It is currently 22 Oct 2017, 19:58

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

When positive integer n is divided by 3, the remainder is 2. When n is

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

Hide Tags

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41912

Kudos [?]: 129370 [2], given: 12197

When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 02 Apr 2015, 06:06
2
This post received
KUDOS
Expert's post
19
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

50% (01:39) correct 50% (01:38) wrong based on 411 sessions

HideShow timer Statistics

When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129370 [2], given: 12197

Expert Post
10 KUDOS received
Math Forum Moderator
avatar
P
Joined: 02 Aug 2009
Posts: 4993

Kudos [?]: 5524 [10], given: 112

When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 02 Apr 2015, 07:03
10
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
Bunuel wrote:
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.


a quick approac to this Q is..

the equation we can form is..
\(3x+2=7y+5\)..
\(3x-3=7y... 3(x-1)=7y\)...

so (x-1) has to be a multiple of 7 and y then will take values of multiple of 3..
here we can see x can be 1,8,15,22,29 so 5 values till 100 is reached
as (29-1)*3=84 and next multiple of 7 will be 84+21>100
..
ans 5.. E
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5524 [10], given: 112

1 KUDOS received
Senior Manager
Senior Manager
avatar
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 361

Kudos [?]: 207 [1], given: 133

GMAT ToolKit User Reviews Badge CAT Tests
When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 02 Apr 2015, 07:42
1
This post received
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.


n=3Q1+2
n=7Q2+5

3Q1+2=7Q2+5
3Q1=7Q2+3
Q1=7Q2/3+1

Approach 1: So Q2 has to be a multiple of 3. Q2 can be 0,3,6,9,12,15....
But when we replace Q2 in 7Q2+5, only 0,3,6,9 and 12 are less than 100

Therefore, n can be 5,26,47,68 or 89--->5

Approach 2: 1st possible value is 1 and then add 1 to multiples of 7. Therefore, possible values of Q1=1,8,15,22,29,36...

But only when Q1=1,8,15,22 and 29 will n<100

n, therefore, can be 5,26,47,68 and 89--->5

Answer : E

Kudos [?]: 207 [1], given: 133

Manager
Manager
avatar
Joined: 26 Dec 2012
Posts: 147

Kudos [?]: 16 [0], given: 4

Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 02 Apr 2015, 15:52
Find out n/7=R=5= 5,12,19,26,33,40,47,54,61,68,75,82,89,96
out of all these 5,26,47,68 & 89 gives R=2 when n/3; therefore there are 5 digits in total

Hence Answer is E

Thanks,

Kudos [?]: 16 [0], given: 4

7 KUDOS received
Current Student
User avatar
Joined: 06 Mar 2014
Posts: 270

Kudos [?]: 113 [7], given: 84

Location: India
GMAT Date: 04-30-2015
Reviews Badge
Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 02 Apr 2015, 17:38
7
This post received
KUDOS
Bunuel wrote:
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.


\(N = 3q+2\) (possible values: 2,5,8,11,14....
\(N = 7z+5\) (possible values: 5,12,19,26....

Therefore,N = (3*7)k+5
\(N = 21k+5\) (possible values:5,26,47,68,89)

Clearly only five values is possible that are less than 100.

Answer:E

Kudos [?]: 113 [7], given: 84

1 KUDOS received
BSchool Forum Moderator
avatar
Joined: 27 Aug 2012
Posts: 1188

Kudos [?]: 1928 [1], given: 152

Premium Member
Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 02 Apr 2015, 22:47
1
This post received
KUDOS

Kudos [?]: 1928 [1], given: 152

2 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2632 [2], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 02 Apr 2015, 23:51
2
This post received
KUDOS
Answer = E = 5

Possible values of n which gives remainder 5 when divided by 7:

12, 19, 26, 33, 38, 46, 53, 60, 67, 74, 81, 88, 95

In red are the 5 values which gives remainder 2 when divided by 3
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2632 [2], given: 193

2 KUDOS received
Manager
Manager
avatar
B
Joined: 26 May 2013
Posts: 98

Kudos [?]: 30 [2], given: 30

Premium Member
Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 03 Apr 2015, 07:50
2
This post received
KUDOS
PareshGmat wrote:
Answer = E = 5

Possible values of n which gives remainder 5 when divided by 7:

12, 19, 26, 33, 38, 46, 53, 60, 67, 74, 81, 88, 95

In red are the 5 values which gives remainder 2 when divided by 3


38 divided by 7 doesn't give a remainer of 5.

