In isosceles triangle DEF, what is the measure of angle E?

Expert replies

Previous Topic Next Topic

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Dec 12, 2018 2:17 am

Timer

00:00

Answers

Stats

Difficulty—

In isosceles triangle DEF, what is the measure of angle E?

(1) Angle D measures 42 degrees
(2) Angle F measures 96 degrees

OA B

Source: Veritas Prep

Like this post

Source: Beat The GMAT — Data Sufficiency | Wed Dec 12, 2018 2:17 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

In isosceles triangle DEF, what is the measure of angle E?

by fskilnik@GMATH » Wed Dec 12, 2018 4:20 am

BTGmoderatorDC wrote:In isosceles triangle DEF, what is the measure of angle E?

(1) Angle D measures 42 degrees
(2) Angle F measures 96 degrees
Source: Veritas Prep

All measures are in degrees.

$$\Delta DEF\,\,{\rm{isosceles}}\,\,\,\,\left( * \right)$$
$${\rm{?}}\,\,{\rm{ = }}\,\,\angle {\rm{E}}$$
$$\left( 1 \right)\,\,\angle {\rm{D}}\,\,{\rm{ = }}\,\,{\rm{42}}\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {\angle {\rm{D}}\,{\rm{;}}\,\angle {\rm{E;}}\,\,\angle {\rm{F}}} \right)\,\, = \,\,\left( {42\,;\,42\,;96} \right)\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,{\rm{42}} \hfill \cr
\,{\rm{Take}}\,\,\left( {\angle {\rm{D}}\,{\rm{;}}\,\angle {\rm{E;}}\,\,\angle {\rm{F}}} \right)\,\, = \,\,\left( {42\,;69\,;69} \right)\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,{\rm{69}}\,\, \hfill \cr} \right.\,$$
$$\left( 2 \right)\,\,\angle {\rm{F}}\,\,{\rm{ = }}\,\,{\rm{96}}\,\,\,\left( { \ne \,\,\angle {\rm{D}}\,\,{\rm{and}}\,\, \ne \angle {\rm{E}}} \right)\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,\angle {\rm{D}}\,\, = \,\,\angle {\rm{E}}\,\,{\rm{ = }}\,\,{{{\rm{180}} - 96} \over 2}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\,$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 12, 2018 1:39 pm

BTGmoderatorDC wrote:In isosceles triangle DEF, what is the measure of âˆ E?

(1) âˆ D measures 42 degrees
(2) âˆ F measures 96 degrees

Target question: What is the measure of âˆ E?

Given: Triangle DEF is an ISOSCELES triangle
This tells us that there are 2 equal angles

Statement 1: âˆ D measures 42 degrees
Here it's hard to tell whether there's a second 42-degree angle or whether the other two angles are different.
Consider these two possible cases that satisfy statement 1:
Case a: âˆ D = 42Â°, âˆ E = 42Â° and âˆ F = 96Â° . In this case, the answer to the target question is âˆ E = 42Â°
Case b: âˆ D = 42Â°, âˆ E = 69Â° and âˆ F = 69Â° . In this case, the answer to the target question is âˆ E = 69Â°
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: âˆ F measures 96 degrees
In this case we KNOW that there are no other angles that measure 96 degrees.
How do we know this?
If we have a 2nd angle measuring 96 degrees, then the sum of those two angles is GREATER THAN 180Â°
This means the two other angles (âˆ D and âˆ E) must be equal
So, it MUST be the case that âˆ D = 42Â°, âˆ E = 42Â° and âˆ F = 96Â°
The answer to the target question is âˆ E = 42Â°
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review