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Original post by As.1997
Sorry, I meant do you agree with the approach in post 36.

Forget about D. Why do the 3 mileage roundings work for E?
Reply 41
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Original post by mqb2766
Forget about D. Why do the 3 mileage roundings work for E?

I believe it is because it is the only one at W20 rounds to 20.
W18 (18.4,18.5) --> rounds to 18 and 19
W19 (18.9,19.0) --> rounds to 19
W20 (19.4,19.5) --> rounds to 19 and 20.
(we discussed this previously?) So you may be referring to something else?
Original post by As.1997
I believe it is because it is the only one at W20 rounds to 20.
W18 (18.4,18.5) --> rounds to 18 and 19
W19 (18.9,19.0) --> rounds to 19
W20 (19.4,19.5) --> rounds to 19 and 20.
(we discussed this previously?) So you may be referring to something else?

The w20 - w19 is a bit over half a mile. So modify your ans a bit?
Between 18.4 and 18.5 would go to 18.4. You could argue that it could be exactly 18.5 which would indeed be rounded to 19, but assuming the data is represented to a few dps, this will "never" happen.
Reply 43
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Modifying my answer I get:
W18 (18.4,18.4999) — rounds to 18
W19 (18.9,18.999) — rounds to 19
W20 (19.5-20)— rounds to 20
Original post by As.1997
Modifying my answer I get:
W18 (18.4,18.4999) — rounds to 18
W19 (18.9,18.999) — rounds to 19
W20 (19.5-20)— rounds to 20

Renerally round brackets means < or > whereas square ones mean <= or >=. So you were ok.
Looks good now and you should see why the others don't work.
If you work forwards from another value, see what is wrong to understand the reasoning.
Reply 45
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Original post by mqb2766
Renerally round brackets means < or > whereas square ones mean <= or >=. So you were ok.
Looks good now and you should see why the others don't work.
If you work forwards from another value, see what is wrong to understand the reasoning.

Working forwards for every other option ABCD, it will never get a value that rounds to 20 which is why the others don't work.
Original post by As.1997
Working forwards for every other option ABCD, it will never get a value that rounds to 20 which is why the others don't work.

Even if you were not using the multichoice answers, can you see how E lies on the rounding boundaries for the 18 and 20 mile markers, so that is the only solution? To derive in a forwards fashion,
At 20 miles, must be in (19.5,20.5)
At 19 miles, must have been in (19.5,20) as subtracting 0.5 gives (19,19.5)
At 18 miles, must have been 19.5 as subtractung 1+ gives 18.5-
Where we have used the small distance (>0.5) from 20-19 to give a tiny bit of wiggle room.
Reply 47
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Original post by mqb2766
Even if you were not using the multichoice answers, can you see how E lies on the rounding boundaries for the 18 and 20 mile markers, so that is the only solution? To derive in a forwards fashion,
At 20 miles, must be in (19.5,20.5)
At 19 miles, must have been in (19.5,20) as subtracting 0.5 gives (19,19.5)
At 18 miles, must have been 19.5 as subtractung 1+ gives 18.5-
Where we have used the small distance (>0.5) from 20-19 to give a tiny bit of wiggle room.

I'm quite lost.
You lost me here, "At 19 miles, must have been in (19.5,20.5) as subtracting 0.5 gives (19,19.5)".
At 20 miles (20.5,19.5) made sense to me.
At 19 miles, I thought it should be (19.5,18.5) (since we are subtracting by just over 0.5? which is roughly 0.5)
At 18 miles, I thought it should be (18.5,17.5) (here we are just supposed to decrease the upper and lower boundaries at 19miles by 0.5?)
Original post by As.1997
I'm quite lost.
You lost me here, "At 19 miles, must have been in (19.5,20.5) as subtracting 0.5 gives (19,19.5)".
At 20 miles (20.5,19.5) made sense to me.
At 19 miles, I thought it should be (19.5,18.5) (since we are subtracting by just over 0.5? which is roughly 0.5)
At 18 miles, I thought it should be (18.5,17.5) (here we are just supposed to decrease the upper and lower boundaries at 19miles by 0.5?)

