Which of these statements is (are) necessarily true?

eddy2017

eddy2017

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hello and warm greetings to professors, tutors, and helpers alike: I need help with this.
A circular bracelet contains 5 charms, A, B, C, D, and E, attached at specific points around the bracelet, with the clasp located between charms A and B. The bracelet is unclasped and stretched out into a straight line. On the resulting linear bracelet, charm C is between charms A and B, charm D is between charms A and C, and charm E is between charms C and D.
Which of these statements is (are) necessarily true?
I. The distance between charms B and E is greater than the distance between charms A and D.
II. Charm E is between charms B and D.
III. The distance between charms D and E is less than the distance of bracelet between charms A and C.
  • II and III
  • None of these is necessarily true
  • I, II, and III
  • II only
I have even tried to represent the whoe thing with a drawing. I tried to do it. makes some sense. i want you to confirm it for me.
i will go for II, and III because, when i compare that statement with the drawing i made, it checks out.
 

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eddy2017 said:
hello and warm greetings to professors, tutors, and helpers alike: I need help with this.
A circular bracelet contains 5 charms, A, B, C, D, and E, attached at specific points around the bracelet, with the clasp located between charms A and B. The bracelet is unclasped and stretched out into a straight line. On the resulting linear bracelet, charm C is between charms A and B, charm D is between charms A and C, and charm E is between charms C and D.
Which of these statements is (are) necessarily true?
I. The distance between charms B and E is greater than the distance between charms A and D.
II. Charm E is between charms B and D.
III. The distance between charms D and E is less than the distance of bracelet between charms A and C.
  • II and III
  • None of these is necessarily true
  • I, II, and III
  • II only
I have even tried to represent the whoe thing with a drawing, still, notihng comes to mind.
any hint appreciated.
if i have to give it a try i will go for I, II, and III because, when i compare that statement with the drawing i made, it checks out.
Click to expand...
You need to follow the problem statement exactly in order to draw the correct diagram. Don't assume the order A, B, C, D, E.
 
eddy2017 said:
hello and warm greetings to professors, tutors, and helpers alike: I need help with this.
A circular bracelet contains 5 charms, A, B, C, D, and E, attached at specific points around the bracelet, with the clasp located between charms A and B. The bracelet is unclasped and stretched out into a straight line. On the resulting linear bracelet, charm C is between charms A and B, charm D is between charms A and C, and charm E is between charms C and D.
Which of these statements is (are) necessarily true?
I. The distance between charms B and E is greater than the distance between charms A and D.
II. Charm E is between charms B and D.
III. The distance between charms D and E is less than the distance of bracelet between charms A and C.
  • II and III
  • None of these is necessarily true
  • I, II, and III
  • II only
I have even tried to represent the whole thing with a drawing. I tried to do it. makes some sense. i want you to confirm it for me.
i will go for II, and III because, when i compare that statement with the drawing i made, it checks out.
Click to expand...
Excellent idea of locating the charms on a straight-line. But pay attention to the statements as you are drawing the locations of the charms.

pay special attention to:

"....with the clasp located between charms A and B. The bracelet is unclasped and stretched out....."​
​
According to those parts

Where are the relative locations of A & B​
 
lev888 said:
You need to follow the problem statement exactly in order to draw the correct diagram. Don't assume the order A, B, C, D, E.
Click to expand...
then is
  • II and III
  • lev888 said:
    You need to follow the problem statement exactly in order to draw the correct diagram. Don't assume the order A, B, C, D, E.
    Click to expand...
    but if i can't assume the order how can i pinpoint where the charms are. i don't find a way to map out the points. the problems says for example that on the resulting linear line C is between A and B. if i can't assign physical points in this order, how can i do it, then?.
 
eddy2017 said:
then is
  • II and III
  • but if i can't assume the order how can i pinpoint where the charms are. i don't find a way to map out the points. the problems says for example that on the resulting linear line C is between A and B. if i can't assign physical points in this order, how can i do it, then?.
Click to expand...
Draw a line. Then draw the charms on it one at a time as you read the question.
"the clasp located between charms A and B. The bracelet is unclasped and stretched out into a straight line." - what does this tell you about the location of A and B?
 
Subhotosh Khan said:
Excellent idea of locating the charms on a straight-line. But pay attention to the statements as you are drawing the locations of the charms.

pay special attention to:

"....with the clasp located between charms A and B. The bracelet is unclasped and stretched out....."​
​
According to those parts

Where are the relative locations of A & B​
Click to expand...
nothing comes to mind. all i get is that between A and B i found charm C. can't deduct anything about the clasp.
 
lev888 said:
Draw a line. Then draw the charms on it one at a time as you read the question.
"the clasp located between charms A and B. The bracelet is unclasped and stretched out into a straight line." - what does this tell you about the location of A and B?
Click to expand...
okay, let me noodle it a bit.
 
eddy2017 said:
nothing comes to mind. all i get is that between A and B i found charm C. can't deduct anything about the clasp.
Click to expand...
i think A and B are at the enpoints of the bracelet, right, cos the clasp is located between them.
 
lev888 said:
Draw the bracelet with the clasp closed and note that "the clasp located between charms A and B". Then "open" the clasp. Where are A and B now?
Click to expand...
But like you say, if i open it and lay it out in all its length then A and B are the startpoints.

A_____________________________________B
 
eddy2017 said:
at the startpoints.
A_____________________________________B
Click to expand...
Good. I would say "end points". Now draw the remaining charms one at a time using only info from the question, without making any assumptions. The final diagram will show only the order of charms, we know nothing about distances between each pair of neighboring charms. Then see what must be true based on the info you have. Again, no assumptions.
 
think this is a representation of what the problem says, once i know where A and B are.
yes, endpoints. that is the correct term.
The distance between charms B and E is greater than the distance between charms A and D.
false cos it could be the same.
II. Charm E is between charms B and D . :thumbup: true statement according to the diagram.
III. The distance between charms D and E is less than the distance of bracelet between charms A and C.:thumbup: true
like you well pointed out, assuming physical points does not work cos they can be anywhere within a certain space. i see it now clearly.
 
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thanks lev and Dr Khan. thanks for teaching me to think rationally. there is no other path in math.
 
lev888 said:
I agree with False. But why only "it could be the same"?
Click to expand...
yes, you're right. it is not because of that. Can't tell for sure. maybe because A and B are closely together.
i get no tip by looking at the drawing.
 
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eddy2017 said:
yes, you're right. it is not because of that. Can't tell for sure. maybe because A and B are closely together.
Click to expand...
As I wrote earlier, we know nothing about how close any 2 adjacent charms are.
 
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