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Emily and Tammi must both run from point A to reach the finish line, w

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Emily and Tammi must both run from point A to reach the finish line, w  [#permalink]

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New post Updated on: 25 Oct 2015, 05:48
3
7
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

66% (02:55) correct 34% (02:34) wrong based on 166 sessions

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Emily and Tammi must both run from point A to reach the finish line, which stretches from the origin to point B, but they have to run on two different paths, where Emily will end up 4 yards away from Tammi on the finish line. If Tammi ran a total of 10 yards, how many yards more did Emily run than Tammi?

A. 2
B. \(4\sqrt{2}−10\)
C. \(6\sqrt{5}−10\)
D. \(4\sqrt{2}−8\)
E. \(6\sqrt{5}\)


Attachment:
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Geometry_Img67.png [ 7.83 KiB | Viewed 4220 times ]

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Originally posted by shasadou on 24 Oct 2015, 05:32.
Last edited by Bunuel on 25 Oct 2015, 05:48, edited 1 time in total.
Edited the question.
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Emily and Tammi must both run from point A to reach the finish line, w  [#permalink]

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New post 02 Dec 2015, 00:12
2
Hi everyone, I took close to 4 minutes to solve this. :| Are there any suggestions on how I can halve my time spent in a question like this?

here's how i solved this question..

we know that Tammi ran 10 yards (t= 10) and we do not know how far Emily (e) ran.
question: e - t = ?

1) using the Pythagorean theorem, I solved for x.
10^2 = 6^2 + x^2
x = \(\sqrt{64}\)

2) next, I solved for the distance that Emily ran,e.
[given Emily will end up 4 yards away from Tammi on the finish line, the base of the triangle is \(\sqrt{64}\)+4]

e^2 = 6^2 + (\(\sqrt{64}\)+4)^2
e^2 = 36 + (\(\sqrt{64}\)+4)(\(\sqrt{64}\)+4)
e^2 = 36 + 64 + 4\(\sqrt{64}\) + 4\(\sqrt{64}\) + 16
e^2 = 116 + 8\(\sqrt{64}\)
e^2 = 116 + 8(8)
e^2 = 180
e =\(\sqrt{180}\)

3) now that I've obtained both e and t, time to plug it into the original question, e - t = ?
\(\sqrt{180}\) - 10
=\(\sqrt{36*5}\) - 10
= 6\(\sqrt{5}\) - 10

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Re: Emily and Tammi must both run from point A to reach the finish line, w  [#permalink]

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New post 13 May 2016, 09:19
Foxed :( , marked E ; did not realize that the question asked for how much more ! A classic GMAT trap !
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Re: Emily and Tammi must both run from point A to reach the finish line, w  [#permalink]

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New post 01 Aug 2016, 02:31
whitehalo wrote:
Hi everyone, I took close to 4 minutes to solve this. :| Are there any suggestions on how I can halve my time spent in a question like this?

here's how i solved this question..

we know that Tammi ran 10 yards (t= 10) and we do not know how far Emily (e) ran.
question: e - t = ?

1) using the Pythagorean theorem, I solved for x.
10^2 = 6^2 + x^2
x = \(\sqrt{64}\)

2) next, I solved for the distance that Emily ran,e.
[given Emily will end up 4 yards away from Tammi on the finish line, the base of the triangle is \(\sqrt{64}\)+4]

e^2 = 6^2 + (\(\sqrt{64}\)+4)^2
e^2 = 36 + (\(\sqrt{64}\)+4)(\(\sqrt{64}\)+4)
e^2 = 36 + 64 + 4\(\sqrt{64}\) + 4\(\sqrt{64}\) + 16
e^2 = 116 + 8\(\sqrt{64}\)
e^2 = 116 + 8(8)

e^2 = 180
e =\(\sqrt{180}\)

3) now that I've obtained both e and t, time to plug it into the original question, e - t = ?
\(\sqrt{180}\) - 10
=\(\sqrt{36*5}\) - 10
= 6\(\sqrt{5}\) - 10

Image


The approach is correct. I would only simply the highlighted section further to make it
\(x = \sqrt{64} = 8\)

That would in in turn simplify the calculation for e.
\(e^2 = 6^2 + (8+4)^2\)
\(e^2 = 36 + (12)^2\)
\(e^2 = 36 + 144\)
\(e^2 = 180\)
\(e = \sqrt{180}\)
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Emily and Tammi must both run from point A to reach the finish line, w  [#permalink]

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New post 17 Jun 2017, 03:56
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shasadou wrote:
Image
Emily and Tammi must both run from point A to reach the finish line, which stretches from the origin to point B, but they have to run on two different paths, where Emily will end up 4 yards away from Tammi on the finish line. If Tammi ran a total of 10 yards, how many yards more did Emily run than Tammi?

