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

 It is currently 17 Jan 2019, 01:17

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 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.

# How many positive integers less than 100 have a remainder of

Author Message
Manager
Joined: 11 Sep 2009
Posts: 129
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

21 Sep 2009, 20:42
1
00:00

Difficulty:

(N/A)

Question Stats:

50% (00:00) correct 50% (00:00) wrong based on 5 sessions

### HideShow timer Statistics

$$\frac{X-2}{13} = n$$ where n is a non-negative integer, and X is a positive integer less than 100. Basically determine how big the subset for possible values of n, and you have your answer.

Rearrange the above equation to:

13n + 2 = X

and since X < 100,

13n + 2 < 100
13n < 98
n < 98/13

Since n must be an integer....

n < 8

So there are 8 possible values for n (0 to 7), and therefore 8 positive integers less than 100 that have a remainder of 2 when divided by 13.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Senior Manager
Joined: 31 Aug 2009
Posts: 376
Location: Sydney, Australia
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

21 Sep 2009, 21:42
My working was like AKProdigy87's
Except that 0 is not considered positive (or negative) so the answer should be 7.
Manager
Joined: 28 Jul 2009
Posts: 114
Location: India
Schools: NUS, NTU, SMU, AGSM, Melbourne School of Business
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

21 Sep 2009, 23:41
[quote="pejmanjohn"]How many positive integers less than 100 have a remainder of 2 when divided by 13?

Easy one.
Number closest to 100 but less than 100 and divisible by 13 = 91.
91 = 13 * 7.
91+2 < 100.

Satisfies all the conditions.
Ans : 7. What is the OA?
_________________

GMAT offended me. Now, its my turn!
Will do anything for Kudos! Please feel free to give one.

Intern
Joined: 01 Sep 2009
Posts: 31
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

22 Sep 2009, 11:47
I say 8

13n + 2 < 100

There are 7 possibilities that fit this, but that was not counting 2 (2 / 13 = 0 remainder 2)

So you have 8 positive integers with remainder 2 when divided by 13.... 2, 15, 28, 41, 54, 67, 80, 93
Intern
Joined: 04 Sep 2009
Posts: 49
WE 1: Real estate investment consulting
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

22 Sep 2009, 12:36
7

0 divided by anything is a 0 - not counted
1st to count is 15

We get
15+13x<100
13x<85
x<6

Plus 15 => 7 integers
Senior Manager
Joined: 31 Aug 2009
Posts: 376
Location: Sydney, Australia
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

22 Sep 2009, 17:20
Actually 8 might be the right answer because the question stem is asking what are “the positive integers with a remainder”. This could be interpreted as referring to the dividend, in this case 2 is a valid dividend as 2/13 = 0r2. If this is the case the answer is 8. What is the OA?
Manager
Joined: 27 Oct 2008
Posts: 177
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

24 Sep 2009, 10:54
How many positive integers less than 100 have a remainder of 2 when divided by 13?

Simple question.
Let the number be A
A = 13 * q + 2
here q can take values 0,1,...

since A has to be a two digit number, thus the max value of q that satisfies this condition is
q = 7
A = 13 * 7 + 2 = 93

Thus the number of positive integers is from 0 through to 7 inclusive
total of 8 numbers
Manager
Joined: 11 Aug 2008
Posts: 125
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

21 Oct 2009, 20:26
1
0 is even number but is not a positive or negative number, so the sol should be 7
SVP
Joined: 29 Aug 2007
Posts: 2359
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

21 Oct 2009, 21:50
AKProdigy87 wrote:
$$\frac{X-2}{13} = n$$ where n is a non-negative integer, and X is a positive integer less than 100. Basically determine how big the subset for possible values of n, and you have your answer.

Rearrange the above equation to:

13n + 2 = X

and since X < 100,

13n + 2 < 100
13n < 98
n < 98/13

Since n must be an integer....

n < 8

So there are 8 possible values for n (0 to 7), and therefore 8 positive integers less than 100 that have a remainder of 2 when divided by 13.

Two things:

i. n is a non-negative integer
ii. X is a positive integer less than 100

If so, n has to be 8 including 0.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Senior Manager
Joined: 12 Apr 2010
Posts: 420
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

03 Jul 2011, 00:46
I dont understand how 2 can be included in the set.

2 div by 13

13) 2 ( -> 13) 20 (0. -> 13) 20 (0.1

Where do you get a reminder of 13?

Thanks.
_________________

Intern
Joined: 01 Mar 2006
Posts: 22
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

11 Oct 2011, 08:49
+1 for 8.

similar to the previous explanation.
x is positive & n is just a "non negative number" which means '0' is ok. So 0 through 7 = total 8.
Non-Human User
Joined: 09 Sep 2013
Posts: 9420
Re: How many positive integers less than 100 have a remainder of  [#permalink]

### Show Tags

20 Jan 2018, 04:24
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.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: How many positive integers less than 100 have a remainder of &nbs [#permalink] 20 Jan 2018, 04:24
Display posts from previous: Sort by