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# If triangles ABC and CDE are each equilateral, what is the

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Senior Manager
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If triangles ABC and CDE are each equilateral, what is the [#permalink]

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08 Feb 2014, 01:47
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55% (hard)

Question Stats:

48% (00:28) correct 52% (00:33) wrong based on 280 sessions

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If triangles ABC and CDE are each equilateral, what is the sum of the perimeters of the two triangles?

(1) Line segment AE measures 25 meters.

(2) Side BC is 2/3 as long as side DE.

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Re: If triangles ABC and CDE are each equilateral, what is the [#permalink]

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09 Feb 2014, 02:30
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If triangles ABC and CDE are each equilateral, what is the sum of the perimeters of the two triangles?

Let the length of each side of equilateral triangle ABC be x and the length of each side of equilateral triangle CDE be y. The sum of their perimeters is $$3x + 3y =3(x+y)$$.

(1) Line segment AE measures 25 meters --> x+y=25 --> $$perimeter=3(x+y)=3*25=75$$. Sufficient.

(2) Side BC is 2/3 as long as side DE --> x=2/3*y. Not sufficient.

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Re: If triangles ABC and CDE are each equilateral, what is the [#permalink]

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09 Feb 2014, 05:55
Bunuel wrote:

If triangles ABC and CDE are each equilateral, what is the sum of the perimeters of the two triangles?

Let the length of each side of equilateral triangle ABC be x and the length of each side of equilateral triangle CDE be y. The sum of their perimeters is $$3x + 3y =3(x+y)$$.

(1) Line segment AE measures 25 meters --> x+y=25 --> $$perimeter=3(x+y)=3*25=75$$. Sufficient.

(2) Side BC is 2/3 as long as side DE --> x=2/3*y. Not sufficient.

Thanks alot for reply Bunuel !

so we assume that ab+cd=25 and bc+de=25...
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Re: If triangles ABC and CDE are each equilateral, what is the [#permalink]

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24 Apr 2014, 01:50
1
Here since DE is not parallel to AB these lines will meet if extended in the upward direction. (diagram is not to actual scale) But if you look at the picture you can notice that if we take point C and superimpose on the point obtained by the intersection of DE and AB, line AB and BC will become one line and line DC and DE will become one more line. Hence ACE will be a equilateral triangle. Again if AE = 25 then the perimeter of ACE will be 75 which is equal to the sum of the perimeters of ABC and CDE
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Re: If triangles ABC and CDE are each equilateral, what is the [#permalink]

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28 May 2015, 23:01
Hi All,

This is a great 'concept' question that many Test Takers would probably get wrong (because they would refuse to do any work on the pad).

We're told that triangles ABC and CDE are EQUILATERAL (meaning that each has 3 equal sides). We're asked for the total PERIMETERS of the two triangles.

Fact 1: Line segment AE measures 25 meters.

At first glance, you might think that you don't know the exact side lengths of either triangle, so you won't be able to figure out the perimeters. Instead of assuming that this is insufficient data, take a moment to 'play around' with the information. Let's TEST VALUES and see what happens.

Since we're adding one side from each triangle and getting a total of 25 meters....

IF we have....
A side of 1 and a side of 24.
Total perimeter would be 3(1) + 3(24) = 3+72 = 75

A side of 2 and a side of 23.
Total perimeter would be 3(2) + 3(23) = 6+69 = 75

A side of 3 and a side of 22.
Total perimeter would be 3(3) + 3(22) = 9+66 = 75

The total perimeter is ALWAYS 75.
Fact 1 is SUFFICIENT

Fact 2: Side BC is 2/3 as long as side DE.

This Fact gives us no 'numbers' to work with, so there's no way to calculate either perimeter (much less the total perimeter).
Fact 2 is INSUFFICIENT

The take-away from this question is that it doesn't take much effort to prove whether a pattern exists or not. Get in the habit of doing that little bit of extra work (especially when you 'think' that a Fact is insufficient) and you'll be better able to pick up all of the available DS points on Test Day.

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Re: If triangles ABC and CDE are each equilateral, what is the [#permalink]

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28 May 2015, 23:08
Eq triangle perimeter = 3s ; Sum of perimeters of the 2 triangles = 3(S1+S2)

(1) S1+S2 = 25 - Suff
(2) NO info on length - Insuff
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Re: If triangles ABC and CDE are each equilateral, what is the [#permalink]

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21 Sep 2017, 03:23
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Re: If triangles ABC and CDE are each equilateral, what is the   [#permalink] 21 Sep 2017, 03:23
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