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October 18th, 2009, 03:42 AM   #1
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logic question

My logic is not working. Someone pls help me out. Here the question is :

On the M53 is a sign Warrington 20. Just over half a mile further on is another sign ‘Warrington 19’. This is not surprising, since the distances are rounded to the nearest whole number of miles e.g numbers of 4.5 and over but less than 5.5 become 5, numbers of 4 and over but less than 4.5 become 4. Half a mile further along the road is a sign showing ‘Warrington 18’.
The distance must now be between ?

A) 17.5 miles and 17.6 miles
B) 17.6 miles and 18.0 miles
C) 18.0 miles and 18.2 miles
D) 18.2 miles and 18.4 miles
E) 18.4 miles and 18.5 miles

Thanks a ton.
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October 18th, 2009, 04:09 AM   #2
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Re: logic question

You're welcome. What reasoning did you apply yet to each statement?
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October 18th, 2009, 06:04 AM   #3
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The answer needn't mention the Warrington 19 sign.

Is it clear that the Warrington 20 sign is at least 19.5 miles from Warrington (due to rounding)?

If "a little over" a mile is less than 1.1 miles, the Warrington 18 sign must be more than how far from Warrington? Also, it must be less than how far from Warrington? The answers are the distances to look for in the list of candidate answers.
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October 18th, 2009, 08:37 AM   #4
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Re:

Quote:
Originally Posted by skipjack
The answer needn't mention the Warrington 19 sign.

Is it clear that the Warrington 20 sign is at least 19.5 miles from Warrington (due to rounding)?

If "a little over" a mile is less than 1.1 miles, the Warrington 18 sign must be more than how far from Warrington? Also, it must be less than how far from Warrington? The answers are the distances to look for in the list of candidate answers.
Thanks Skipjack , but i still cant figure out . THis is what i tought .

Warrington 20 - the 20 here refers to the distance from Warrington.

in the begining , over a half a mile away from W 20 , so the distance from Warrington can now be 19.4 , 19.3 .. anything less than 19.5 .. The distance becomes W 19 due to rounding .

Now , it says half a mile away from W19 , so its 18.5 away .. but when you round it off , it becomes 19 .. supposedly to be 18 ??
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October 18th, 2009, 11:32 AM   #5
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Try to be more concise. You made a slip at the end by saying "so it's 18.5 away". The distance of W19 is 19 after rounding, not exactly 19. If, for example, W19 is 18.95 miles from Warrington, W18 will be 18.45 miles from Warrington, which does round to 18 miles.

Try again to follow the method I outlined previously. If you bear in mind that the distance from W20 to W18 is a little over 1 mile, the questions I asked should be quite easy to answer (without considering W19 at all).
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October 18th, 2009, 09:14 PM   #6
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Re:

Quote:
Originally Posted by skipjack
Try to be more concise. You made a slip at the end by saying "so it's 18.5 away". The distance of W19 is 19 after rounding, not exactly 19. If, for example, W19 is 18.95 miles from Warrington, W18 will be 18.45 miles from Warrington, which does round to 18 miles.

Try again to follow the method I outlined previously. If you bear in mind that the distance from W20 to W18 is a little over 1 mile, the questions I asked should be quite easy to answer (without considering W19 at all).
Thanks again Skipjack , i think i am getting what u mean ..

Firstly , W20 must be at least 19.5 miles from W . Then it says here W19 is just over half a mile which assumed to be 0.6 from W20 .

How do we know the assumption we made above ' more than half a mile is 0.6 is valid , cant it be 0.7 ?

I just realised you have given me the answer , which is E .
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October 19th, 2009, 05:08 PM   #7
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Re: logic question

Skipjack, you read that the question said "just over a mile," when it says "just over half a mile."

I was confused about this too, but just figured it out.

From the 20-mile marker, we know that the driver has gone just over a mile total ("just over half a mile" to 19, then half a mile to 1. Let's assume the driver has traveled 1.1 miles.

