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Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD

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Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD  [#permalink]

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New post 09 Mar 2017, 01:25
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A
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C
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E

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  45% (medium)

Question Stats:

77% (01:53) correct 23% (01:54) wrong based on 127 sessions

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Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD equal to 30 degrees.

(1) One side of Triangle ABD is equal to 2.

(2) One side of Rectangle ABCD is 1.

Attachment:
img_3862.png
img_3862.png [ 4.97 KiB | Viewed 2903 times ]

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Re: Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD  [#permalink]

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New post 09 Mar 2017, 09:17
2
Bunuel wrote:
Image
Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD equal to 30 degrees.

(1) One side of Triangle ABD is equal to 2.

(2) One side of Rectangle ABCD is 1.

Attachment:
The attachment img_3862.png is no longer available



Combined statements are also not sufficient
Consider below attached images
where Case 1 is unknown triangle & case 2 is 30-60-90 triangle
Hence insuff

Ans E
Attachments

img_386.png
img_386.png [ 11.19 KiB | Viewed 2375 times ]

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Re: Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD  [#permalink]

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New post 12 Mar 2017, 20:23
Okay so I made an educated guess and got this question right- but kudos for feedback in my reasoning because I don't want to choke or second guess myself on test day.



Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD equal to 30 degrees.

(1) One side of Triangle ABD is equal to 2.

(2) One side of Rectangle ABCD is 1.


Statement (1) tells us that one side of triangle ABD is equal to 2- well, which side is that? Is it the side that corresponds to one of the two 90 degree angles in the rectangle. Also, we cannot just assume that the two triangles are 45 45 for the sake of not falling into GMAT DS traps. If that were true then, that is if mathematically the question and diagram in itself validated a 45 45 90 triangle, then the purpose of the question is defeated- in other words, the whole point of this question is to establish whether or not we have enough information to conclude angle ABD is equal to 30; therefore, nothing in the question or diagram itself can solve that question. The information needed to solve the question, or lack of it, is derived from the two statements.


Statement (2) tells us one side of the rectangle is 1- which side is that though? And how can we compute the length of the other side with this data. If we could do that then maybe we could extrapolate ratios through degrees based on the side lengths but the side lengths have no limitation (etc. you could have two sides of 1 and two sides of 3, or two sides of 1 and two sides of 2). Hence, this statement is insufficient.


If we combine both of these statements, we still do not have enough information- we cannot just use the Pythagorean theorem to find the hypotenuse length and derive a conclusion about the angles of the triangle by squaring 1 and 2. This is my best guest/ reasoning.
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Re: Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD  [#permalink]

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New post 07 Jul 2017, 03:47
Bunuel wrote:
Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD equal to 30 degrees.

(1) One side of Triangle ABD is equal to 2.

(2) One side of Rectangle ABCD is 1.

Attachment:
img_3862.png


Hi,

I had a very basic doubt here.

If a line divides a rectangle into two equal triangles, shouldn't this line be the rectangle's diagonal and create a 45 degree angle at the vertices?


Thanks,
Novice
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Re: Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD  [#permalink]

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New post 07 Jul 2017, 04:16
1
Novice90 wrote:
Bunuel wrote:
Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD equal to 30 degrees.

(1) One side of Triangle ABD is equal to 2.

(2) One side of Rectangle ABCD is 1.

Attachment:
img_3862.png


Hi,

I had a very basic doubt here.

If a line divides a rectangle into two equal triangles, shouldn't this line be the rectangle's diagonal and create a 45 degree angle at the vertices?


Thanks,
Novice


A diagonal in a rectangle makes 45 degree angle at the sides only when a rectangle is a square. In all other cases the angles can be anything ranging from 0 to 90, not inclusive obviously.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD  [#permalink]

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New post 13 Sep 2018, 08:00
Question: Is Angle ABD equal to 30 degrees?

After combining both 1) and 2), we see that it does not follows triangle 30-60-90 pattern.
Will there be a flaw to deduce that Angle ABD is not equal to 30 degree. Hence answering question.

Can the answer be option C (both statement together sufficient to answer).
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Re: Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD &nbs [#permalink] 13 Sep 2018, 08:00
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Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD

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