Problem Solving 101?

Question

Please help I honestly don't know how to do this one.

Jim knows that x is an integer greater than 2 and less tahn 8. Kim knows that x is an integer less tahn 9 and greater than 4. Tim knowns that x is an integer greater than or eqaul to 2 and less than or equal to 6. How many possible values are there for x? What are the possible values for x?

Answer 1

x is an integer.
Jim knows
2 Kim knows
4 Tim knows
2
IF both the statements ARE TRUE:

1.THERE EXIST 2 POSSIBLE VALUES OF x.
2.The Possible VALUES OF x ARE 5 and 6

Answer 2

Jim 2> 3 4 5 6 7 <8
Kim 4>5 6 7 8 <9
Tim 2>=3 4 5=<6

5 or 6

Answer 3

Let us first represent the "filters":

2 < x < 8 is 3, 4, 5, 6, 7
4 < x < 9 is 5, 6, 7, 8
2 <= x <= 6 is 2, 3, 4, 5, 6

now, let us have the values COMMON in the three conditions, with no repeating numbers:

5, 6

There are positive integers which qualified in the three conditions.
The numbers are 5 and 6.

Answer 4

Jim = 2 < x < 8 => ]2; 8[
Kim = 4 < x < 9 => ]4; 9[
Tim = 2 =< x >=6 => ]4; 6]

For intersection: ]2; 8[/\]4; 9[/\]4; 6] = ]4; 6]
So, ]2; 8[U]4; 9[U]4; 6] = ]2; 9] => {x E R | 2 < x < 8 ou 2 =< x >=6}.
:: /\ = intersection
<><

Answer 5

two; 5 or 6

Answer 6

Entirely depends on how many of the given statements are true.

If all are true then only two values 5 & 6.

Answer 7

x>4 (Kim). x equal to or less than 6
x = 5 or 6

Answer 8

5 and 6 are your only two possibilities

Answer 9

You've got the answer, but you can get it by a process of elimination - you start by knowing it must be 3,4,5,6,or 7 and each statement reduces your choices.