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# a, b, x and y are positive integers. If ay = bx, is 7 a factor of x?

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Math Expert
Joined: 02 Sep 2009
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a, b, x and y are positive integers. If ay = bx, is 7 a factor of x?  [#permalink]

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26 Jun 2018, 05:24
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64% (01:39) correct 36% (01:38) wrong based on 61 sessions

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a, b, x and y are positive integers. If ay = bx, is 7 a factor of x?

(1) 35 is a factor of a
(2) b when prime factorized will be of the form (5)^s

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Re: a, b, x and y are positive integers. If ay = bx, is 7 a factor of x?  [#permalink]

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26 Jun 2018, 05:38
Starting with statement (2):

(2) b when prime factorized will be of the form (5)^s

This in insufficient on its own because it provides nothing to help us figure out what X could be.

Statement (1)
(1) 35 is a factor of a

This tells us that that A's prime factorization are at least one 5, and at least one 7.
Insufficient on its own because it tells us nothing about X. B could contain the 7 or X could contain the 7.

Together: It looks like we can solve it since we'd know that B is 5 raised to some power, leaving X with the factorization of 7.
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Joined: 08 Oct 2015
Posts: 241
a, b, x and y are positive integers. If ay = bx, is 7 a factor of x?  [#permalink]

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26 Jun 2018, 06:06
quyanhle24 wrote:
Starting with statement (2):

(2) b when prime factorized will be of the form (5)^s

This in insufficient on its own because it provides nothing to help us figure out what X could be.

Statement (1)
(1) 35 is a factor of a

This tells us that that A's prime factorization are at least one 5, and at least one 7.
Insufficient on its own because it tells us nothing about X. B could contain the 7 or X could contain the 7.

Together: It looks like we can solve it since we'd know that B is 5 raised to some power, leaving X with the factorization of 7.

Answer should be e, because even together if a is 35, and b is 5x5 then we would not have an integer, whereas we would with b as 5
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Joined: 28 Jul 2016
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Re: a, b, x and y are positive integers. If ay = bx, is 7 a factor of x?  [#permalink]

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26 Jun 2018, 10:39
rahulkashyap wrote:
quyanhle24 wrote:
Starting with statement (2):

(2) b when prime factorized will be of the form (5)^s

This in insufficient on its own because it provides nothing to help us figure out what X could be.

Statement (1)
(1) 35 is a factor of a

This tells us that that A's prime factorization are at least one 5, and at least one 7.
Insufficient on its own because it tells us nothing about X. B could contain the 7 or X could contain the 7.

Together: It looks like we can solve it since we'd know that B is 5 raised to some power, leaving X with the factorization of 7.

Answer should be e, because even together if a is 35, and b is 5x5 then we would not have an integer, whereas we would with b as 5

should be C as it mentions are all positive integers
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Re: a, b, x and y are positive integers. If ay = bx, is 7 a factor of x?  [#permalink]

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26 Jun 2018, 17:46
Ans is c you're right

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Joined: 02 Aug 2009
Posts: 7106
Re: a, b, x and y are positive integers. If ay = bx, is 7 a factor of x?  [#permalink]

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26 Jun 2018, 18:33
a, b, x and y are positive integers. If ay = bx, is 7 a factor of x?

(1) 35 is a factor of a
So ay is a multiple of 35 or 7, thus the right hand side bx also will be multiple of 7..
But it is possible that only b or only x or both b and x are multiple of 7
Insufficient

(2) b when prime factorized will be of the form (5)^s
Insufficient

Combined
From statement I, b or x or both can be multiple of 7
But statement II tells us that b is multiple of only one prime number 5
So x has to be a multiple of 7
Sufficient

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: a, b, x and y are positive integers. If ay = bx, is 7 a factor of x? &nbs [#permalink] 26 Jun 2018, 18:33
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