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

It is currently 23 May 2019, 06:41

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

If x is an integer greater than 0, what is the remainder when x is div

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
If x is an integer greater than 0, what is the remainder when x is div  [#permalink]

Show Tags

New post 26 Apr 2019, 02:41
1
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:40) correct 39% (01:46) wrong based on 104 sessions

HideShow timer Statistics

GMAT Tutor
avatar
S
Joined: 24 Jun 2008
Posts: 1524
Re: If x is an integer greater than 0, what is the remainder when x is div  [#permalink]

Show Tags

New post 26 Apr 2019, 07:11
3
The question is asking "x is how much larger than a multiple of 4". If, from Statement 1, we know x+1 is 3 greater than a multiple of 4, then x itself must be 2 greater than a multiple of 4, so Statement 1 is sufficient.

Statement 2 tells us that 2x is divisible by 4, but that will be true any time x is even. So the remainder can be 0 or 2 when we divide x by 4, and Statement 2 is not sufficient.
_________________
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
CEO
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 3505
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: If x is an integer greater than 0, what is the remainder when x is div  [#permalink]

Show Tags

New post 27 Apr 2019, 07:28
Bunuel wrote:
If x is an integer greater than 0, what is the remainder when x is divided by 4 ?

(1) The remainder is 3 when x + 1 is divided by 4.
(2) The remainder is 0 when 2x is divided by 4.


DS49502.01
OG2020 NEW QUESTION


#1
x= 6, 14 we get remainder 2 sufficeint
#2
remainder is 0 so x= 0 or x = 2,4
insfficient
IMO A
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3724
Location: Canada
Re: If x is an integer greater than 0, what is the remainder when x is div  [#permalink]

Show Tags

New post 30 Apr 2019, 19:10
1
Top Contributor
1
Bunuel wrote:
If x is an integer greater than 0, what is the remainder when x is divided by 4 ?

(1) The remainder is 3 when x + 1 is divided by 4.
(2) The remainder is 0 when 2x is divided by 4.


DS49502.01
OG2020 NEW QUESTION


Target question: What is the remainder when x is divided by 4 ?

Statement 1: The remainder is 3 when x + 1 is divided by 4.
------ASIDE----------------------
There's a nice rule that says, "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
--------------------------------
We don't know how many times 4 divides into x+1. So, let's just say 4 divides into x+1 k times.
So, we can write: x + 1 = 4k + 3 (for some integer k)
Subtract 1 from both sides to get x = 4k + 2
Since 4k is a multiple of 4, we can see that x is 2 greater than some multiple of 4
So, when we divide x by 4, the remainder will be 2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The remainder is 0 when 2x is divided by 4.
We can write: 2x = 4k (for some integer k)
Divide both sides by 2 to get: x = 2k
This tells us that x is an even integer.
There are several values of x that satisfy statement 2. Here are two:
Case a: x = 2. In this case, the answer to the target question is when we divide x by 4, the remainder will be 2
Case b: : x = 4. In this case, the answer to the target question is when we divide x by 4, the remainder will be 2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

RELATED VIDEO FROM MY COURSE

_________________
Test confidently with gmatprepnow.com
Image
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6206
Location: United States (CA)
Re: If x is an integer greater than 0, what is the remainder when x is div  [#permalink]

Show Tags

New post 07 May 2019, 18:45
Bunuel wrote:
If x is an integer greater than 0, what is the remainder when x is divided by 4 ?

(1) The remainder is 3 when x + 1 is divided by 4.
(2) The remainder is 0 when 2x is divided by 4.


DS49502.01
OG2020 NEW QUESTION


We need to determine the remainder when x is divided by 4.

Statement One Alone:

The remainder is 3 when x + 1 is divided by 4.

x + 1 can be values such as 3, 7, 11, 15, and so forth. Thus, x is 2, 6, 10, 14, etc..

When any of those values of x is divided by 4, the remainder is 2.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

The remainder is 0 when 2x is divided by 4.

2x can be values such as 4, 8, 12 ,16, and so forth. Thus, x is 2, 4, 6, 8, etc.

We see that 2/4 = 0 remainder 2 and 4/4 = 1 remainder 0.

Statement two alone is not sufficient to answer the question.

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14194
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x is an integer greater than 0, what is the remainder when x is div  [#permalink]

Show Tags

New post 16 May 2019, 14:24
1
Hi All,

We're told that X is an INTEGER GREATER than 0. We're asked for the remainder when X is divided by 4. This question is based around some basic Arithmetic rules (and you can TEST VALUES to define the patterns involved). To start, here are the first several positive integers - and what happens when you divide by 4...

1/4 = 0r1
2/4 = 0r2
3/4 = 0r3
4/4 = 1r0
5/4 = 1r1
6/4 = 1r2
7/4 = 1r3
8/4 = 2r0
Etc.

(1) The remainder is 3 when (X + 1) is divided by 4.

Based on the pattern defined above, if we get a remainder of 3 when dividing (X+1) by 4, then removing the "+1" would move us one position 'up' in the pattern - meaning that the remainder when X/4 will ALWAYS equal 2. You can see this in a couple of examples:
IF...
X = 2, then (2+1)/4 = 0r3 and 2/4 = 0r2
X = 6, then (6+1)/4 = 1r3 and 6/4 = 0r2
Etc.
Fact 1 is SUFFICIENT

(2) The remainder is 0 when 2x is divided by 4.

Fact 2 asks us to focus on values that would create a remainder of 0. That will occur with any multiple of 4. However, Fact 2 asks us to consider "2X" and that does not necessarily mean that X is a multiple of 4...
IF...
X = 2, then (2)(2)/4 = 1r0 and 2/4 = 0r2
X = 4, then (2)(4)/4 = 2r0 and 4/4 = 1r0
Thus, the answer to the question could be 2 OR 0.
Fact 2 is INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
GMAT Club Bot
Re: If x is an integer greater than 0, what is the remainder when x is div   [#permalink] 16 May 2019, 14:24
Display posts from previous: Sort by

If x is an integer greater than 0, what is the remainder when x is div

  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®.