A. 2
B. \(4\sqrt{2}−10\)
C. \(6\sqrt{5}−10\)
D. \(4\sqrt{2}−8\)
E. \(6\sqrt{5}\)


Attachment:
The attachment Geometry_Img67.png is no longer available


The hidden inference in this question is that distance Tammi travels represents a pythagorean triplet triangle ( 6 8 10)- there's really only two ways that Tammi could have traveled 10 yards- she could go straight down from (0,6) to the origin (0,0) and then travel to (4,0); however, if this was done then the distance Emily runs would actually be the same as Tammie and thus false. Therefore, the distance Tammi runs represents the hypotenuse of the triangle - 10. If the hypotenuse of the triangle is 10 then the x coordinate of Tammi's current position is 8 as in (8,0). And because Emily must be 4 yards away, Emily's coordinate is (12,0). From here apply the distance formula- Emily's distance from her current position and Point A and then subtract it by the distance Tammi traveled- 10 yards.

Thus

"C"
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Emily and Tammi must both run from point A to reach the finish line, w  [#permalink]

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New post Updated on: 19 Jul 2017, 03:08
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shasadou wrote:
Image
Emily and Tammi must both run from point A to reach the finish line, which stretches from the origin to point B, but they have to run on two different paths, where Emily will end up 4 yards away from Tammi on the finish line. If Tammi ran a total of 10 yards, how many yards more did Emily run than Tammi?

A. 2
B. \(4\sqrt{2}−10\)
C. \(6\sqrt{5}−10\)
D. \(4\sqrt{2}−8\)
E. \(6\sqrt{5}\)


Attachment:
Geometry_Img67.png


Let the origin be O. Let the position of Tammi shown in diagram be T and the position of Emily shown is diagram be E.
So, OA =6
AT = 10 ( Tammi ran a total of 10 yards)
From right angled triangle OAT
OT =\(\sqrt{(10^2 - 6^2)}\) = 8 (we can also figure it out from pythagorean triplet 3,4,5 or 6,8,10

So, OE = OT + TE = 8 + 4 = 12

AE = \(\sqrt{(OA^2 + OE^2)} = \sqrt{6^2 + 12 ^2} = \sqrt{36+144} =\sqrt{180} = 6\sqrt{5}\)


Emily ran \(6\sqrt{5} - 10\) yards more than Tammi.

Answer C
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Originally posted by shashankism on 19 Jul 2017, 02:16.
Last edited by shashankism on 19 Jul 2017, 03:08, edited 2 times in total.
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Re: Emily and Tammi must both run from point A to reach the finish line, w  [#permalink]

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New post 19 Jul 2017, 02:26
shashankism wrote:
shasadou wrote:
Image
Emily and Tammi must both run from point A to reach the finish line, which stretches from the origin to point B, but they have to run on two different paths, where Emily will end up 4 yards away from Tammi on the finish line. If Tammi ran a total of 10 yards, how many yards more did Emily run than Tammi?

A. 2
B. \(4\sqrt{2}−10\)
C. \(6\sqrt{5}−10\)
D. \(4\sqrt{2}−8\)
E. \(6\sqrt{5}\)


Attachment:
Geometry_Img67.png


Let the origin be O.
So, OA =6
AT = 10 ( Tammi ran a total of 10 yards)
From right angled triangle OAT
OT =\sqrt{(10^2 - 6^2)} = 8 (we can also figure it out from pythagorean triplet 3,4,5 or 6,8,10

So, OE = OT + TE = 8 + 4 = 12

AE = \sqrt{(OA^2 + OE^2)} = \sqrt{6^2 + 12 ^2} = \sqrt{36+144} =\sqrt{180} = 6\sqrt{5}


Emily ran 6\sqrt{5} - 10 yards more than Tammi.

Answer C


Very simple and straightforward approach, thank you.
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Re: Emily and Tammi must both run from point A to reach the finish line, w  [#permalink]

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New post 21 Jul 2017, 01:58
TimeTraveller wrote:

Very simple and straightforward approach, thank you.


That's the beauty of solving questions in GMAT Club w, we get to know the shortest and the best possible approach to solve a problem. Many people contribute to the solution and hence we get the best one .. :)
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Re: Emily and Tammi must both run from point A to reach the finish line, w  [#permalink]

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Re: Emily and Tammi must both run from point A to reach the finish line, w   [#permalink] 19 Feb 2019, 01:44
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