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# If a and b are two distinct positive integers, what is the largest

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Joined: 28 May 2014
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If a and b are two distinct positive integers, what is the largest  [#permalink]

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16 Mar 2018, 21:29
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Difficulty:

75% (hard)

Question Stats:

53% (02:08) correct 47% (02:09) wrong based on 30 sessions

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If a and b are two distinct positive integers, what is the largest number that leaves no remainder when it divides a and b?

(1) a and b can be written as 8x and 8y respectively, where x and y are distinct integers with no common prime factors.
(2) a is equal to 24 and both a and b are divisible by the same perfect cubes.

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Re: If a and b are two distinct positive integers, what is the largest  [#permalink]

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16 Mar 2018, 22:00

(1) a and b can be written as 8x and 8y respectively, where x and y are distinct integers with no common prime factors.
Now as it is clear from the statement, the HCF is 8, which is the required value of the largest integer. Hence sufficient.

(2) a is equal to 24 and both a and b are divisible by the same perfect cubes.
Here, the "same perfect cubes " can be 8 ... a= 24 , b = 24 , largest integer will be 24, or a=24, b =40. the largest integer is 8.
hence insufficient.

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Re: If a and b are two distinct positive integers, what is the largest  [#permalink]

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16 Aug 2019, 14:08
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Re: If a and b are two distinct positive integers, what is the largest   [#permalink] 16 Aug 2019, 14:08
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