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# M04-24

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Math Expert
Joined: 02 Sep 2009
Posts: 41872

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16 Sep 2014, 00:23
Expert's post
20
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00:00

Difficulty:

95% (hard)

Question Stats:

33% (01:05) correct 67% (01:11) wrong based on 214 sessions

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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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Math Expert
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16 Sep 2014, 00:23
Expert's post
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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.

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

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20 Oct 2014, 03:51
tangt16 wrote:
How do we know that BD is median to AC and not AB or BC?

Draw triangle ABC. The median BD (the median from vertex B) can be only from B to side AC.
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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.

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

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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.

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

Check here: math-triangles-87197.html
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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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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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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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23 Jul 2015, 11:29
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RSK70 wrote:
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.
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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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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11 Jul 2016, 13:32
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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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24 Nov 2016, 19:17
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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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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.

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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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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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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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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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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My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html

My CR notes - https://gmatclub.com/forum/patterns-in-cr-questions-243450.html

Rest of the Notes coming soon.

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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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# M04-24

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