number properties

[sud21]

K,N are integers. S is a set, and S=K^N. K=?
1). The difference between two numbers in S is 1
2). One of the numbers in S is more than 1/4 and less than 1

[shankar.ashwin]

(1) The only value which could satisfy this is 2^0 = 1 and 2^1 =2 and 2-1=1. Hence we can say K=2 - Sufficient

(2) Given K and N are integers, any (integer)^(integer) = integer. This statement is faulty and can never hold true.

A IMO

[pemdas]

@shankar, any integer^integer is not always integer
example:
2 is integer
-2 is integer
2^(-2)=1/4 non-integer

the condition doesnt' suggest K and N are the elements of set S either

To start the question says S is a set and S is the sum [spoiler]/assumption made is that S can be only the sum of elements in a set S/[/spoiler] of elements equal to K^N, where K and N are integers

st(1) implies a difference between two numbers. Can be any two numbers with any values, hence Insuff
st(2) suggests some number, a has restriction 1/4<a<1. Nothing more about numbers in S, Insuff
combining st(1&2): b-a or a-b equals 1. Since we are not told explicitly positive or negative integers, we may consider both a-b or b-a
Case 1) a-b=1 and 1/4<a<1, a=b+1, 1/4-1<b<1-1 OR -3/4<b<0
a+b>-3/4+1/4, a+b>-1/2
a+b<0+1, a+b<1. Thus -1/2<a+b<0 which is possible for several values K=-4, N=-1, K^N=-1/4 also K=-3, N=-1, K^N=-1/3

we don't need to test b-a=1 as there are too many choices already and this is Insuff

e

(1) The only value which could satisfy this is 2^0 = 1 and 2^1 =2 and 2-1=1. Hence we can say K=2 - Sufficient

(2) Given K and N are integers, any (integer)^(integer) = integer. This statement is faulty and can never hold true.

A IMO

[neelgandham]

To start the question says S is a set and S is the sum of elements equal to K^N, where K and N are integers

where is it mentioned in the question that S = Sum sum of elements equal to K^N ??

[rijul007]

(2) Given K and N are integers, any (integer)^(integer) = integer. This statement is faulty and can never hold true.

Are you sure?

coz 2^(-2) = 1/4

where both 2 and -2 are integers

[rijul007]

K,N are integers. S is a set, and S=K^N. K=?
1). The difference between two numbers in S is 1
2). One of the numbers in S is more than 1/4 and less than 1

St(1)The difference between two numbers in S is 1

This can be true only for K=2
K^0 = 1
K^1 = 2
The differece is 1
SUFFICIENT

St(2)One of the numbers in S is more than 1/4 and less than 1

K=2
K^(-1) = 1/2
1/4 < 1/2 < 1

K=3
K^(-1) = 1/3
1/4 < 1/3 < 1

NOT SUFFICIENT

Option A

[pemdas]

what does S=K^N stand for then? is it function of something else?

To start the question says S is a set and S is the sum of elements equal to K^N, where K and N are integers

where is it mentioned in the question that S = Sum sum of elements equal to K^N ??

[neelgandham]

what does S=K^N stand for then? is it function of something else?

I am sorry mate, I am not really sure what it is. I just wanted to know if 'S = Sum of all integers' is an assumption or If I missed a thing or two in interpreting the question.

What I think it is :
S=K^N, for a constant K and variable N(e.g, K = 2, N={set of all integers))
S={.......2^-2, 2^-1, 2^0, 2^1, 2^2,......}

[shankar.ashwin]

Oops sorry guys... Forgot to include -ve numbers..

Thanks for pointing out pemdas,rijul007 and Neel.. You guys the best

Though I guess A remains the answer..