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

 It is currently 18 Apr 2019, 12:20

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

If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an

Author Message
TAGS:

Hide Tags

Senior Manager
Joined: 13 Jun 2013
Posts: 274
If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an  [#permalink]

Show Tags

19 Nov 2014, 05:20
1
4
00:00

Difficulty:

85% (hard)

Question Stats:

49% (02:26) correct 51% (02:07) wrong based on 109 sessions

HideShow timer Statistics

If P and Q are positive integers and Q = 10 + 4P, find the GCD of P and Q

(1) Q = 10 x, where x is a positive integer

(2) P = 10 y, where y is a positive integer
Current Student
Status: Chasing my MBB Dream!
Joined: 29 Aug 2012
Posts: 1115
Location: United States (DC)
WE: General Management (Aerospace and Defense)
Re: If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an  [#permalink]

Show Tags

19 Nov 2014, 06:26
1
1
manpreetsingh86 wrote:
If P and Q are positive integers and Q = 10 + 4P, find the GCD of P and Q

(1) Q = 10 x, where x is a positive integer

(2) P = 10 y, where y is a positive integer

St-1: We only know about Q, that it is multiple of 10. but nothing about P. It can be either 10 or 5 or any multiple of 5. So insufficient.

St-2 : If P is multiple of 10 and if we multiply with 4, it will remain multiple of 10. And if add 10 this value, it will still be multiple of 10. The GCD for P and Q will be 10.

Statement 2 is sufficient.

_________________
Current Student
Joined: 12 Aug 2015
Posts: 2613
Schools: Boston U '20 (M)
GRE 1: Q169 V154
If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an  [#permalink]

Show Tags

24 Aug 2016, 02:36
Excellent Question
Here is my approach
Statement 1 => Q=30 Y=5 => GCD=5
Q=90 P=20 => GCD = 10 =>INSUFF
Statement 2 => P=10Y so Q=10(4y+1)
now here y and 4y+1 are co-primes always
Hence GCD = 10

SMASH THAT B
_________________
SVP
Joined: 12 Dec 2016
Posts: 1536
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
Re: If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an  [#permalink]

Show Tags

31 Aug 2017, 01:48
stonecold wrote:
Excellent Question
Here is my approach
Statement 1 => Q=30 Y=5 => GCD=5
Q=90 P=20 => GCD = 10 =>INSUFF
Statement 2 => P=10Y so Q=10(4y+1)
now here y and 4y+1 are co-primes always
Hence GCD = 10

SMASH THAT B

can you elabortae your solution more?
"y and 4y + 1" are 2 coprimes?
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an  [#permalink]

Show Tags

31 Aug 2017, 01:55
Y and 4Y have the same prime factors. 2 will also be a prime factor of 4Y (if 2 is not a prime factor of Y already)

It is known that numbers Y and Y+1 are co-prime numbers. Using the same logic, Y and 4Y+1 will also be co-prime.

Hope that helps you!
_________________
You've got what it takes, but it will take everything you've got
Re: If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an   [#permalink] 31 Aug 2017, 01:55
Display posts from previous: Sort by