Direction problem

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neya: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Sun Jul 10, 2011 11:19 pm

by neya » Mon Jul 25, 2011 8:38 pm

A man starting from place P walks 2000 steps east,4000 steps south,2828 steps northeast, 4242 steps northwest and 1414 south west in that order. Where He is finally in relation to P?
1. At or very close to P.
2. About 1000 steps north of P.
3. About 1000 steps East of P
4. About 1000 steps west of P
5. About 1000 steps northeast of P

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Source: Beat The GMAT — Problem Solving | Mon Jul 25, 2011 8:38 pm

winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

by winniethepooh » Mon Jul 25, 2011 9:07 pm

The answer is E.
The solution can be well understood if you can draw the directions where P moves from start point.

Well, though I have applied simple logic I don't have a concrete formula or mathematical solution!

As you can see, p first walks Right then goes down South then again moves up in the east direction for 2828 then in the direction of p but surpasses it and goes 4242
the difference between 4242 and 2828(4242+2828= 7000; and the 2000 east and 4000(2000+4000=6000) south is 1000 steps.

Hence, E.

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naveen451: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Sat Jul 16, 2011 11:56 pmFollowed by: 1 member; Location: hyderabad; Thanked: 2 times

by naveen451 » Thu Jul 28, 2011 3:33 am

IMO 5

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ECMoyano: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Jul 14, 2011 7:11 amFollowed by: 1 member; Thanked: 1 times

by ECMoyano » Thu Jul 28, 2011 8:17 am

I tried substituting the numbers in terms of 2000
(i.e. walked x feet east, than 2x south, than roughly 1.5x northeast, so on and so on) but I couldn't really get a clear cut answer. I believe this is a geomotry question, I just wish I had sharper skills in that category.

Just drawing this out, it looks like the person is definitely North east of Point P, but I don't know the exact distance. This looks like a trick question. I may be wrong, but when my first gut jumps at an answer after little to no work, I can almost guarentee that its the wrong answer.

I tried numerous approaches
First I looked at the answers
Only the directions N, E, W, and NE are given (or at point P)
Since South is not taken into account, I disgard the 4000 steps the person went down south.
1 way I did this was I add East vs. West.
2000 + 2828 - 4242 - 1414 = 828. He's about 1,000 steps West of Point P using that approach.

Good question. Would love to see other's approach on this

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