Bet Sequence

[yellowho]

An inÂ…nite sequence of positive integers is called a "beta
sequence" if the number of odd integers in the sequence is
Â…nite. If S is an inÂ…nite sequence of positive integers, is S a
beta sequence?

(1) The Â…rst ten integers in S are even.
(2) The di¤erence between each successive pair of
terms in S is a constant.

I don't understand why this is C.

[Night reader]

to make it more readable, add "fi"

The problem inquires about finite values of odd numbers. It does not put restrictions, numbers can be consecutive and non-consecutive, the same or not the same. The only restriction is numbers must be +ve integers.

st(1) that the first ten integers in S are even is Not Sufficient, as we get no relative data per odd-even and even-odd numbers in set S;
st(2) also Not Sufficient as we don't know the distribution of numbers in set S; the numbers may start even or odd; we know only that --> a(n+3)+ a(n+4) - a(n) - a(n+1) is const
Combined st(1&2) makes Sufficiency as we can arrange our set in infinite number of ways to keep odd numbers running, hence my answer is NO and Sufficient.

IOM C

An infiÂ…nite sequence of positive integers is called a "beta
sequence" if the number of odd integers in the sequence is
Â…finite. If S is an infiÂ…nite sequence of positive integers, is S a
beta sequence?

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

I don't understand why this is C.

[ankur.agrawal]

2) sufficient.

If difference is same between each successive pair then we can arrange our set in infinite number of ways to keep odd numbers running / we can even create sets without any odd nos. Both of them denies thats it is not a beta sequence. So should be sufficient.

An inÂ…nite sequence of positive integers is called a "beta
sequence" if the number of odd integers in the sequence is
Â…nite. If S is an inÂ…nite sequence of positive integers, is S a
beta sequence?

(1) The Â…rst ten integers in S are even.
(2) The di¤erence between each successive pair of
terms in S is a constant.

I don't understand why this is C.

[Night reader]

@ankur, st(2) implies only difference between each successive pairs.
The question did not provide that the numbers must be even. It says S is an infinite number of positive integers.
Beta set --> 1,3,5,7,9,11,13,15 ... / differences (5+7-1-3=8, 9+11-5-7=8, 9+11-13-15=8...)
OR
Not Beta set --> 2,4,6,8,10,12...

statement (2) is Not Sufficient.

2) sufficient.

If difference is same between each successive pair then we can arrange our set in infinite number of ways to keep odd numbers running / we can even create sets without any odd nos. Both of them denies thats it is not a beta sequence. So should be sufficient.

An inÂ…nite sequence of positive integers is called a "beta
sequence" if the number of odd integers in the sequence is
Â…nite. If S is an inÂ…nite sequence of positive integers, is S a
beta sequence?

(1) The Â…rst ten integers in S are even.
(2) The di¤erence between each successive pair of
terms in S is a constant.

I don't understand why this is C.

[ankur.agrawal]

Oh Careless reading. Misinterpreted each successive pairs .

Thanks .

@ankur, st(2) implies only difference between each successive pairs.
The question did not provide that the numbers must be even. It says S is an infinite number of positive integers.
Beta set --> 1,3,5,7,9,11,13,15 ... / differences (5+7-1-3=8, 9+11-5-7=8, 9+11-13-15=8...)
OR
Not Beta set --> 2,4,6,8,10,12...

statement (2) is Not Sufficient.

2) sufficient.

If difference is same between each successive pair then we can arrange our set in infinite number of ways to keep odd numbers running / we can even create sets without any odd nos. Both of them denies thats it is not a beta sequence. So should be sufficient.

An inÂ…nite sequence of positive integers is called a "beta
sequence" if the number of odd integers in the sequence is
Â…nite. If S is an inÂ…nite sequence of positive integers, is S a
beta sequence?

(1) The Â…rst ten integers in S are even.
(2) The di¤erence between each successive pair of
terms in S is a constant.

I don't understand why this is C.