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# X is the least integer in a set of 7 consecutive positive integers. Ar

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Joined: 02 Sep 2009
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X is the least integer in a set of 7 consecutive positive integers. Ar  [#permalink]

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26 Nov 2019, 01:23
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Difficulty:

75% (hard)

Question Stats:

35% (02:20) correct 65% (02:00) wrong based on 26 sessions

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X is the least integer in a set of 7 consecutive positive integers. Are three distinct integers in this set divisible by 3?

(1) The product of all 7 integers is divisible by 27.
(2) X is not a multiple of 3.

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X is the least integer in a set of 7 consecutive positive integers. Ar  [#permalink]

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26 Nov 2019, 12:01
There are three distinct integers in this set divisible by 3, if X is divisible by 3.

Statement 1- doesn't tell us whether x is divisible by 3
Insufficient

Statement 2- X is not a multiple of 3

Sufficient

Bunuel wrote:
X is the least integer in a set of 7 consecutive positive integers. Are three distinct integers in this set divisible by 3?

(1) The product of all 7 integers is divisible by 27.
(2) X is not a multiple of 3.
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Joined: 14 Jul 2019
Posts: 137
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Concentration: Accounting, Finance
GPA: 3.9
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Re: X is the least integer in a set of 7 consecutive positive integers. Ar  [#permalink]

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26 Nov 2019, 12:51
X is the least integer in a set of 7 consecutive positive integers. Are three distinct integers in this set divisible by 3?

(1) The product of all 7 integers is divisible by 27.
(2) X is not a multiple of 3.

3 distinct integers of the set of 7 consecutive integers will be divisible by 3 only when the 1st and last integer is divisible by 3. For example, {2,3,4,5,6,7,8} has only 2 integers that are divisible by 3. But {3,4,5,6,7,8,9} fulfills the condition.

(1) Let the set be {23,24,25,26,27,28,29}, here only 24 and 27 are divisible by 3. But in{27,28,29,30,31,32,33} exactly 3 integers are divisible by 3. Insufficient.

(2) The last term of the set of consecutive integers is divisible by 3. It means the 1st integer is also divisible by 3. Sufficient.
Re: X is the least integer in a set of 7 consecutive positive integers. Ar   [#permalink] 26 Nov 2019, 12:51
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