Although I prefer to tackle questions like these conceptually or by using SMART numbers, the algebraic approach outlined above looks like the best way to solve the problem.

As per the question stem:

3x + 2 = 7y + 5

3x - 3 = 7y

3(x-1) = 7y

Therefore (x-1) is a multiple of 7.

Possible values of x for x-1 being a multiple of 7 include; 1, 8, 15, 22, 29, 36, ...etc

The answer choices that fit the less than 100 parameter are: 1,8,15,22,29.

Choice E. 5.

Kudos [?]: 30 [2], given: 30

1 KUDOS received
Director
Director
User avatar
S
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 512

Kudos [?]: 576 [1], given: 6

Location: India
GMAT 1: 780 Q51 V46
Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 03 Apr 2015, 22:55
1
This post received
KUDOS
3
This post was
BOOKMARKED
Hi Guys,

The first integer when divided by 3 leaves the remainder 2 is 5.
Also when 5 is divided by 7 the remainder is 5 itself.
To find out the next number which satisfies both the condition, take LCM of 3 and 7 which is 21.
So the next number which will satisfy both the conditions is 26(5+21).
The next number is 47(26+21) , 68(47+21) and 89(68+1).
So the number less than 100 which satisfy the conditions 5,26,47,68 and 89.
Answer is 5. Choice is E.
_________________

Enroll for our GMAT Trial Course here -
http://gmatonline.crackverbal.com/

Learn all PS and DS strategies here-
http://gmatonline.crackverbal.com/p/mastering-quant-on-gmat

For more info on GMAT and MBA, follow us on @AskCrackVerbal

Kudos [?]: 576 [1], given: 6

Director
Director
avatar
G
Joined: 21 May 2013
Posts: 535

Kudos [?]: 71 [0], given: 487

Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 04 Apr 2015, 02:31
Bunuel wrote:
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.



Answer=E
The 5 values are 5,26,47,68,89

Kudos [?]: 71 [0], given: 487

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41912

Kudos [?]: 129370 [2], given: 12197

Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 06 Apr 2015, 06:31
2
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
Bunuel wrote:
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

So n is a number 2 greater than a multiple of 3 (or we can say, it is 1 less than the next multiple of 3). It is also 5 greater than a multiple of 7 (or we can say it is 2 less than the next multiple of 7)

n = 3a + 2 = 3x – 1
n = 7b + 5 = 7y – 2

No common remainder! When we have a common remainder,the smallest value of n would be the common remainder. Say, if n were of the forms: (3a + 1) and (7b + 1), the smallest number of both these forms is 1. When 1 is divided by 3, the quotient is 0 and the remainder is 1. When 1 is divided by 7, the quotient is 0 and the remainder is 1. But that is not the case here. So then, what do we do now? Let’s try and work with some trial and error now. n belongs to both the lists given below:

Numbers of the form (3a+2): 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50…
Numbers of the form (7b + 5): 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, 75…

Which numbers are common to both the lists? 5, 26, 47 and there should be more. Do you see some link between these numbers? Let me show you some connections:
– 26 is 21 more than 5.
– 47 is 21 more than 26.
– 21 is the LCM of 3 and 7.

How do we explain these? Say, we identified that the smallest positive number which gives a remainder of 2 when divided by 3 and a remainder of 5 when divided by 7 is 5 (note here that when we divide 5 by 7, the quotient is 0 and the remainder is 5). What will be the next such number? Since the next number will also belong to both the lists above so it will be 3/6/9/12/15/18/21… away from 5 and it will also be 7/14/21/28/35/42… away from 5 i.e. it will be a multiple of 3 and a multiple of 7 away from 5. The smallest such multiple is obviously the LCM (lowest common multiple) of 3 and 7 i.e. 21. Hence the next such number will be 21 away from 5. We get 26. Use the same logic to get the next such number. It will be another 21 away from 26 so we get 47. By the same logic, the next few such numbers will be 68, 89, 110 etc. How many such numbers will be less than 100? 5, 26, 47, 68, 89 i.e. 5 such numbers.