Yes, i was just trying to be brief.
The values i was giving represented the range of values at 20 which satisfy the constraints at 19 and at 18.
Reply 49
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Original post by mqb2766
Even if you were not using the multichoice answers, can you see how E lies on the rounding boundaries for the 18 and 20 mile markers, so that is the only solution? To derive in a forwards fashion,
At 20 miles, must be in (19.5,20.5)
At 19 miles, must have been in (19.5,20) as subtracting 0.5 gives (19,19.5)
At 18 miles, must have been 19.5 as subtractung 1+ gives 18.5-
Where we have used the small distance (>0.5) from 20-19 to give a tiny bit of wiggle room.

For the 19 miles -> how did you get (19.5,20)? Comparing it to the range for 20 miles (19.5,20.5) you kept 19.5 the same but for 20.5 you did 20.5-0.5=20.0. Shouldn't you have taken 0.5 from both 19.5 and 20.5 to give (19,20).

Would I be right in saying, I think you were trying to explain that from W20 it can be anything between 20.5-19.5 and if we assume from W20 to Warrington it is 19.5 subtracting 1 gives us 18.5 at least for W18. But since it is supposed to be just over 1 i.e. due to >0.5+0.5=just over 1 we should get just under 18.5. E satisfies this and is, therefore, the answer.
(edited 3 years ago)
Original post by As.1997
For the 19 miles -> how did you get (19.5,20)? Comparing it to the range for 20 miles (19.5,20.5) you kept 19.5 the same but for 20.5 you did 20.5-0.5=20.0. Shouldn't you have taken 0.5 from both 19.5 and 20.5 to give (19,20).

Would I be right in saying, I think you were trying to explain that from W20 it can be anything between 20.5-19.5 and if we assume from W20 to Warrington it is 19.5 subtracting 1 gives us 18.5 at least for W18. But since it is supposed to be just over 1 i.e. due to >0.5+0.5=just over 1 we should get just under 18.5. E satisfies this and is, therefore, the answer.

20 gives:
(19.5,20.5)
The intersection of 20 (-0.5) and 19:
(19.5,20.5)-0.5 AND (18.5,19.5) = (19.5,20)
Then its intersection with 18:
(19.5,20)-1 AND (17.5,18.5) = 19.5
(edited 3 years ago)
Reply 51
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Original post by mqb2766
20 gives:
(19.5,20.5)
The intersection of 20 (-0.5) and 19:
(19.5,20.5)-0.5 AND (18.5,19.5) = (19.5,20)
Then its intersection with 18:
(19.5,20)-1 AND (17.5,18.5) = 18.5

If 20 gives (19.5,20.5)
Then (19.5,20.5)-0.5 = (19,20)?
19 gives (18.5,19.5)
The intersection between 20 (-0.5) and 19 should give (19,19.5)?
(I've put an attachment to show what I got (19,19.5) --> the intersection being the block of red)
(edited 3 years ago)
IMG_1DE2B44D5194-1.jpg92.2KB
Original post by As.1997
If 20 gives (19.5,20.5)
Then 20-(0.5) = (19,20)?
19 gives (18.5,19.5)
The intersection between 20 (-0.5) and 19 should give (19,19.5)?
(I've put an attachment to show what I got (19,19.5)

I was keeping it in terms of the original interval, but yes.
Reply 53
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Original post by mqb2766
I was keeping it in terms of the original interval, but yes.

I think you're trying to illustrate that the distance between W18 to Warrington should be really close to 18.5. Therefore, the only option that is closest to 18.5 is E since we include the idea of just over half which makes it go slightly below 18.5.
Original post by As.1997
I think you're trying to illustrate that the distance between W18 to Warrington should be really close to 18.5. Therefore, the only option that is closest to 18.5 is E since we include the idea of just over half which makes it go slightly below 18.5.

When you pass the 20 milemarker, the true distance must be ~19.5. Thats it.
Reply 55
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Original post by mqb2766
When you pass the 20 milemarker, the true distance must be ~19.5. Thats it.

Fair enough. Also, I tried to use 20.5 instead of 19.5 to see if I could still get the correct answer.
20.5-1=19.5. Since it is supposed to be just over 1, we should get just below 19.5 (we have no options that fit this).
Therefore the only approach left is to use the lower boundary i.e. 19.5-1=18.5 since it is supposed to be just over 1 we take it to be E.

Thank you for your help :smile:

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