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Is CB || ED?

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Is CB || ED? [#permalink]

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New post 10 Jun 2018, 06:17
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A
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C
D
E

Difficulty:

  85% (hard)

Question Stats:

32% (01:16) correct 68% (01:03) wrong based on 37 sessions

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Is CB || ED?

(1) ∆ABC and ∆AED are both isosceles triangles
(2) ∠C = ∠E

*kudos for all correct solutions

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Re: Is CB || ED? [#permalink]

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New post 10 Jun 2018, 08:56
can we not deduct from the diagram that angle(CAB) = angle (EAD)??
Can someone give the solution?
I got C based on the above assumption.
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Is CB || ED? [#permalink]

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New post 10 Jun 2018, 10:09
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GMATPrepNow wrote:
Image

Is CB || ED?

(1) ∆ABC and ∆AED are both isosceles triangles
(2) ∠C = ∠E

*kudos for all correct solutions


This question asks us to check the parallel line & it's transversal.

Here, BC & ED are the lines to be checked for parallelism and CD & BE are the transversals.

BC|| ED when the alternate angles in the given figure are equal. i.e, \(\angle{CBA}\)=\(\angle{AED}\) and \(\angle{ACB}\)=\(\angle{ADE}\)

Question stem: BC || ED? (Y/N)

Statement1:-∆ABC and ∆AED are both isosceles triangles

we only know that vertically opposite angles are equal, i.e, \(\angle{CAB}\)=\(\angle{EAD}\) and we don't know their measure in degrees.-----------(a)

Remaining two angles of both the isosceles triangles can have 'n' no of possible combinations.

hence st1 is not sufficient.

Statement1:-∠C = ∠E --------(b)

In ∆ABC and ∆AED, from (a) and (b) ,we have \(\angle{CBA}\)=\(\angle{ADE}\)

So, we can't say whether \(\angle{CBA}\)=\(\angle{AED}\) and \(\angle{ACB}\)=\(\angle{ADE}\) or not.

Hence statement2 is not sufficient.

(1)+(2), we have

(i) ∠C = ∠E
(ii)\(\angle{CAB}\)=\(\angle{EAD}\)
(iii) \(\angle{CBA}\)=\(\angle{ADE}\)
(iv) Both the triangles are isosceles; it has 2 cases:-

1.when \(\angle{E}\)=\(\angle{D}\)

then \(\angle{C}=\angle{D}\) & \(\angle{B}=\angle{E}\)

So, Is BC || ED? Yes (As alternate angles are found equal)

2.when \(\angle{E}=\angle{A}\)

then \(\angle{C}\neq\angle{D}\) & \(\angle{B}\neq\angle{E}\)

So, Is BC || ED? No (As alternate angles are not equal)

Ans. E
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Re: Is CB || ED? [#permalink]

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New post 10 Jun 2018, 10:12
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SajjitaKundu wrote:
can we not deduct from the diagram that angle(CAB) = angle (EAD)??
Can someone give the solution?
I got C based on the above assumption.


Many people will feel that the correct answer is C, but it's E

Keep at it!

Cheers,
Brent
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Re: Is CB || ED? [#permalink]

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New post 10 Jun 2018, 11:17
1
Okay, so this is tricky.

Basically, the triangles are isosceles but it is not given which sides are equal. So assuming angle C = angle B would be incorrect.
Similarly, assuming angle E = angle D would be incorrect as well.
They could be equal.
Statement 1 is insufficient.

Statement 2 by itself is pretty clearly insufficient.

Let's add both of these together and see what happens.
It eventually boils down to the reasoning used in statement 1 where there are two cases, one in which the lines are parallel and one in which they are not.

So E is the answer in my opinion.
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Re: Is CB || ED? [#permalink]

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New post 12 Jun 2018, 04:38
Statements combined:
Case 1:
Image
In this case, ∠B = ∠E and ∠C = ∠D, so CB || ED.

Case 2:
Image
In this case, ∠B ≠ ∠E and ∠C ≠ ∠D, so CB is NOT parallel to ED.

Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT.


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Re: Is CB || ED? [#permalink]

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New post 12 Jun 2018, 05:18
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GMATPrepNow wrote:
Image

Is CB || ED?

(1) ∆ABC and ∆AED are both isosceles triangles
(2) ∠C = ∠E

*kudos for all correct solutions


Target question: Is CB || ED?

Let's jump straight to....

Statements 1 and 2 combined
Statement 1 tells us that ∆ABC and ∆AED are both isosceles triangles
Statement 2 tells us that ∠C = ∠E

Let's start with 2 identical isosceles triangles:
Image

If we arrange the triangles this way....
Image
....we can see that the answer to the target question is YES, side CB IS parallel to side ED

HOWEVER, if we arrange the triangles this way....
Image
....we can see that the answer to the target question is NO, side CB is NOT parallel to side ED

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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Re: Is CB || ED? [#permalink]

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New post 12 Jun 2018, 05:20
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GMATPrepNow wrote:
Image

Is CB || ED?

(1) ∆ABC and ∆AED are both isosceles triangles
(2) ∠C = ∠E

*kudos for all correct solutions


An immediate observation..

We can easily have both statements true and have the top triangle tilted on top of the bigger one...
So we cannot restrict the two triangles in any particular position, and thus we can not say anything about CB||ED

E
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Re: Is CB || ED?   [#permalink] 12 Jun 2018, 05:20
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