number properties

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sud21: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sat Nov 12, 2011 3:21 am; Thanked: 1 times; Followed by:2 members

number properties

by sud21 » Fri Jan 27, 2012 9:40 am

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

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Source: Beat The GMAT — Data Sufficiency | Fri Jan 27, 2012 9:40 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 am; Thanked: 230 times; Followed by:21 members

by shankar.ashwin » Fri Jan 27, 2012 7:31 pm

(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

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Sat Jan 28, 2012 2:50 pm

@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

shankar.ashwin wrote:(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

Success doesn't come overnight!

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 am; Location: Utrecht, The Netherlands; Thanked: 318 times; Followed by:52 members

by neelgandham » Sat Jan 28, 2012 3:46 pm

pemdas wrote: 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 ??

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 am; Location: New Delhi, India; Thanked: 130 times; Followed by:9 members; GMAT Score:720

by rijul007 » Sat Jan 28, 2012 8:23 pm

shankar.ashwin wrote: (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

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 am; Location: New Delhi, India; Thanked: 130 times; Followed by:9 members; GMAT Score:720

by rijul007 » Sat Jan 28, 2012 8:32 pm

sud21 wrote: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

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Sun Jan 29, 2012 10:04 am

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

neelgandham wrote:
pemdas wrote: 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 ??

Success doesn't come overnight!

Quote

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 am; Location: Utrecht, The Netherlands; Thanked: 318 times; Followed by:52 members

by neelgandham » Sun Jan 29, 2012 10:11 am

pemdas wrote: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,......}

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/