It is currently 20 Oct 2017, 07:36

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 18 Aug 2009
Posts: 417

Kudos [?]: 144 [0], given: 16

Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
If 4 is divided into the positive integer x, it leaves a rem [#permalink]

### Show Tags

23 Jun 2010, 14:40
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:00) correct 34% (02:49) wrong based on 64 sessions

### HideShow timer Statistics

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,,,

Kudos [?]: 144 [0], given: 16

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2761

Kudos [?]: 1885 [1], given: 235

Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35

### Show Tags

23 Jun 2010, 14:54
1
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

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Kudos [?]: 1885 [1], given: 235

Manager
Joined: 12 Jun 2007
Posts: 124

Kudos [?]: 78 [0], given: 2

### Show Tags

16 Jul 2010, 05:18
really good question

Kudos [?]: 78 [0], given: 2

Intern
Joined: 07 Dec 2011
Posts: 5

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

### Show Tags

14 Dec 2011, 11:35
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!!

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

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1339

Kudos [?]: 1954 [3], given: 6

### Show Tags

14 Dec 2011, 17:52
3
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

Kudos [?]: 1954 [3], given: 6

Intern
Joined: 07 Dec 2011
Posts: 5

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

### Show Tags

14 Dec 2011, 18:06
Thank you Ian for that explanation, very helpful!

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

Re: KNEWTON TEST   [#permalink] 14 Dec 2011, 18:06
Display posts from previous: Sort by