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555-605 Level|   Sequences|      
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manishuol
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An infinite sequence of positive integers is called a "beta 01 May 2013, 10:08
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C
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64% (01:22) correct 36% (01:21) wrong based on 828 sessions

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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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C
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An infinite sequence of positive integers is called a "beta 03 May 2013, 01:47
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[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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An infinite sequence of positive integers is called a "beta 01 May 2013, 10:16
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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?


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

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

Hope it helps.
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An infinite sequence of positive integers is called a "beta 01 May 2013, 10:18
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Bunuel
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?


(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.
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Thanks !! Bunuel .........
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An infinite sequence of positive integers is called a "beta 27 Jun 2017, 18:40
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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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An infinite sequence of positive integers is called a "beta 20 Apr 2023, 20:34
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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?


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

Is S a beta sequence? Or in other words, does S have a finite number of odd integers? This is a Yes or No question.

1) The first statement tells us that the first ten integers in S are even but gives no info about the rest of the terms. Statement 1 is not sufficient, we can eliminate answer choices A and D.

2) The second statement tells us that the difference between each two successive terms is a constant, therefore we know that S is an arithmetic progression but we have no information about the terms composing the sequence. Statement 2 is not sufficient. We can eliminate answer choice B and we are left with answer choices C and E.

1)+2) Now combining both statements together, we know that the constant in the arithmetic progression is an even number and because adding an even number to an even number will always yield to an even number; this sequence is composed of only even positive integers. Hence there are 0 odd terms on this sequence, which consequently has a finite number of odd integers. Both statements together are sufficient.

Correct answer is C.


Bunuel KarishmaB chetan2u can you please check the answer above and share an official answer to this question?
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An infinite sequence of positive integers is called a "beta 21 Apr 2023, 00:26
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HoudaSR
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?


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

Is S a beta sequence? Or in other words, does S have a finite number of odd integers? This is a Yes or No question.

1) The first statement tells us that the first ten integers in S are even but gives no info about the rest of the terms. Statement 1 is not sufficient, we can eliminate answer choices A and D.

2) The second statement tells us that the difference between each two successive terms is a constant, therefore we know that S is an arithmetic progression but we have no information about the terms composing the sequence. Statement 2 is not sufficient. We can eliminate answer choice B and we are left with answer choices C and E.

1)+2) Now combining both statements together, we know that the constant in the arithmetic progression is an even number and because adding an even number to an even number will always yield to an even number; this sequence is composed of only even positive integers. Hence there are 0 odd terms on this sequence, which consequently has a finite number of odd integers. Both statements together are sufficient.

Correct answer is C.


Bunuel KarishmaB chetan2u can you please check the answer above and share an official answer to this question?
Show more

I do not know the source of the question and do not have the official solution, but your solution is correct.
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An infinite sequence of positive integers is called a "beta 07 Jun 2024, 02:29
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