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

 It is currently 26 Aug 2019, 02:19 ### 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. ### Request Expert Reply # When positive integer W is divided by 4233

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

### Hide Tags

CEO  V
Joined: 12 Sep 2015
Posts: 3922
Location: Canada
When positive integer W is divided by 4233  [#permalink]

### Show Tags

1
Top Contributor
5 00:00

Difficulty:   25% (medium)

Question Stats: 76% (01:53) correct 24% (01:58) wrong based on 87 sessions

### HideShow timer Statistics

When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83?

A) 11
B) 12
C) 39
D) 44
E) 61

*kudos for all correct solutions

_________________
Senior SC Moderator V
Joined: 14 Nov 2016
Posts: 1323
Location: Malaysia
Re: When positive integer W is divided by 4233  [#permalink]

### Show Tags

1
When W is divided by 4233, the remainder is 61.
The possible value of W = 61, 61+4233, 61+4233 (2), .....
2W = 122, 8588, ...

Example : 2W=122 is divided by 83, the remainder is 39.

Answer : 39
_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/
Director  P
Joined: 14 Nov 2014
Posts: 611
Location: India
GMAT 1: 700 Q50 V34 GPA: 3.76
Re: When positive integer W is divided by 4233  [#permalink]

### Show Tags

1
GMATPrepNow wrote:
When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83?

A) 11
B) 12
C) 39
D) 44
E) 61

*kudos for all correct solutions

W=4233K + 61
2W=2*4233k + 61* 2

By applying remainder theorem
4233 is completely divided by 83 , so remainder will be 0 + 39 (122/83=39)
39. answer
CEO  V
Joined: 12 Sep 2015
Posts: 3922
Location: Canada
Re: When positive integer W is divided by 4233  [#permalink]

### Show Tags

2
Top Contributor
2
GMATPrepNow wrote:
When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83?

A) 11
B) 12
C) 39
D) 44
E) 61

IMPORTANT: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, for this question, we're told that, when positive integer W is divided by 4233, the remainder is 61.
This means the possible values of W are: 61, 61 + 4233, 61 + (2)(4233), 61 + (3)(4233), 61 + (4)(4233), . . . etc.

So, rather than test much bigger values of W, let's see what happens when W = 61
If W = 61, then 2W = 2(61) = 122

What is the remainder when 2W is divided by 83?
83 divides into 122 one time with remainder 39

Answer: C
_________________
CEO  V
Joined: 12 Sep 2015
Posts: 3922
Location: Canada
Re: When positive integer W is divided by 4233  [#permalink]

### Show Tags

Top Contributor
GMATPrepNow wrote:
When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83?

A) 11
B) 12
C) 39
D) 44
E) 61

*kudos for all correct solutions

Another (much longer) solution involves another important rule regarding remainders:

"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

Aside: We'll also use the fact that 8466 = (83)(102)

When positive integer W is divided by 4233, the remainder is 61
So, we can say W = 4233Q + 61 for some integer Q.

This means that...
2W = 2(4233Q + 61)
= 8466Q + 122
= (83)(102)Q + 122
= (83)(102)Q + 83 + 39
= 83(102Q + 1) + 39

In other words, 2W is 39 greater than some multiple of 83.
So, when we divide 2W by 83, the remainder will be 39

Answer: C
_________________
Current Student S
Joined: 23 Jul 2015
Posts: 146
When positive integer W is divided by 4233  [#permalink]

### Show Tags

1
1. Check if 4233 is a multiple of 83 -- Yes it is ==> when w is divided by 83 remainder is also 61
2. for 2w, remainder will be 61*2 = 122, which is > than 83 ==> remainder will be 122-83 = 39

Ans.: C
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4573
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: When positive integer W is divided by 4233  [#permalink]

### Show Tags

1
GMATPrepNow wrote:
When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83?

A) 11
B) 12
C) 39
D) 44
E) 61

*kudos for all correct solutions

Least value of W = 4294

So, 2W = 8588

2W/83 = Remainder 39

Hence, remainder when 2W is divided by 83 will be (C) 39
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager  S
Joined: 25 Mar 2013
Posts: 233
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: When positive integer W is divided by 4233  [#permalink]

### Show Tags

1
$$\frac{4294}{4233}$$ reminds 61

twice ( 4294 )

$$\frac{8588}{83}$$reminds 39

C
_________________
I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7482
Location: United States (CA)
Re: When positive integer W is divided by 4233  [#permalink]

### Show Tags

1
GMATPrepNow wrote:
When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83?

A) 11
B) 12
C) 39
D) 44
E) 61

Since W divided by 4,233 yields a remainder of 61, W could equal 4,233 + 61 = 4,294.

Thus, 2W = 2 x 4,294 = 8,588.

We can now divide 8,588 by 83 and we have:

8,588/83 = 103 remainder 39

Alternate Solution: W divided by 4233 produces a remainder of 61 means that W = 4233q + 61 for some integer q. Multiplying each side of the equation by 2, we obtain 2W = 8466q + 122. Note that 83 divides evenly into 8466 (because 8466 = 83 x 102) and that 122 = 83 + 39. Then, 2W = 83(102)q + 83 + 39 = 83(102q + 1) + 39. Since 83 divides evenly into 83(102q+1), the remainder is 39.

Answer: C
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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.

Non-Human User Joined: 09 Sep 2013
Posts: 12095
Re: When positive integer W is divided by 4233  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: When positive integer W is divided by 4233   [#permalink] 05 Aug 2019, 03:44
Display posts from previous: Sort by

# When positive integer W is divided by 4233

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  