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Alpha Sequence

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by pareekbharat86 » Thu Nov 14, 2013 4:30 pm
An infinite sequence of positive integers is called an "alpha sequence" if the number of even integers in the sequence is finite. If S is an infinite sequence of positive integers, is S an alpha sequence?
(1) The first ten integers in S are even.
(2) An infinite number of integers in S are odd.

OA is E.
Thanks,
Bharat.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Nov 14, 2013 5:00 pm
pareekbharat86 wrote:An infinite sequence of positive integers is called an "alpha sequence" if the number of even integers in the sequence is finite. If S is an infinite sequence of positive integers, is S an alpha sequence?

(1) The first ten integers in S are even.
(2) An infinite number of integers in S are odd.
Target question: Is S an alpha sequence?

Let's jump straight too . . .

Statements 1 and 2 combined
There are several possible sets that satisfy both conditions. Here are two:
Case a: S = {2,4,6,8,10,12,14,16,18,20,21,23,25,27,29,31...all odd integers...etc}, in which case S is an alpha sequence
Case b: S = {2,4,6,8,10,12,14,16,18,20,21,22,23,24,25,26,27,28,29,30...}, in which case S is NOT an alpha sequence
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
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by Uva@90 » Thu Nov 14, 2013 8:28 pm
pareekbharat86 wrote:An infinite sequence of positive integers is called an "alpha sequence" if the number of even integers in the sequence is finite. If S is an infinite sequence of positive integers, is S an alpha sequence?
(1) The first ten integers in S are even.
(2) An infinite number of integers in S are odd.

OA is E.
Hi Pareekbharat86,
To Find: Does Sequence S has finite number of Even Integers. (YES/NO Type)

Statement1 : It talk about only first ten. Rest of the sequence is unsaid.
So Insufficient.

Statement2 : It talks about Odd.
Hence Insufficient.

1+2
Nothing about Finite sequence of Even Integers is said.
Hence Insufficient.

Answer is E

Regards,
Uva.
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by Mathsbuddy » Fri Nov 22, 2013 9:49 am
An infinite sequence of positive integers is called an "alpha sequence" if the number of even integers in the sequence is finite. If S is an infinite sequence of positive integers, is S an alpha sequence?
(1) The first ten integers in S are even: this doesn't say that these are the only even numbers, therefore INSUFFICIENT
(2) An infinite number of integers in S are odd: this doesn't say if there are any even numbers INSUFFICIENT

Combined: No certainty that the even numbers are finite: INSUFFICIENT
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