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

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

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

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.

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

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

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

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

Understood. Thank you sir.

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