Set A contains infinite number of integers. Are all the integers in Se

Question

Set A contains infinite number of integers. Are all the integers in Set A even?

(1) Infinite integers in set A are divisible by 2.
(2) The difference by any 2 integers in Set A is a multiple of 4.

GMATBusters · Accepted Answer

Official Solution: 
 Statement1:  
It states that infinite integers in Set A are even, but there may be a few odd integers.
So we cannot be sure that all integers are even. 
 NOT SUFFICIENT. 
 
Statement2: 
It states that difference between any 2 integers in the set is multiple of 4 which is even.
It is only possible if all the integers are either even or odd.
 NOT SUFFICIENT.

Combining Statement 1 & 2  , we get that infinite integers are even and we have either only even or only odd integers in the Set.
So all the integers are EVEN. 
 SUFFICIENT.

Answer C

Chethan92 · Answer

From statement 1:

All integers in set A is divisible by 2.

Set A may contain 0,2,4,6.. All are divisible by 2 and all are even. 1 is sufficient.

From statement 2:

The difference by any 2 integers in Set A is 4. So set A may contain 1,5,9,13.... or 0,4,8,12....
Set A could be even or odd. Hence 2 is insufficient.

A is the answer.

Archit3110 · Answer

Set A contains infinite number of integers. Are all the integers in Set A even?
1) Infinite integers in set A are divisible by 2.
2) The difference by any 2 integers in Set A is 4.

A

Gladiator59 · Answer

Set A contains infinite number of integers. Are all the integers in Set A even?
1) Infinite integers in set A are divisible by 2.
2) The difference by any 2 integers in Set A is 4.

SOlution :

I feel option (E) is correct but statement 2 is kind of contradictory. Please look into it.

Are all integers of SET A even? Set A has an infinite number of integers.

St 1.  Not sufficient . Consider the set of all natural numbers ( positive integers ) the set is infinite and all even numbers ( an infinite # of them) are divisible by two but not all the numbers in the set are even.

St 2. Difference between any 2 integers in Set A is 4.  Which is a contradiction as if there are any two integers say 1 and 5 whose difference is 4, then we could choose two 1's or two 5's and the difference between them would be 0 .  Hence there have to be exactly two integers in the set ( again either even or odd for ex. 0,4 OR 1,5) with difference of 4.  Not sufficient.

Hence Option (E) is correct!

Regards,
Gladi

saukrit · Answer

Answer is A as statement 1 alone is sufficient to confirm that All set numbers are even. Statement 2 is not sufficient as even 1 and 5 can have a difference of 4, bu that does not make them even.

baru · Answer

Set A contains infinite number of integers. Are all the integers in Set A even?
 1) Infinite integers in set A are divisible by 2.  ==>  Sufficient  divisible by 2 means even
2) The difference by any 2 integers in Set A is a multiple of 4.--> Insufficient ==> as 55-35= 20 ,which is divisible by 4 , but 35 and 55 are not even
 
So OA is A

u1983 · Answer

1) Infinite integers in set A are divisible by 2...... Suff.... as all div by 2, all are even
2) The difference by any 2 integers in Set A is a multiple of 4....................NS ..... as the integers could be an arithmetic series of odd numbers with common difference of 4 ( 1,5,9,13......) or could be an arithmetic series of odd numbers with common difference of 4 ( 2,6,10,14......)

Thus ans A

Chethan92 · Answer

gmatbusters . How can Set A contain few Odd integers when S1 clearly states that Set A is divisible by 2? Can you explain

GMATBusters · Answer

Hi
St1: says that infinite no of element are even, NOT ALL elements are even.
For example,  The set of of positive integers has infinite no of EVEN integers and it also has infinite number of ODD integers also. 
Hope it is clear.
Feel free to tag me again

Chethan92 · Answer

Understood. Thank you sir.

Shwetabh54 · Answer

I do not think its a correct answer,

13 and 17 are number whose difference is a multiple of 4 and there is a possibility of set as below:

A= { Infinite even numbers, 13, 17, .....}

Since infinite is not defined, Infinite - infinite is not zero, and hence above set satisfies both statement and exist. Also, a set A can exist in which all A can be even as below:

A= { Infinite even numbers, 12, 16, .....further even numbers}

Hence, correct answer should be E.

Set A contains infinite number of integers. Are all the integers in Se

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Set A contains infinite number of integers. Are all the integers in Se

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