Answer: E.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129370 [2], given: 12197

Intern
Intern
avatar
Joined: 30 Jul 2008
Posts: 19

Kudos [?]: 3 [0], given: 23

Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 05 Jul 2015, 18:35
earnit wrote:
Bunuel wrote:
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.


\(N = 3q+2\) (possible values: 2,5,8,11,14....
\(N = 7z+5\) (possible values: 5,12,19,26....

Therefore,N = (3*7)k+5
\(N = 21k+5\) (possible values:5,26,47,68,89)

Clearly only five values is possible that are less than 100.

Answer:E


Can anyone pls. explain how N became 21k+5?

Kudos [?]: 3 [0], given: 23

Expert Post
1 KUDOS received
Math Forum Moderator
avatar
B
Joined: 20 Mar 2014
Posts: 2675

Kudos [?]: 1728 [1], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 05 Jul 2015, 18:54
1
This post received
KUDOS
Expert's post
robinpallickal wrote:
earnit wrote:
Bunuel wrote:
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.


\(N = 3q+2\) (possible values: 2,5,8,11,14....
\(N = 7z+5\) (possible values: 5,12,19,26....

Therefore,N = (3*7)k+5
\(N = 21k+5\) (possible values:5,26,47,68,89)

Clearly only five values is possible that are less than 100.

Answer:E


Can anyone pls. explain how N became 21k+5?


Think of it this way. You have been given that a number leaves a reminder of 2 when divided by 3 and the same number when divided by 7, leaves a remainder of 5. Now as 3 and 7 are prime numbers, there is only one way of denoting such a number so that we take the above mentioned divisibilities by both 3 and 7 into account. LCM of 3,7 = 21 and thus Bunuel mentions that the number can be written as 21r+5.

You can also solve this by looking at a few values that this number can take: 5,26,47, 68, 89 etc. These numbers satisfy the 2 conditions of divisibilities with 3 and 7 mentioned above. This way, you don't have to worry about how all of it led to 21r+5.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1728 [1], given: 792

Intern
Intern
avatar
Joined: 30 Jul 2008
Posts: 19

Kudos [?]: 3 [0], given: 23

When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 07 Jul 2015, 07:40
[/quote]

Think of it this way. You have been given that a number leaves a reminder of 2 when divided by 3 and the same number when divided by 7, leaves a remainder of 5. Now as 3 and 7 are prime numbers, there is only one way of denoting such a number so that we take the above mentioned divisibilities by both 3 and 7 into account. LCM of 3,7 = 21 and thus Bunuel mentions that the number can be written as 21r+5.

You can also solve this by looking at a few values that this number can take: 5,26,47, 68, 89 etc. These numbers satisfy the 2 conditions of divisibilities with 3 and 7 mentioned above. This way, you don't have to worry about how all of it led to 21r+5.[/quote]

Thanks a lot...

Kudos [?]: 3 [0], given: 23

Expert Post
Math Forum Moderator
avatar
P
Joined: 02 Aug 2009
Posts: 4993

Kudos [?]: 5524 [0], given: 112

Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 07 Jul 2015, 07:55
robinpallickal wrote:
earnit wrote:
Bunuel wrote:
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.


\(N = 3q+2\) (possible values: 2,5,8,11,14....
\(N = 7z+5\) (possible values: 5,12,19,26....

Therefore,N = (3*7)k+5
\(N = 21k+5\) (possible values:5,26,47,68,89)

Clearly only five values is possible that are less than 100.

Answer:E


Can anyone pls. explain how N became 21k+5?


Hi robinpallickal,
to your Q that how N=21k+5..
first we find the first number that is ccommon to two eqs..
in case of 3.. it is 2,5,8 and so on
in case of 7.. it is 5,12,19..
so if 5 is the first number next number will be 5+ LCM of 3 & 7=5+21.. next 5+21*2.. next 5+21*3.. and so on...
therefore you get the eq 21k + 5
hope it is clear
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5524 [0], given: 112

Expert Post
1 KUDOS received
SVP
SVP
User avatar
G
Joined: 08 Jul 2010
Posts: 1836

Kudos [?]: 2285 [1], given: 51

Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 07 Jul 2015, 09:07
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.


