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# A set contains 24 even positive integers

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Intern
Joined: 10 Jul 2017
Posts: 30

Kudos [?]: 6 [1], given: 51

A set contains 24 even positive integers [#permalink]

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28 Oct 2017, 09:28
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Difficulty:

25% (medium)

Question Stats:

58% (01:02) correct 42% (00:22) wrong based on 24 sessions

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A set contains 24 even positive integers, not necessarily distinct. Does atleast one integer repeat in the set?

(1) When the integers are arranged in the increasing order, the difference between any two consecutive terms is not more than 2.

(2) The median of the set is an integer in the set.

Source- Experts' Global Test 7

Please provide an explanation for the solution as I am not able to understand the one provided. Thanks!
[Reveal] Spoiler: OA

Kudos [?]: 6 [1], given: 51

Math Expert
Joined: 02 Aug 2009
Posts: 5229

Kudos [?]: 5883 [0], given: 118

Re: A set contains 24 even positive integers [#permalink]

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28 Oct 2017, 09:48
akanksha.setiya wrote:
A set contains 24 even positive integers, not necessarily distinct. Does atleast one integer repeat in the set?

(1) When the integers are arranged in the increasing order, the difference between any two consecutive terms is not more than 2.

(2) The median of the set is an integer in the set.

Source- Experts' Global Test 7

Please provide an explanation for the solution as I am not able to understand the one provided. Thanks!

Hi..

There are 24 even integers..

Let's see what each statement tells us..
1) arranged in ascending order, difference between two consecutive integers is not more than 2..
So integers could be 24 CONSECUTIVE even integers OR any of the two can be same, even all 24 can be same..
Example..
2,4,6,...... Or 2,2,4,6,6,6,6....
Insufficient

2)the median of the set is an integer in the set..

Median of ODD Number of integers is the central integer, which would be Surely in the set..
Median of even number of integers is always the middle of two central number..
Here 24 is even, so median will be centre of 12 and 13 number.
But if it is the integer in the set, 12 and 13 have to be SAME number..
Thus atleast one value is repeated.
Suff

B
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5883 [0], given: 118

Manager
Joined: 21 Jun 2014
Posts: 59

Kudos [?]: 3 [0], given: 1

Re: A set contains 24 even positive integers [#permalink]

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28 Oct 2017, 10:00
Is it B?
St 1: the numbers are arranged in increasing order. Difference between 2 consecutive terms not more than 2 . Can be 0 or can be 2. If 2, no repetitions occur. If 0, repetitions occur. Not sufficient.

St 2: There are even number of items in the set. So median will be the average of 11th and 12 the term. The number can be equal to one of the numbers in the set only if repetition happens.

IMO B

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app

Kudos [?]: 3 [0], given: 1

Intern
Joined: 10 Jul 2017
Posts: 30

Kudos [?]: 6 [0], given: 51

Re: A set contains 24 even positive integers [#permalink]

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28 Oct 2017, 10:41
chetan2u wrote:
akanksha.setiya wrote:
A set contains 24 even positive integers, not necessarily distinct. Does atleast one integer repeat in the set?

(1) When the integers are arranged in the increasing order, the difference between any two consecutive terms is not more than 2.

(2) The median of the set is an integer in the set.

Source- Experts' Global Test 7

Please provide an explanation for the solution as I am not able to understand the one provided. Thanks!

Hi..

There are 24 even integers..

Let's see what each statement tells us..
1) arranged in ascending order, difference between two consecutive integers is not more than 2..
So integers could be 24 CONSECUTIVE even integers OR any of the two can be same, even all 24 can be same..
Example..
2,4,6,...... Or 2,2,4,6,6,6,6....
Insufficient

2)the median of the set is an integer in the set..

Median of ODD Number of integers is the central integer, which would be Surely in the set..
Median of even number of integers is always the middle of two central number..
Here 24 is even, so median will be centre of 12 and 13 number.
But if it is the integer in the set, 12 and 13 have to be SAME number..
Thus atleast one value is repeated.
Suff

B

Although, what you have written is same as the official solution, reading your answer clicked me well!

Thanks!

Kudos [?]: 6 [0], given: 51

Re: A set contains 24 even positive integers   [#permalink] 28 Oct 2017, 10:41
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