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16 Dec 2020, 01:15
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If x and y are positive integers, is x divisible by 26 ?
(1) The least common multiple of x and y is 169
(2) The greatest common factor of x and 39 is 13
Are You Up For the Challenge: 700 Level Questions
(1) The least common multiple of x and y is 169
(2) The greatest common factor of x and 39 is 13
Are You Up For the Challenge: 700 Level Questions
Bryan180599
Joined: 07 Nov 2020
Last visit: 25 Mar 2022
Posts: 10
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Location: Belgium
Schools: HEC MFin "23 ESSEC ESCP Europe HEC MiM "25
GMAT 1: 710 Q48 V38
16 Dec 2020, 05:54
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If x and y are positive integers, is x divisible by 26 ?
26 = 13*2. x needs to have as factors 2 and 13 to be divisible by 26.
(1) The least common multiple of x and y is 169
Sufficient. 169 = 13². So we know that x and y are only composed of factor 13. For example x = 13 and y = 169. Or x = 169 y = 1,... Hence there are no factors 2 and thus x is not divisible.
(2) The greatest common factor of x and 39 is 13
Insufficient. Here we just know the greatest common factors of x and 39 is 13, we do not know if x has a factor 2.
Answer A
26 = 13*2. x needs to have as factors 2 and 13 to be divisible by 26.
(1) The least common multiple of x and y is 169
Sufficient. 169 = 13². So we know that x and y are only composed of factor 13. For example x = 13 and y = 169. Or x = 169 y = 1,... Hence there are no factors 2 and thus x is not divisible.
(2) The greatest common factor of x and 39 is 13
Insufficient. Here we just know the greatest common factors of x and 39 is 13, we do not know if x has a factor 2.
Answer A
16 Dec 2020, 10:08
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If x and y are positive integers, is x divisible by 26 ?
(1) The least common multiple of x and y is 169
This confirms that x definitely has 13*13 - which means 169 is not divisible by 2.
(A) is sufficient.
(2) The greatest common factor of x and 39 is 13
Here, x can be 26, 52 , 169.
(B) is not sufficient.
(1) The least common multiple of x and y is 169
This confirms that x definitely has 13*13 - which means 169 is not divisible by 2.
(A) is sufficient.
(2) The greatest common factor of x and 39 is 13
Here, x can be 26, 52 , 169.
(B) is not sufficient.
