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

1. ABC is an isosceles triangle
2. \(AC^2=AB^2+BC^2\)

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“The length of the median BD in a triangle ABC is 12 centimeters, what is the length of the side AC?” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer:

Approach Solution 1

Firstly consider S(1), it is given that ABC is an isosceles triangle. Hence this statement is clearly insufficient.
Now consider S(2), we have \(AC^2=AB^2+BC^2\)

The statement implies that ABC is a right triangle and AC is its hypotenuse.
Important Property: Median from the right triangle is half of the hypotenuse.

Hence, BD = 12 = \(\frac{AC}{2}\) , from which we have AC = 24

Hence this statement is sufficient in itself.

Correct option: B

Suggested GMAT Quant Questions

• Buster Leaves the Trailer at Noon and Walks Towards the Studio at a Constant Rate of B Miles Per Hour., GMAT Data Sufficiency
• If ab = ac is b = 2?, GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency, GMAT Data Sufficiency
• Is Quadrilateral ABCD a Rectangle?, GMAT Data Sufficiency
• If \(x^2\)=\(2^x\), What is the Value of x ?, GMAT Data Sufficiency
• A Pentagon With 5 Sides Of Equal Length And 5 Interior Angles Of Equal measure is Inscribed in a Circle, GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency
• If L \(\neq\) 0, is \(\frac{18K}{L}\) an Integer?
• If 0 < x < 53, What is the Value of Integer x? GMAT Data Sufficiency
• If @ x=x^2/2x^2-2 , What is the Units Digit of @ (@4)? GMAT Problem Solving
• If m is a positive integer, is \(\sqrt{m}>25\) ? , GMAT Data Sufficiency
• What is the value of \(6x^2+9y^2\)?, GMAT Data Sufficiency
• What is the Radius of the Circle above with Center O?, GMAT Data Sufficiency
• Is the Average of a Set of 5 Distinct Positive Integers {a, b, 6, 4, 2} Greater than the Median?, GMAT Data Sufficiency
• If \(\sqrt{3+\sqrt{x-1}}=4\) , what is the value of x?, GMAT Data Sufficiency
• If There are 78 People Working at an Office, How Many of Them are Women Older than 40?, GMAT Data Sufficiency
• Is P – 1 Even?, GMAT Data Sufficiency
• If x and y are integers and \(x=\frac{y}{5}+2\) , is xy even?, GMAT Data Sufficiency
• P and Q are Prime Numbers Less than 70. What is the Units Digit of P*Q?, GMAT Data Sufficiency
• The Cardinality of a Finite Set is the Number of Elements in the Set., GMAT Data Sufficiency