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(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.

(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?

(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?

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?

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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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 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.

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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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...

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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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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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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I'd appreciate learning about the grammatical errors in my posts

Please hit Kudos If my Solution helps

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