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04 Jul 2019, 03:17
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (02:37) correct
34%
(02:35)
wrong
based on 92
sessions
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ABC is an isosceles triangle with sides AB=AC=5. D is a point in between B and C such that BD=2 and DC=4.5. Find the length of AD.
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
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04 Jul 2019, 04:47
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I'll post the simplest solution that'll help you get through this question < 1 min.
IMO (D) 4 is the correct answer.
Since BD = 2, in triangle ABD (and AB =5), applying the property sum of two sides of a triangle is always greater than third side, AD can definitely not be 1, 2 or 3
So AD has to be between 4 or 5, but for AD = 5, angle ABD has to be equal to angle ADB, but that would be only possible if D coincides with C, since angle ABD = angle ACD (given) and for that DC = 0, but again, since we're given DC = 0, that's not a possible case
Hence, the correct answer choice is (D) 4
PLEASE GIVE KUDOS IF YOU LIKE MY SOLUTION
IMO (D) 4 is the correct answer.
Since BD = 2, in triangle ABD (and AB =5), applying the property sum of two sides of a triangle is always greater than third side, AD can definitely not be 1, 2 or 3
So AD has to be between 4 or 5, but for AD = 5, angle ABD has to be equal to angle ADB, but that would be only possible if D coincides with C, since angle ABD = angle ACD (given) and for that DC = 0, but again, since we're given DC = 0, that's not a possible case
Hence, the correct answer choice is (D) 4
PLEASE GIVE KUDOS IF YOU LIKE MY SOLUTION
l1ll1ll1ll1ll1l
GMAT 3: 700 Q49 V35
Posts: 33
07 Jul 2019, 13:24
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You can solve this problem by using the property of Triangle sides.
It's always helpful to draw it out so you can visualize the physics.
We can estimate the range of the unknown side AD by using two other known sides.
AB=5
BD=2
Minimum length of the AD is the difference of the two known sides. AB - BD = 5 - 2 = 3
Maximum length of the AD is the sum of the two known sides. AB + BD = 5 + 2 = 7
Therefore, 3 < AD < 7
AC = 5
DC = 4.5
0.5 < AD < 9.5
This one is not as useful since the range is bigger than what we already know.
From the given range, 3 < AD < 7
Answer choices A, B, and C are out of the bounds.
Between D and E, you know that AD must be smaller than the length of AB = AC = 5. Otherwise, the line will be outside the triangle.
Therefore only D can be the answer.
It's always helpful to draw it out so you can visualize the physics.
We can estimate the range of the unknown side AD by using two other known sides.
AB=5
BD=2
Minimum length of the AD is the difference of the two known sides. AB - BD = 5 - 2 = 3
Maximum length of the AD is the sum of the two known sides. AB + BD = 5 + 2 = 7
Therefore, 3 < AD < 7
AC = 5
DC = 4.5
0.5 < AD < 9.5
This one is not as useful since the range is bigger than what we already know.
From the given range, 3 < AD < 7
Answer choices A, B, and C are out of the bounds.
Between D and E, you know that AD must be smaller than the length of AB = AC = 5. Otherwise, the line will be outside the triangle.
Therefore only D can be the answer.
