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

It is currently 20 Aug 2018, 19:16

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

How many two-digit numbers yield a remainder of 1 when divided by both

  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: 48067
How many two-digit numbers yield a remainder of 1 when divided by both  [#permalink]

Show Tags

New post 24 Jul 2015, 00:53
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (01:08) correct 39% (01:14) wrong based on 188 sessions

HideShow timer Statistics

Manager
Manager
User avatar
Joined: 26 Dec 2011
Posts: 116
Schools: HBS '18, IIMA
Re: How many two-digit numbers yield a remainder of 1 when divided by both  [#permalink]

Show Tags

New post 24 Jul 2015, 02:21
2
Bunuel wrote:
How many two-digit numbers yield a remainder of 1 when divided by both 4 and 14?

A. 0
B. 1
C. 2
D. 3
E. 4


Kudos for a correct solution.


Solution -

In order to divide both 4 and 14 by a number, the number must be divisible by their least common multiple, which is 28.

Two-digit multiple of 28 are 28, 56, and 84.

The numbers that have remainder 1 when divided by 4 and 14 are 29, 57, or 85. ANS D.
_________________

Thanks,
Kudos Please

Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2643
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: How many two-digit numbers yield a remainder of 1 when divided by both  [#permalink]

Show Tags

New post 24 Jul 2015, 03:54
Bunuel wrote:
How many two-digit numbers yield a remainder of 1 when divided by both 4 and 14?

A. 0
B. 1
C. 2
D. 3
E. 4


Kudos for a correct solution.


Easier to start with numbers that are of the form 14p+1 ---> 15,29,43,57,71,85,99.

Out of these 3 (29,57,85) are also of the form 4q+1. Thus 3 is the answer. D is the correct answer.
Senior Manager
Senior Manager
User avatar
B
Joined: 28 Jun 2015
Posts: 295
Concentration: Finance
GPA: 3.5
Re: How many two-digit numbers yield a remainder of 1 when divided by both  [#permalink]

Show Tags

New post 24 Jul 2015, 05:16
2 digit numbers that are multiples of 14 are 14,28,42,56,70,84,98. So, there are 7 numbers, viz., 15, 29, 43, 57, 71, 85, 99 that would give a remainder of 1 when divided by 14.

Multiples of 14 that are also multiples of 4 are 28, 56, 84. So, there are 3 such numbers, viz., 29, 57, and 85.

Ans (D).
_________________

I used to think the brain was the most important organ. Then I thought, look what’s telling me that.

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6559
Re: How many two-digit numbers yield a remainder of 1 when divided by both  [#permalink]

Show Tags

New post 24 Jul 2015, 06:48
Bunuel wrote:
How many two-digit numbers yield a remainder of 1 when divided by both 4 and 14?

A. 0
B. 1
C. 2
D. 3
E. 4


Kudos for a correct solution.


the correct method would be to find LCM and then add 1 to LCM, 2*LCM, and so on
LCM of 4 &14=28..
first required number=29, next 2*28+1 and third 3*28+1...
thereafter it will be a 3 digit number
so ans 3 D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
User avatar
Joined: 08 Jul 2012
Posts: 49
Re: How many two-digit numbers yield a remainder of 1 when divided by both  [#permalink]

Show Tags

New post 24 Jul 2015, 08:01
1
Bunuel wrote:
How many two-digit numbers yield a remainder of 1 when divided by both 4 and 14?

A. 0
B. 1
C. 2
D. 3
E. 4


Kudos for a correct solution.


LCM of 4 & 14 is 28, hence 1st 2-digit no. which yields rem. of 1 when divided by both 4 & 14 is 28+1 = 29
2nd no. would be 28*2 +1 = 57

this is of the form 28k+1, where k is an integer and k>0

hence,
for k = 1, 28k+1 = 29
k = 2, = 57
k = 3, = 85
k = 4, = 113......we will stop here as this is now 3 digits,

hence total 2-digit nos. are 3

And. D
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time. - Thomas A. Edison

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48067
Re: How many two-digit numbers yield a remainder of 1 when divided by both  [#permalink]

Show Tags

New post 26 Jul 2015, 12:18
1
Bunuel wrote:
How many two-digit numbers yield a remainder of 1 when divided by both 4 and 14?

A. 0
B. 1
C. 2
D. 3
E. 4


Kudos for a correct solution.


800score Official Solution:

Let’s use n to denote a two-digit number that fits the requirement in the question.

Since we are looking for a remainder of 1 when n is divided by 4 or 14, then (n – 1) must be divisible by both 4 and 14. All numbers divisible by both 4 and 14 must be divisible by their least common multiple, which is 28.

So n – 1 can equal any two-digit multiple of 28. These possible values are:
n – 1 = 28, 56, or 84.

Therefore, n = 29, 57, or 85 (3 different two-digit numbers).

The correct answer is choice (D).
_________________

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

Intern
Intern
User avatar
Joined: 08 Jul 2012
Posts: 49
Re: How many two-digit numbers yield a remainder of 1 when divided by both  [#permalink]

Show Tags

New post 26 Jul 2015, 22:18
1
Bunuel wrote:
Bunuel wrote:
How many two-digit numbers yield a remainder of 1 when divided by both 4 and 14?

A. 0
B. 1
C. 2
D. 3
E. 4


Kudos for a correct solution.


800score Official Solution:

Let’s use n to denote a two-digit number that fits the requirement in the question.

Since we are looking for a remainder of 1 when n is divided by 4 or 14, then (n – 1) must be divisible by both 4 and 14. All numbers divisible by both 4 and 14 must be divisible by their least common multiple, which is 28.

So n – 1 can equal any two-digit multiple of 28. These possible values are:
n – 1 = 28, 56, or 84.

Therefore, n = 29, 57, or 85 (3 different two-digit numbers).

The correct answer is choice (D).


Thanks Bunuel, this is more smarter way!
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time. - Thomas A. Edison

Intern
Intern
User avatar
Status: My heart can feel, my brain can grasp, I'm indomitable.
Affiliations: Educator
Joined: 16 Oct 2012
Posts: 39
Location: Bangladesh
WE: Social Work (Education)
Re: How many two-digit numbers yield a remainder of 1 when divided by both  [#permalink]

Show Tags

New post 27 Jul 2015, 06:57
2
LCM (4, 14) =28
two digit multiple of 28 are 28, 56 and 84
two digits numbers that yield remainder of 1 when divisible by 4 and 14 are 28+1, 56+1 and 84+1
ans: D
_________________

please press "+1 Kudos" if useful

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7774
Premium Member
Re: How many two-digit numbers yield a remainder of 1 when divided by both  [#permalink]

Show Tags

New post 01 Oct 2017, 06:56
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: How many two-digit numbers yield a remainder of 1 when divided by both &nbs [#permalink] 01 Oct 2017, 06:56
Display posts from previous: Sort by

How many two-digit numbers yield a remainder of 1 when divided by both

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

Events & Promotions

PREV
NEXT


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®.