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

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

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New post 19 Nov 2014, 05:20
1
4
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A
B
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D
E

Difficulty:

  95% (hard)

Question Stats:

47% (01:57) correct 53% (01:51) wrong based on 107 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
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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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New post 19 Nov 2014, 06:26
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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.

So Answer is B.
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If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an  [#permalink]

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New post 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
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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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New post 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?
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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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New post 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!
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Re: If P and Q are positive integers and Q = 10 + 4P, find the GCD of P an &nbs [#permalink] 31 Aug 2017, 01:55
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