GMAT Quant Questions | Geometry #9

Properties of acute angled triangles | Data Sufficiency Questions

A GMAT Data Sufficiency practice question in Geometry. Concept: properties of sides of Obtuse & Acute angled triangles and properties relating to location of the center of the circumscribing circle of a triangle. A GMAT hard math question.

GMAT Data Sufficiency | Directions | Click Here ▼

This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  4. EACH statement ALONE is sufficient to answer the question asked.
  5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Numbers

All numbers used are real numbers.

Figures

A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2)

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight

You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

Note

In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Question 9: Is triangle ABC with sides a, b, and c acute angled?

  1. Triangle with sides a2, b2, c2 has an area of 140 sq cms.
  2. Median AD to side BC is equal to altitude AE to side BC.

Get to Q51 in GMAT Quant


Online GMAT Course
@ INR 3500


Video Explanation


GMAT Live Online Classes


Starts Tue, Oct 12, 2021


Explanatory Answer | GMAT Geometry DS

Step 1 of solving this GMAT DS question: Understand the Question Stem

Q1. What kind of an answer will the question fetch?
An "IS" question will fetch a definite "Yes" or a "No" as an answer.

Q2. When is the data sufficient?
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
If the statements independently or together do not provide a DEFINITE YES or DEFINITE NO, the data is NOT sufficient.

Q3. What do we know from the question stem?
The question stem states that a, b, and c are the measures of the sides of a triangle.

Key property of acute angled triangles
If a, b, and c are the measures of the sides of a triangle, and if 'a' is the longest side of the triangle, then
  1. the triangle is acute angled if a2 < b2 + c2
  2. right angled if a2 = b2 + c2 and
  3. obtuse angled if a2 > b2 + c2

Step 2 of solving this GMAT DS question: Evaluate Statement (1) ALONE
Triangle with sides a2, b2, c2 has an area of 140 sq cms.

The statement provides us with one valuable information: we can form a triangle with sides a2, b2, c2.
For any triangle we know that sum of two sides is greater than the third side.
So, we can infer that a2 < b2 + c2.
The inequality above is the condition to be met if the triangle with sides a, b, and c were to be an acute triangle.

We are able to answer the question with a DEFNITE answer using Statement 1.
Hence, statement 1 alone is sufficient.
Choices narrow down to A or D.


Step 3 of solving this GMAT DS question: Evaluate Statement (2) ALONE
Median AD to side BC is equal to altitude AE to side BC.

For an equilateral triangle, medians to the sides of the triangle are the corresponding altitudes. i.e., the median and altitude of all 3 sides are coincident lines.

For an isosceles triangle, the median to the side whose measure is different is the altitude to that side. i.e., only one median is the same as the altitude.

From statement 2, we can infer that the triangle is either equilateral or isosceles.
An equilateral triangle is definitely an acute angled triangle. However, an isosceles triangle need not be an acute angled triangle.

We are unable to answer the question with a DEFNITE YES/NO using Statement 2.
Hence, statement 2 alone is not sufficient.
Eliminate answer option B.

Choice A is the correct answer.



GMAT Online Course
Try it free!

Register in 2 easy steps and
Start learning in 5 minutes!

★ Sign up

Already have an Account?

★ Login

GMAT Live Online Classes

Next Batch Oct 12, 2021

★ GMAT Live Info

GMAT Coaching in Chennai

Next Batch
after Lockdown

★ GMAT Class Info

GMAT Coaching in Chennai

Sign up for a Free Demo of our GMAT Classes in Chennai

★ Schedule Demo

GMAT Geometry & Solid Geometry Videos On YouTube


GMAT Sample Questions | Topicwise GMAT Questions


Where is Wizako located?

Wizako - GMAT, GRE, SAT Prep
An Ascent Education Initiative
14B/1 Dr Thirumurthy Nagar 1st Street
Nungambakkam
Chennai 600 034. India

How to reach Wizako?

Phone: (91) 44 4500 8484
Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com
Leave A Message