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

It is currently 16 Jul 2018, 19:20

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 p and q are positive integers such that when they are divided by 5,

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

Hide Tags

Intern
Intern
avatar
B
Joined: 25 Apr 2015
Posts: 8
If p and q are positive integers such that when they are divided by 5, [#permalink]

Show Tags

New post Updated on: 04 Jul 2017, 06:02
5
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

74% (02:00) correct 26% (02:44) wrong based on 150 sessions

HideShow timer Statistics

If p and q are positive integers such that when they are divided by 5, the remainder is 3 for each; and when they are divided by 9, the remainder is 4 for each. If q>p, then which of the following must be a factor of q - p ?

A) 12
B) 20
C) 27
D) 36
E) 45

Originally posted by franz711 on 04 Jul 2017, 05:22.
Last edited by Bunuel on 04 Jul 2017, 06:02, edited 1 time in total.
Added the OA.
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47019
Re: If p and q are positive integers such that when they are divided by 5, [#permalink]

Show Tags

New post 04 Jul 2017, 05:43
1
2
franz711 wrote:
If p and q are positive integers such that when they are divided by 5, the remainder is 3 for each; and when they are divided by 9, the remainder is 4 for each. If q>p, then which of the following must be a factor of q - p ?

A) 12
B) 20
C) 27
D) 36
E) 45


When p is divided by 5, the remainder is 3: p= 5m + 3, so it can be 3, 8, 13, 18, ...
When p is divided by 9, the remainder is 4: p= 9n + 4, so it can be 4, 13, 22, 31, ...

There is a way to derive general formula for p (of a type p = kx + r, where x is divisor and r is a remainder) based on above two statements:

Divisor x would be the least common multiple of above two divisors 5 and 9, hence x=45.
Remainder r would be the first common integer in above two patterns, hence r = 13.

Therefore general formula based on both statements is p = 45x + 13. (check HERE to know to to derive general formula from these two)

Similarly, general formula for q will be 45y + 13.

q - p = (45y + 13) - (45x + 13) = 45(y - x).

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

1 KUDOS received
SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1825
Premium Member CAT Tests
Re: If p and q are positive integers such that when they are divided by 5, [#permalink]

Show Tags

New post 04 Jul 2017, 05:47
1
franz711 wrote:
If p and q are positive integers such that when they are divided by 5, the remainder is 3 for each; and when they are divided by 9, the remainder is 4 for each. If q>p, then which of the following must be a factor of q - p ?

A) 12
B) 20
C) 27
D) 36
E) 45

I went the long way :-|, but it wasn't too time consuming because these numbers turn out to be very manageable:

1. When positive integers p and q are divided by 5, the remainder for each is 3.

p = 5a + 3
q = 5b + 3

2. When positive integers p and q are divided by 9, the remainder for each is 4

p = 9c + 4
q = 9d + 4

3. Possible values for p and q for both sets of equations, and from each list of possibilities we need two values that match because q > p:

#1: 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58

#2: 4, 13, 22, 31, 40, 49, 58

q = 58, p = 13

q - p = (58 - 13) = 45

Answer E
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1033
If p and q are positive integers such that when they are divided by 5, [#permalink]

Show Tags

New post Updated on: 08 Jul 2018, 17:30
franz711 wrote:
If p and q are positive integers such that when they are divided by 5, the remainder is 3 for each; and when they are divided by 9, the remainder is 4 for each. If q>p, then which of the following must be a factor of q - p ?

A) 12
B) 20
C) 27
D) 36
E) 45


because divisor ratio of 5:9≈1:2,
assume quotient ratio inversely=2:1
[(p-3)/5)]/[(p-4)/9]=2
p=13
13+(5*9)=58=q
q-p=58-13=45
E

Originally posted by gracie on 04 Jul 2017, 13:41.
Last edited by gracie on 08 Jul 2018, 17:30, edited 1 time in total.
1 KUDOS received
Intern
Intern
avatar
B
Joined: 18 Aug 2017
Posts: 30
GMAT 1: 670 Q49 V33
Re: If p and q are positive integers such that when they are divided by 5, [#permalink]

Show Tags

New post 22 Aug 2017, 06:42
1
I used this rule: remainder can be added or subtracted directly when adding or subtracting two dividends (the excess needs to be corrected after)

So p and q has the same remainder when divided by 5, therefore q-p will have the remainder of 0, which means q-p is divisible by 5. The same goes for 9.

E) 45 is the only answer that is a multiple of 9 and 5, so E is the right answer.
Intern
Intern
User avatar
B
Joined: 07 Jul 2018
Posts: 7
Re: If p and q are positive integers such that when they are divided by 5, [#permalink]

Show Tags

New post 08 Jul 2018, 12:34
I went this way:
p=5x+3 p=9x'+4
q=5y+3 q=9y'+4

=> q-p =5(y-x) = 9(y'-x') =>9*5=45 is a factor of q-p

same as NamVu1990

Hope it will help someone :)
_________________

Welcoming critics is my way to improvement. So do not hesitate, tell me how I can improve. Thx :)

Re: If p and q are positive integers such that when they are divided by 5,   [#permalink] 08 Jul 2018, 12:34
Display posts from previous: Sort by

If p and q are positive integers such that when they are divided by 5,

  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®.