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M04-24

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The length of the median BD in triangle ABC is 12 centimeters, what is the length of side AC?


(1) ABC is an isosceles triangle.

(2) \(AC^2 = AB^2 + BC^2\).
[Reveal] Spoiler: OA

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Official Solution:


(1) ABC is an isosceles triangle. Clearly insufficient.

(2) \(AC^2 = AB^2 + BC^2\). This statement implies that ABC is a right triangle and AC is its hypotenuse. Important property: median from right angle is half of the hypotenuse, hence BD=12=AC/2, from which we have that AC=24. Sufficient.


Answer: B
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New post 19 Oct 2014, 10:58
How do we know that BD is median to AC and not AB or BC?

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New post 27 Dec 2014, 05:41
Bunuel wrote:
Official Solution:


(1) ABC is an isosceles triangle. Clearly insufficient.

(2) \(AC^2 = AB^2 + BC^2\). This statement implies that ABC is a right triangle and AC is its hypotenuse. Important property: median from right angle is half of the hypotenuse, hence BD=12=AC/2, from which we have that AC=24. Sufficient.


Answer: B



Is there any other rule for relation between the triangles and median?

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New post 28 Dec 2014, 06:02
GmatDestroyer2013 wrote:
Bunuel wrote:
Official Solution:


(1) ABC is an isosceles triangle. Clearly insufficient.

(2) \(AC^2 = AB^2 + BC^2\). This statement implies that ABC is a right triangle and AC is its hypotenuse. Important property: median from right angle is half of the hypotenuse, hence BD=12=AC/2, from which we have that AC=24. Sufficient.


Answer: B



Is there any other rule for relation between the triangles and median?


Check here: math-triangles-87197.html
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New post 23 Jul 2015, 04:33
Bunuel wrote:
Official Solution:
(1) ABC is an isosceles triangle. Clearly insufficient.


It is not clear to me how this is insufficient. If A=B=C and BD = 12 couldn't you find the other sides, x, (that are all equal to each other) with pythagorean's theorem?

i.e. \(2x^2=12\)

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New post 23 Jul 2015, 04:42
gmatser1 wrote:
Bunuel wrote:
Official Solution:
(1) ABC is an isosceles triangle. Clearly insufficient.


It is not clear to me how this is insufficient. If A=B=C and BD = 12 couldn't you find the other sides, x, (that are all equal to each other) with pythagorean's theorem?

i.e. \(2x^2=12\)


It says isosceles not equilateral.
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New post 23 Jul 2015, 11:26
Newbie here; am I missing something or were there no multiple choice answers for the math question?

Thanks

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Newbie here; am I missing something or were there no multiple choice answers for the math question?

Thanks


Hi, and welcome to GMAT Club.

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post ALL YOU NEED FOR QUANT.

Hope this helps.
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New post 23 Jul 2015, 14:50
Thank you for that info! Appreciate the help and will do better to get acclimated to the rest of the forum.

MCAT down, GMAT to go

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Hi,

Towards the proof for the question, pls refer:
https://www.algebra.com/algebra/homewor ... use.lesson

rgds.

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I chose A as sufficent since 1 states ABC is an isosceles triangle and thus assuming Angle BAC and Angle BCA as 45. Thus using 45-45-90 rule I was able to deduce that AC is 24. Not able to understand what was wrong with my logic.

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New post 25 Nov 2016, 00:16
haroon747 wrote:
I chose A as sufficent since 1 states ABC is an isosceles triangle and thus assuming Angle BAC and Angle BCA as 45. Thus using 45-45-90 rule I was able to deduce that AC is 24. Not able to understand what was wrong with my logic.


You made several wrong assumptions:
1. How do you know that ABC is not only isosceles but also a right triangle?
2. How do you know which sides of ABC are equla?
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New post 01 Mar 2017, 00:51
BRUNEL I HAVE A DOUBT PERTAINING TO THE PROPERTY : MEDIAN IS HALF OF HYPOTNUSE IN A RIGHT ANGLE TRIANGLE

IS THIS PROPERTY APPLICABLE TO TALL THE RIGHT ANGLE TRIANGLE'S SUCH AS 30:60:90 / 45-45-90 ETC

I HAVE APPLIED THIS PROPERTY TO ONE OF THE QUESTION IN CO ORDINATE GEOMETRY WHILE FINDING THE MEDIAN IN A RIGHT ANGLE TRIANGLE IN WHICH HYPOTNUSE WAS GIVEN BUT THE I WAS GETTING WAS INCORRECT...

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New post 01 Mar 2017, 01:27
sidagar wrote:
BRUNEL I HAVE A DOUBT PERTAINING TO THE PROPERTY : MEDIAN IS HALF OF HYPOTNUSE IN A RIGHT ANGLE TRIANGLE

IS THIS PROPERTY APPLICABLE TO TALL THE RIGHT ANGLE TRIANGLE'S SUCH AS 30:60:90 / 45-45-90 ETC

I HAVE APPLIED THIS PROPERTY TO ONE OF THE QUESTION IN CO ORDINATE GEOMETRY WHILE FINDING THE MEDIAN IN A RIGHT ANGLE TRIANGLE IN WHICH HYPOTNUSE WAS GIVEN BUT THE I WAS GETTING WAS INCORRECT...


The property is as follows: median from right angle is half of the hypotenuse. So, it can be applied to any right triangle.

P.S. Please turn Caps Lock off when posting.
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New post 01 Jul 2017, 11:24
How about we deduce (B) in this way.

The median splits Angle B in halves of 45 degrees each while making an angle of 90 degrees on the hypot AC. So essentially we get two triangles of 45-90-45 in which we know the hypot length. Rest should be easy with the special triangles property?

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M04-24 [#permalink]

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New post 27 Jul 2017, 06:18
gmat7m wrote:
How about we deduce (B) in this way.

The median splits Angle B in halves of 45 degrees each while making an angle of 90 degrees on the hypot AC. So essentially we get two triangles of 45-90-45 in which we know the hypot length. Rest should be easy with the special triangles property?

This is only 1 special case of Isosceles Right Triangle while bunuel is talking about a general case. Hence, your explanations supports Option C while OA is B.
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New post 22 Aug 2017, 12:26
I think this is a high-quality question and I agree with explanation.

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Re M04-24   [#permalink] 22 Aug 2017, 12:26
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