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

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7 00:00

Difficulty:   65% (hard)

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

HideShow timer Statistics 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 [ 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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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 Senior Manager  S
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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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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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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 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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2 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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2 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.

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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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shashankism wrote: 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.

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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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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