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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  [#permalink]

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New post 13 Oct 2018, 09:39
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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.

Weekly Quant Quiz #4 Ques 9


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Re: Set A contains infinite number of integers. Are all the integers in Se  [#permalink]

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New post 13 Oct 2018, 20:21

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

gmatbusters wrote:
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.

Weekly Quant Quiz #4 Ques 9


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Re: Set A contains infinite number of integers. Are all the integers in Se  [#permalink]

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New post 13 Oct 2018, 09:45
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.
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Re: Set A contains infinite number of integers. Are all the integers in Se  [#permalink]

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New post 13 Oct 2018, 09:50
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
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Re: Set A contains infinite number of integers. Are all the integers in Se  [#permalink]

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New post 13 Oct 2018, 09:54
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!

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Gladi
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Re: Set A contains infinite number of integers. Are all the integers in Se  [#permalink]

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New post 13 Oct 2018, 10:03
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.
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Re: Set A contains infinite number of integers. Are all the integers in Se  [#permalink]

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New post 13 Oct 2018, 10:22
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
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Re: Set A contains infinite number of integers. Are all the integers in Se  [#permalink]

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New post 13 Oct 2018, 10:25
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
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Re: Set A contains infinite number of integers. Are all the integers in Se  [#permalink]

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New post 13 Oct 2018, 21:09
gmatbusters wrote:

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

gmatbusters wrote:
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.

Weekly Quant Quiz #4 Ques 9



gmatbusters. How can Set A contain few Odd integers when S1 clearly states that Set A is divisible by 2? Can you explain
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Set A contains infinite number of integers. Are all the integers in Se  [#permalink]

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New post 13 Oct 2018, 21:14
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

Afc0892 wrote:
gmatbusters wrote:

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

gmatbusters wrote:
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.

Weekly Quant Quiz #4 Ques 9



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

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Re: Set A contains infinite number of integers. Are all the integers in Se  [#permalink]

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New post 13 Oct 2018, 21:18
gmatbusters wrote:
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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Re: Set A contains infinite number of integers. Are all the integers in Se   [#permalink] 13 Oct 2018, 21:18
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