GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 23 Jan 2020, 16:45

### 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

Math Expert
Joined: 02 Sep 2009
Posts: 60627
If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an  [#permalink]

### Show Tags

11 Nov 2019, 04:43
00:00

Difficulty:

95% (hard)

Question Stats:

24% (02:05) correct 76% (02:03) wrong based on 29 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

Are You Up For the Challenge: 700 Level Questions

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8335
Re: If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an  [#permalink]

### Show Tags

11 Nov 2019, 08:15
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
$$10x=10+4p.....4p=10x-10$$
For 10x-10 to be a multiple of 4, x will always be ODD...
so Q=10x=10*3=30....30=10+4p.....4p=20.....p=5.......GCD(30,5)=5
Q=10x=10*5=50....50=10+4p.....4p=40.....p=10.......GCD(50,10)=10
Insuff

(2) P = 10 y, where y is a positive integer
$$P=10+4*10y.....P=10(1+4y)$$
Now, 1+4y is one more than a multiple of y, that is 4y, so 1+4y and y are co-prime, that is they do not have any factors in common..
Thus GCD(10(1+4y),10y) =10
Suff

B
_________________
Manager
Joined: 10 Dec 2017
Posts: 177
Location: India
Re: If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an  [#permalink]

### Show Tags

12 Nov 2019, 05:11
Bunuel 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

Are You Up For the Challenge: 700 Level Questions

From 1)
$$10X=10+4P$$
LHS is always be a multiple of 10. For RHS to be a multiple of 10
P= 5n( n is integer) or P=10n(n is integer)
it depends upon P
Not sufficient
From 2)
$$Q=10+40Y$$
Q=50,90,130....always a multiple of 10
P=10Y
GCD=10
SUFFICIENT
B:)
Re: If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an   [#permalink] 12 Nov 2019, 05:11
Display posts from previous: Sort by