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69% (02:17) correct
31%
(03:10)
wrong
based on 49
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In diagram above, ABCD is a rectangle, AD = 10, and AE = 5. What is the length of EC?
(A) 5√3
(B) 10
(C) 15
(D) 25
(E) 25√3
14 Dec 2021, 18:11
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BrentGMATPrepNow
APPROACH #1: Visual estimation
Key property: The diagrams in GMAT problem solving questions are DRAWN TO SCALE unless stated otherwise.
If AE has length 5. . . .
. . . we can visually estimate additional lengths of 5 from E to C:
So, it looks like the length of EC is approximately 15.
When we check the answer choices, only answer choice C is close to our estimated length.
Answer: C
Aside: On test day, you can hold your finger to the monitor and use your marker to copy the length of AE on your finger. Then determine how many of those lengths fit into line segment EC.
---------------------------------------------------------------
APPROACH #2: Apply triangle properties
Let's first focus on RIGHT triangle AED below:
Since the hypotenuse (AD) is twice the length of leg AE, we know that triangle AED is a special 30-60-90 right triangle, which means ∠ADE = 30° and ∠DAE = 60°
Now, when we focus on RIGHT triangle ADC...
...we can see that ∠DCA = 30°.
Since we have another special 30-60-90 right triangle, we know that the hypotenuse will be twice the length of the side opposite the 30° angle (aka side AD).
This means the hypotenuse (AC) must have length 20.
Since AE + EC = AC, we can substitute values to get: 5 + EC = 20, which means EC = 15
Answer: C