So while it seems like the answer should be essentially 19 miles away, the trick is that the original 20 sign could be almost .5 miles off. So at worst, the 20 mile sign would have been at approx 19.5-19.6, at which point the 18 mile one would be around 18.4-18.5, which would also let the 18-mile marker be accurate by the question's definition (roundable to 1.
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October 19th, 2009, 09:31 PM   #8
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Re: logic question

Quote:
Originally Posted by Mortifera
Skipjack, you read that the question said "just over a mile," when it says "just over half a mile."

I was confused about this too, but just figured it out.

From the 20-mile marker, we know that the driver has gone just over a mile total ("just over half a mile" to 19, then half a mile to 1. Let's assume the driver has traveled 1.1 miles.

So while it seems like the answer should be essentially 19 miles away, the trick is that the original 20 sign could be almost .5 miles off. So at worst, the 20 mile sign would have been at approx 19.5-19.6, at which point the 18 mile one would be around 18.4-18.5, which would also let the 18-mile marker be accurate by the question's definition (roundable to 1.
Thanks , but i still have a little doubt here .

Say if the a little over than 1 mile is < 1.3 instead of 1.1 ..

THen C can be the answer too .

From 19.5 - 20.0 ,

19.7 - 1.3 = 18.4

19.5 -1.3 =18.2

where 19.7 and 19.5 would round off to 20 and 18.4 and 18.2 would round off to 18 .

So my question remains , why can we be so sure that the assumption of a little over is < 1.1 ??
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October 20th, 2009, 09:58 AM   #9
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That doesn't work, since 1.2 is less than 1.3, but 19.65 - 1.2 = 18.45, so it isn't the case that the W18 sign must be less than 18.4 miles from Warrington.
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October 20th, 2009, 05:14 PM   #10
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Re: logic question

In math problems, if something says "Just over..." it is standard for this to mean literally just enough to push it past whatever limit you're observing.

An odd example that mightn't even be relevant, but whatever:

if three towns lie on a straight line with each other, like: Muddywater------Dullville---------------------Sudstown

and Muddywater to Dullville is 1 mile exactly, and Dullville to Sudstown is 5 miles.

We have a cyclist at Muddywater, and he cycles just over 1 mile towards Sudstown. We now know that the cyclist is between Dullville and Sudstown, but we also know that the cyclist is almost touching Dullville - he's literally JUST gone past it.




Now, if we draw a map of the M53 out like so:

Code:
         20.5        19.5        18.5        17.5                ...             Warrington
-----------------------------------------------------------------------------------------------
           |  *        |       *   |    *      |     
Driver     | W20       | W19       | W18       |     
Start      | in here   | in here   | in here   |     
           | somewhere | somewhere | somewhere |     
-----------------------------------------------------------------------------------------------
we know that the driver travels JUST OVER half a mile between W20 and W19, and EXACTLY half a mile between W19 and W18,

for this to work, our map must look like:
Code:
         20.5        19.5        18.5        17.5                ...             Warrington
-----------------------------------------------------------------------------------------------
           |          *|     *     |*          |     
Driver     |           |           |           |
Start      |           |           |           |
           |           |           |           | 
-----------------------------------------------------------------------------------------------
where the *s are the signs. Any arrangement other than that will have the W20 sign in the W19 region or the W18 sign in the W19 region, which isn't allowed.

So, the W18 sign must be JUST past the 18.5 mile mark (like the cyclist was JUST past Dullville), which means it must be in the region 18.4 < W18 < 18.5, answer E.



@skipjack - don't wanna steal your show, you've been explaining this well, I'm just trying to lay it out differently.

@gladtoknow - It's a pretty difficult thing to pick up if you don't automatically understand it right off the bat, and if you need to I'll try to lay it out a different way again, with clearer steps, but it's late and i'm tired and have to be up in 4 hours for class =P
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