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akanksha.setiya
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A set contains 24 even positive integers, not necessarily distinct. Do 28 Oct 2017, 09:28
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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
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B
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A set contains 24 even positive integers, not necessarily distinct. Do 28 Oct 2017, 09:48
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akanksha.setiya
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


Kudos Please!! :-)

Please provide an explanation for the solution as I am not able to understand the one provided. Thanks!
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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
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A set contains 24 even positive integers, not necessarily distinct. Do 28 Oct 2017, 10:00
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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

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A set contains 24 even positive integers, not necessarily distinct. Do 28 Oct 2017, 10:41
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akanksha.setiya
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


Kudos Please!! :-)

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

Thanks!
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A set contains 24 even positive integers, not necessarily distinct. Do 30 Jan 2018, 08:08
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chetan2u
akanksha.setiya
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


Kudos Please!! :-)

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
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i don't understand how the 12th and 13th have to be the same number

lets say 12th is 5 and the 13th is 7 here the median is 6 there is no repetition
12th can be 6 and 13th can be 6 and median will be 6 here there is repetition.

so in the first case how is it that 12th and 13th have to be the same number for the median to be an integer?
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A set contains 24 even positive integers, not necessarily distinct. Do 30 Jan 2018, 08:35
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stne
chetan2u
akanksha.setiya
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


Kudos Please!! :-)

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

i don't understand how the 12th and 13th have to be the same number

lets say 12th is 5 and the 13th is 7 here the median is 6 there is no repetition
12th can be 6 and 13th can be 6 and median will be 6 here there is repetition.

so in the first case how is it that 12th and 13th have to be the same number for the median to be an integer?
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Hi...
Few points ..
There are 24 even integers, so 12th and 13th cannot be 5 and 7..
So these will be two even integer say they are 12 and 16 ...what will be the median here (12+16)/2=14, but 14 is NOT in the set..

So only possiblity is that the central two numbers are SAME even integers, say 12 and 12, so median will be 12 itself and is there in the set..
.hope it helps you..
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A set contains 24 even positive integers, not necessarily distinct. Do 31 Jan 2018, 05:32
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Thank you, I missed the " even point " .
also I guess that is why we cannot have 12 and 14 as the 12th and 13th term , because then median will be 26/2= 13 and 13 will not be in the set . Hence the only option for the median to be in the set is when the 13th and 14th are the same even number.
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A set contains 24 even positive integers, not necessarily distinct. Do 29 Jun 2022, 20:07
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Hi chetan2u, since the list contains consecutive even integers, why is that that the 12th and 13th term not be 24 and 26 , in which case the median which is (24+26)/2 would still be an integer, and the set could have all different numbers
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A set contains 24 even positive integers, not necessarily distinct. Do 29 Jun 2022, 21:35
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Hi chetan2u, since the list contains consecutive even integers, why is that that the 12th and 13th term not be 24 and 26 , in which case the median which is (24+26)/2 would still be an integer, and the set could have all different numbers
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The list does not contain consecutive even integers but even integers, and how many of them, again even number that is 24.

Even numbers will have their median equal to average of middle two numbers, that is average of 12th and 13th number.

How can average of two numbers be in the set when there is nothing between 12th and 13th number.
Only when the integers are same.
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A set contains 24 even positive integers, not necessarily distinct. Do 29 Jun 2022, 22:22
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Hi chetan2u, since the list contains consecutive even integers, why is that that the 12th and 13th term not be 24 and 26 , in which case the median which is (24+26)/2 would still be an integer, and the set could have all different numbers


The list does not contain consecutive even integers but even integers, and how many of them, again even number that is 24.

Even numbers will have their median equal to average of middle two numbers, that is average of 12th and 13th number.

How can average of two numbers be in the set when there is nothing between 12th and 13th number.
Only when the integers are same.
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Oh yes I completely missed that part about the median being in the set as well.
The question is not as straightforward as it looks like. Nevertheless thank you for your response :)

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A set contains 24 even positive integers, not necessarily distinct. Do 14 Jan 2026, 00:58
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