When positive integer n is divided by 3, the remainder is 2 i.e. n = 3x + 2

When positive integer n is divided by 7, the remainder is 5 i.e. n = 7y + 5

For some Values of x and y the values of 3x + 2 must be equal to 7y + 5 as both are the values of n

So to find the common Solution

n = 3x + 2 = 7y + 5

PROPERTY: In such liners equations
1) The Value of x always changes by he value of coefficient of y i.e. 7 in this case and
2) The Value of y always changes by he value of coefficient of x i.e. 3 in this case and
3) the value of n always changes by the LCM of coefficients of x and y i.e. 21 in this case


Let's find the first solution of 3x + 2 = 7y + 5
i.e. x = (7y + 3) / 3
i.e. For some Integer value of y, x must be an Integer too

First Value of y = 3 and First value of x = 8 and n = 26
Second Value of y = 6 and First value of x = 15 and n = 47
Third Value of y = 9 and First value of x = 22 and n = 68
Forth Value of y = 12 and First value of x = 29 and n = 89

Answer: Option D
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Kudos [?]: 2285 [1], given: 51

BSchool Forum Moderator
User avatar
P
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 845 [0], given: 595

GMAT ToolKit User Premium Member CAT Tests
When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 31 Mar 2016, 21:19
Here is what i would do in such a question
the first number that satisfies such a case is 5
hence the expression for such an integer becomes => 5+21P
hence between 0 and 100 => 5 values => E
_________________

Give me a hell yeah ...!!!!!


Last edited by stonecold on 18 Oct 2016, 12:26, edited 1 time in total.

Kudos [?]: 845 [0], given: 595

Manager
Manager
avatar
Joined: 01 Mar 2014
Posts: 138

Kudos [?]: 10 [0], given: 616

Schools: Tepper '18
Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 02 Apr 2016, 07:29
earnit wrote:
Bunuel wrote:
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.


\(N = 3q+2\) (possible values: 2,5,8,11,14....
\(N = 7z+5\) (possible values: 5,12,19,26....

Therefore,N = (3*7)k+5
\(N = 21k+5\) (possible values:5,26,47,68,89)

Clearly only five values is possible that are less than 100.

Answer:E


Love this approach, so quick and easy. I did the same thing but got the answer wrong because of a careless calculation error. I hate it when i do that.!! :(

Kudos [?]: 10 [0], given: 616

Math Forum Moderator
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3003

Kudos [?]: 1088 [0], given: 325

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 03 Apr 2016, 03:44
Bunuel wrote:
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?

(A) 0
(B) 2
(C) 3
(D) 4
(E) 5


Kudos for a correct solution.


n/3 remainder 2 = (5, 8 , 11, 14, 17, 20, 23, 26....)
n/7 remainder 5 = ( 5, 12, 19, 26.....)


Possible numbers which are divisible by 3 ( having remainder 2 ) > numbers which are divisible by 7 ( having remainder 5) further the first possible value of n is 5 then 26- with a gap of 21 numbers

Now The best thing to do find all the numbers less than 100, that leaves remainder 2 when divided by 3 and remainder 5 when divided by 7 -

5 , (5 + 21) 26 , 47 (26+ 21) , 68 ( + 21) , 89 ( 68+21)

So, there are only 5 numbers and the only answer is (E)
_________________

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 )

Kudos [?]: 1088 [0], given: 325

BSchool Forum Moderator
avatar
B
Joined: 23 Sep 2015
Posts: 405

Kudos [?]: 89 [0], given: 72

Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)
Premium Member Reviews Badge
Re: When positive integer n is divided by 3, the remainder is 2. When n is [#permalink]

Show Tags

New post 23 Apr 2016, 01:58
\(3a+2=7b+5\)

\(3a=7b+3\)

Now we have to find integer values for b that will yield integer values for a, such that \(3a + 2 < 100\)

\(b=0, a =1\)
\(b=3, a =8\)
\(b=6, a =15\)
\(b=9, a =22\)
\(b=12, a = 29\)

We stop, since the next b 15 would make n larger than 100
_________________

New Application Tracker : update your school profiles instantly!

Kudos [?]: 89 [0], given: 72

Re: When positive integer n is divided by 3, the remainder is 2. When n is   [#permalink] 23 Apr 2016, 01:58

Go to page    1   2    Next  [ 25 posts ] 

Display posts from previous: Sort by

When positive integer n is divided by 3, the remainder is 2. When n is

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.