Triangle ABC is Right Angled at B. BD, the Median to Hypotenuse AC, is 5 Units GMAT Data Sufficiency

Question: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units. What is the area of the triangle?
(1) The sides of triangle ABC are in the ratio 1 : 1 : √2
(2) The hypotenuse AC is 10 units

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

“Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units.”- 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 sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1

There is only one approach to solve the problem statement.

Explanation:
Given:

• Triangle ABC is right angled at B.
• BD, the median to hypotenuse AC, is 5 units.

Find Out:

• The area of the triangle?

Approach:

• We will check each statement one by one.

In case of the triangle we have 3 variables and 2 equations (ang B=90 degree , BD=5).
Thus we need 1 more equation to match the number of variables and equations.
Therefore there is high probability that D is the answer. However, we will check each statement individually.
Let us check the Statement 1
The median is perpendicular to the hypotenuse, as it's an isosceles right triangle.
The ratio of sides is known, and triangle ABD ~ triangle ACB
Therefore, we get:
AB/AC = BD/AB
AB/AC = 1/root(2) = 5/AB
AB = 5root(2)
BC = 5root(2)
So area of triangle ABC = 1/2 * 25 * 2 = 25
Hence, the statement is Sufficient
Let us check the Statement 2
Only, the value of the hypotenuse AC is provided.
It is not clear if the median is perpendicular to the hypotenuse
The other sides are not known either.
Hence, it is Not Sufficient.
Since the statement 1 is sufficient and statement 2 is not.

Correct Answer: A

Some suggested GMAT Data Sufficiency Questions

• If xy = - 6, What is the Value of xy(x + y)? GMAT Data Sufficiency
• A Drawer Contains 8 Socks, and 2 Socks are Selected at Random Without Replacement GMAT Data Sufficiency
• The Average Price of Three Stocks is $25 per Share GMAT Data Sufficiency
• Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1?  GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency
• The Set S of Numbers has the following Properties GMAT Data Sufficiency
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at Random GMAT Data Sufficiency
• Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? GMAT Data Sufficiency
• Juan Bought Some Paperback Books That Cost $8  GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT Data Sufficiency
• X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X? GMAT Data Sufficiency
• 2x+3y GMAT Data Sufficiency
• The Selling Price of an Article is Equal to the Cost of the Article GMAT Data Sufficiency
• Buster leaves the trailer at noon and walks towards the studio GMAT Data Sufficiency