posts: 128
Followers: 5

Kudos [?]: 49 [0], given: 2

Re: KNEWTON TEST [#permalink] New post 16 Jul 2010, 04:18
really good question
thanks for the answer
Intern
Intern
avatar
Joined: 07 Dec 2011
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 6

Re: KNEWTON TEST [#permalink] New post 14 Dec 2011, 10:35
Hi sorry,

I must be missing something basic but how do you get from 4a = 9b +1 to equal 28? I understand how it works but I just don't get how you figure out to set the equation equal to the 28.

Thanks!!
Expert Post
2 KUDOS received
GMAT Tutor
avatar
Joined: 24 Jun 2008
Posts: 1174
Followers: 312

Kudos [?]: 980 [2] , given: 4

Re: KNEWTON TEST [#permalink] New post 14 Dec 2011, 16:52
2
This post received
KUDOS
Expert's post
mirzohidjon wrote:
If 4 is divided into the positive integer x, it leaves a remainder of 3. If 9 is divided into x, it leaves a remainder of 4. If y is a positive integer such that x + y is divisible by 36, what is the smallest possible value of y?

(A) 4
(B) 5
(C) 7
(D) 33
(E) 36


The wording of this question is awful. The GMAT would never talk about one number "dividing into" another. Further, when this question says "it leaves a remainder of 3", the word "it" refers back to "4", when it should actually refer back either to "x" or more correctly, to the division itself. This question would be better as a Sentence Correction question.

This is, mathematically, an exact copy of question 68 in the PS section of the official Quant Review book, but with different numbers and with unclear wording. The first sentence in the official version of this question is worded as follows, and this is the wording you'll typically see on the real GMAT whenever remainders are being discussed:

"When positive integer n is divided by 5, the remainder is 1".

So the question quoted above should be phrased as follows:

When the positive integer x is divided by 4, the remainder is 3. When x is divided by 9, the remainder is 4. What is the smallest positive integer y for which x+y is divisible by 36?

There is no need to use algebra here. If we can find any value for x at all that gives the right remainders, we can use it to answer the question. If we make a list of numbers which give a remainder of 3 when divided by 4:

3, 7, 11, 15, 19, 23, 27, 31, 35, ...

and a list of numbers which give a remainder of 4 when divided by 9:

4, 13, 22, 31, ...

then any potential value of x needs to be in both of the lists above. We can see that x could be equal to 31, in which case y would be 5, so the answer is 5.

In general, using pure algebra in remainders questions can be awkward. It's very often best just to find a number which 'works' and to use that number to answer the question.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Intern
Intern
avatar
Joined: 07 Dec 2011
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 6

Re: KNEWTON TEST [#permalink] New post 14 Dec 2011, 17:06
Thank you Ian for that explanation, very helpful!
Re: KNEWTON TEST   [#permalink] 14 Dec 2011, 17:06
    Similar topics Author Replies Last post
Similar
Topics:
12 Experts publish their posts in the topic The positive integers a and b leave remainders of 4 and 7 bytatia 16 08 Aug 2014, 14:40
19 Experts publish their posts in the topic When the positive integer x divided by the positive integer Bunuel 13 17 Jun 2014, 01:58
188 Experts publish their posts in the topic Positive integer n leaves a remainder of 4 after division by bchekuri 49 05 May 2010, 22:49
26 Experts publish their posts in the topic When the positive integer x is divided by 11, the quotient Hussain15 19 13 Apr 2010, 04:49
1 Experts publish their posts in the topic When the positive integer x is divided by 9, the remainder alimad 8 22 Nov 2007, 17:04
Display posts from previous: Sort by

If 4 is divided into the positive integer x, it leaves a rem

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.