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An infinite sequence of positive integers is called a "beta  [#permalink]

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11 00:00

Difficulty:   45% (medium)

Question Stats: 63% (01:29) correct 37% (01:22) wrong based on 429 sessions

HideShow timer Statistics An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

(1) The first ten integers in S are even.
(2) The difference between each successive pair of terms in S is a constant

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An infinite sequence of positive integers is called a "beta  [#permalink]

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manishuol wrote:
An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

(1) The first ten integers in S are even.
(2) The difference between each successive pair of terms in S is a constant

Similar question to practice:
Quote:
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.

Discussed here: https://gmatclub.com/forum/an-infinite- ... 55723.html

Hope it helps.
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Re: An infinite sequence of positive integers is called a "beta  [#permalink]

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Bunuel wrote:
manishuol wrote:
An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

(1) The first ten integers in S are even.
(2) The difference between each successive pair of terms in S is a constant

Similar question to practice:
Quote:
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.

Discussed here: an-infinite-sequence-of-positive-integers-is-called-an-101758.html

Hope it helps.

Thanks !! Bunuel .........
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Re: An infinite sequence of positive integers is called a "beta  [#permalink]

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1
1
[quote="manishuol"]An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

to become a beta sequence number of odd integers in the sequence must be finite
(1) The first ten integers in S are even.

We dont know the number rest all number are odd or even....so not sufficient.

(2) The difference between each successive pair of terms in S is a constant

difference is constant ..it means this series is an AP.....but as we dont know the numbers...it can be AP Of oDD OR EVEN...so not sufficeint.

combining....we know this is an AP and plus we also know that first 10 terms are even ..it means rest all terms are also even...so we don have odd numbers....so means it is finite...
hence..C

hope it helps.

SKM
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Re: An infinite sequence of positive integers is called a "beta  [#permalink]

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manishuol wrote:
An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

(1) The first ten integers in S are even.
(2) The difference between each successive pair of terms in S is a constant

I thought that if we had an infinite sequence and in this infinite sequence we have 10 integers that are even, then the number of odds in this infinite sequence has to be finite. I don't quite get it.

Anyone thought the same way?

Cheers!
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Re: An infinite sequence of positive integers is called a "beta  [#permalink]

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Given : Beta Sequence = Finite Odd Integers + Infinite Even Integers

From
1) First 10 integers are even - No info about Odd integers ( 1 alone is not enough)
2) Difference between successive pairs is constant => Sequence is in Arithmetic Progression, so it can be a sequence of all Even integers or all Odd integers. (2 alone is not enough)

Combining 1 and 2 we can deduce the sequence to be a Infinite Even Integer Sequence, hence C
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Re: An infinite sequence of positive integers is called a "beta  [#permalink]

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Bunuel wrote:
manishuol wrote:
An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

(1) The first ten integers in S are even.
(2) The difference between each successive pair of terms in S is a constant

Similar question to practice:
Quote:
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.

Discussed here: http://gmatclub.com/forum/an-infinite-s ... 01758.html

Hope it helps.

this will appear in the actual gmat? this problem looks weird.
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Re: An infinite sequence of positive integers is called a "beta  [#permalink]

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_________________ Re: An infinite sequence of positive integers is called a "beta   [#permalink] 15 Sep 2018, 08:49
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