M28-40

Question

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 .

Bunuel · Accepted Answer

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=\frac{AC}{2} , from which we have that  AC=24 . Sufficient.

Answer: B

bigzoo · Answer

could help me please what does it mean: "The length of the median BD" ... first I thought it is the midpoint of BC, but it is not ... and since english is not my mother tounge I do not know what it means

Bunuel · Answer

The median of a triangle is a line from a vertex to the midpoint of the opposite side. Check for more  HERE .

aaigla · Answer

Please correct my reasoning. I do not understand why A is not correct. Let's name each side of our equilateral triangle "x." AB=BC=AC=x. Since we are told BD is a median, it means AD=DC=x/2. In an equilateral triangle, a line drawn from one of the vertices to the midpoint of the opposite line will form a 90 degree angle. So we would have two equal triangles, AB-BD-DA and CB-BD-DC that each have one side, BD, length 12, one side, DC or DA, length x/2, and one side, BC or BA, length x. Since these are right triangles, (x/2)^2+12^2=x^2. We have an equation with one unknown. Why is this not sufficient?  Bunuel  can you help?

Bunuel · Answer

(1) says that ABC is isosceles, not equilateral.

Sriparnacj · Answer

Hi  Bunuel ,

Could you please elaborate (as in how does it come about) on the geometrical property mentioned for the sufficiency of Statement 2 : "Important property: median from right angle is half of the hypotenuse"?

It would just make it easier to remember.

Thanks.

susanz · Answer

Sriparnacj I had the same thought. Draw a line from midpoint D to line BC on the triangle, and call the point "E" on line BC. You can then prove that triangle CDE and BDE are identical. Or, you could prove that BDE and ABC are congruent.

Annoyingly I can't post URLs but I would google the triangle midsegment theorem for more info. Hope this helps

Annoyingly I can't post URLs but I would google the triangle midsegment theorem for more info. Hope this helps

Bunuel · Answer

Duplicate of M04-24. Unpublished.

M28-40

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards