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If y = 30p, and p is prime, what is the greatest common factor of y
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Bunuel
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If y = 30p, and p is prime, what is the greatest common factor of y [#permalink] New post  02 Jul 2015, 01:35
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If y = 30p, and p is prime, what is the greatest common factor of y and 14p, in terms of p?

A. p
B. 2p
C. 5p
D. 7p
E. p^2


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Re: If y = 30p, and p is prime, what is the greatest common factor of y [#permalink] New post  02 Jul 2015, 03:14
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y=30p = 2*3*5*p
14p=2*7*p

GCD of (y,14p)=2*p (taking the common prime factors out of the numbers).

We can even arrive at this answer simply by assuming p=11 (we can choose any prime number as there is no restriction!)
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Re: If y = 30p, and p is prime, what is the greatest common factor of y [#permalink] New post  02 Jul 2015, 01:38
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If y = 30p, and p is prime, what is the greatest common factor of y and 14p, in terms of p?

A. p
B. 2p
C. 5p
D. 7p
E. p^2

IMO
B is the correct answer
Y=30p
other number is 14p
then GCF(30p,14P)=2P
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Re: If y = 30p, and p is prime, what is the greatest common factor of y [#permalink] New post  02 Jul 2015, 01:49
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It has to be 2 p.
y is a mutiple of prime p in terms of 30 & 14 p is also mutiple of p. so common factor wil be the common factor of 14 & 30 multiplied by prime p.
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Re: If y = 30p, and p is prime, what is the greatest common factor of y [#permalink] New post  02 Jul 2015, 05:26
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Let p = 3

y = 30 * 3 = 90
14 * 3 = 42

Greatest Common Factor of 42 and 90 can't be a multiple of 5, nor 7.
It can't be p^2 either, as 42 is not divisible by 9.

Leaves only p and 2*p of which 2p is obviously greater than p.

B
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Re: If y = 30p, and p is prime, what is the greatest common factor of y [#permalink] New post  02 Jul 2015, 06:22
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Bunuel wrote:
If y = 30p, and p is prime, what is the greatest common factor of y and 14p, in terms of p?

A. p
B. 2p
C. 5p
D. 7p
E. p^2


Kudos for a correct solution.


Solution -

Factors of 30p - 1p, 2p, 3p, 5p, 6p, 10p, 15p, 30p
Factors of 14p - 1p, 2p, 7p, 14p

Common factors are 1p and 2p.

Greatest common factor is 2p. ANS B.
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Re: If y = 30p, and p is prime, what is the greatest common factor of y [#permalink] New post  02 Jul 2015, 08:25
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If y = 30p, and p is prime, what is the greatest common factor of y and 14p, in terms of p?

A. p
B. 2p
C. 5p
D. 7p
E. p^2

my approach:
Just picked a prime number for P

P=2
y=60
14p=28

greatest common factor for 60 & 28 is 4 which is 2P

Ans is B
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Re: If y = 30p, and p is prime, what is the greatest common factor of y [#permalink] New post  02 Jul 2015, 21:01
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Bunuel wrote:
If y = 30p, and p is prime, what is the greatest common factor of y and 14p, in terms of p?

A. p
B. 2p
C. 5p
D. 7p
E. p^2


Kudos for a correct solution.


y = 30p = 5*2*3*p
14p = 7*2*p
G common factor = 2*p
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If y = 30p, and p is prime, what is the greatest common factor of y [#permalink] New post  03 Jul 2015, 00:03
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Bunuel wrote:
If y = 30p, and p is prime, what is the greatest common factor of y and 14p, in terms of p?

A. p
B. 2p
C. 5p
D. 7p
E. p^2


Kudos for a correct solution.


Given:
y = 30p, and p is prime

Question : GCD of y and 14p = ?

CONCEPT: Greatest Common Divisor is the Highest possible Number that can divide the set of Numbers completely without leaving any remainder therefore GCD must have the common Prime factors with their Highest Common Power available in each one of the numbers of the set.

y = 30 p = 2*3*5*p
14p = 2*7*p

i.e. GCD (Greatest Common Divisor) = 2*p


Answer: option B
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Re: If y = 30p, and p is prime, what is the greatest common factor of y [#permalink] New post  06 Jul 2015, 03:11
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Bunuel wrote:
If y = 30p, and p is prime, what is the greatest common factor of y and 14p, in terms of p?

A. p
B. 2p
C. 5p
D. 7p
E. p^2


Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

The greatest common factor of y (= 30p) and 14p is the product of all the common prime factors, using the lower power of repeated factors. The only repeated factors are 2 and p: 2^1 x p^1 = 2 x p = 2p. Again, you would get the same answer if p were any positive integer.

Answer: B.
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