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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an

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

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Difficulty:   95% (hard)

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

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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

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Math Expert V
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]

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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

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Re: If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an  [#permalink]

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