Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 0510:00 AM PDT
-11:00 AM PDT
GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.- May 06
08:30 AM PDT
-09:30 AM PDT
In Episode 3 of our GMAT Ninja Critical Reasoning series, we tackle Discrepancy, Paradox, and Explain an Oddity questions. You know the feeling: the passage gives you two facts that seem completely contradictory.... - May 08
08:00 AM PDT
-08:30 AM PDT
Join the special YouTube live-stream for selecting the winners of GMAT Club MBA Scholarships sponsored by Juno live. Watch who gets these coveted MBA scholarships offered by GMAT Club and Juno.
08 Aug 2017, 10:37
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
55% (02:29) correct
45%
(02:48)
wrong
based on 73
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure above, if BD = 6, what is the area of ∆ ABE?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Attachment:
2017-08-08_2136.png [ 15.27 KiB | Viewed 4737 times ]
08 Aug 2017, 14:05
Kudos
Bookmarks
Bunuel
Attachment:
trapezoidabcd_2136.png [ 35.05 KiB | Viewed 4323 times ]
To find area of ∆ABE, use (area of trapezoid) - (area of blue ∆ ADE + area of yellow ∆ BCD)
1. Area of trapezoid
Polygon ABCD is a trapezoid: two right angles mean that side BC is parallel to side AD
BD = height of trapezoid = 6
ABCD area = \(\frac{(8 + 4)}{2}\) * 6 = 36
2. Area of two colored triangles - start with similar triangles to find height of blue ∆ ADE
Use properties of similar triangles to find height of blue triangle ADE
∆ ADE (blue) and ∆ BCE (light yellow) are similar:
Both have right angles. Their vertical angles are equal. AA = AAA. And the other two angles marked in red are alternate interior angles of parallel lines cut by transversal segment AC.
Corresponding sides of similar triangles will be in the same ratio.
Base AD of blue triangle is 8. Corresponding base BC of light yellow triangle is 4. Ratio is 2:1
Use the ratio to find height, DE, of blue triangle ADE.
Height of light yellow triangle BCE is BE
\(\frac{DE}{BE} = \frac{2x}{1x}\)
BD = 6
BD = sum of the heights of both similar triangles, i.e. BD = DE + BE
6 = 2x + x
x = 2
So BE is 2, and DE (height of blue triangle) is 4. See figure.
3. Find area of the two colored triangles (blue ∆ ADE and two-toned yellow ∆ BCD)
Area of blue ∆ ADE = \(\frac{b*h}{2}\) = \(\frac{4*8}{2}\)= 16
Area of two-toned yellow triangle BCD = \(\frac{4*6}{2}\) = 12
Total area of both colored triangles is 16 + 12 = 28
Area of trapezoid = 36
36 - 28 = 8
Area of ∆ ABE = 8
Answer A, IMO
Luckisnoexcuse
Current Student
Joined: 18 Aug 2016
Last visit: 31 Mar 2026
Posts: 513
Given Kudos: 198
Concentration: Strategy, Technology
Schools: Kenan-Flagler '20 (M)
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Products:
08 Aug 2017, 21:08
Kudos
Bookmarks
Bunuel
Area of ∆ BCD = 12
Area of ∆ ABD = 24
From figure ∆ BCE & ∆ AED
BC:AD = 4:8 => BE:ED = 2:4
Area of ∆ AED =16 => Area of ∆ ABE = Area of ∆ ABD - Area of ∆ AED = 24 - 16 =8
A
