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# If x and y are distinct points on a number line,and integer

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Director
Joined: 25 Oct 2008
Posts: 574
Location: Kolkata,India
If x and y are distinct points on a number line,and integer [#permalink]

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20 Jul 2009, 05:22
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If x and y are distinct points on a number line,and integer z is located between x and y,what is the number of different possible values of z?
1. the distance between x and y is 6
2. xy is not an integer.

$$OA:c$$

Guys while solving this question a no. of conceptual questions came to mind.Please clarify?
When we are talking about a number line,are we supposed to think that only (...-2,-1,0,1,2,....) can be represented?(-ives,zero and +ives)What about 2.5 ,2.6 (i.e decimals).Factually they CAn be represented right?I remember reading somewhere the definition of INTEGERS:Numbers that can be represented on the number line are called integers.Tha same question had some to mind then.While -2,0,2 are integers, .5,2.5 etc are not.

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Senior Manager
Joined: 23 Jun 2009
Posts: 355
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Re: distinct points on a number line-conceptual questions [#permalink]

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20 Jul 2009, 06:15
1 insuff; because if x and y are integers (one is integer, the other must be integer too) then there are 5 integers between them. If they are not integers there are 6 integers between them.
2 insuff; we do not know the difference between x and y. We only understand that at least one of them must be a number that is not an integer. Because only two integer form an integer when multiplied.
Both of them sufficient. Because we know that they are not integers. There must be 6 numbers.

Look this example;
x=0 y=6; b/w them 1,2,3,4,5
x=0,1 y=6,1 b/w them 1,2,3,4,5,6

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Re: distinct points on a number line-conceptual questions   [#permalink] 20 Jul 2009, 06:15
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