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# What is the length of the line AD? (1) AC = 10, BD=15 (2) AB/BC=BC/CD

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Math Expert
Joined: 02 Sep 2009
Posts: 58458
What is the length of the line AD? (1) AC = 10, BD=15 (2) AB/BC=BC/CD  [#permalink]

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17 Oct 2018, 00:38
00:00

Difficulty:

45% (medium)

Question Stats:

59% (01:43) correct 41% (01:46) wrong based on 66 sessions

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What is the length of the line AD?

(1) AC = 10, BD = 15

(2) AB/BC = BC/CD

Attachment:

2018-10-17_1136.png [ 2.1 KiB | Viewed 513 times ]

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Re: What is the length of the line AD? (1) AC = 10, BD=15 (2) AB/BC=BC/CD  [#permalink]

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17 Oct 2018, 19:16
From statement 1:

AC = AB+BC = 10
BD = BC+CD = 15

AD = AB+BC+CD. Since BC is unknown. We cant determine the length of AD.
Insufficient.

From statement 2:

$$\frac{AB}{BC}$$ = $$\frac{BC}{CD}$$ Cross multiplying gives $$BC^2$$ = AB*CD.
Clearly Insufficient.

Combining both From 1:
AB = 10-BC
CD = 15-BC
From 2 $$BC^2$$ = AB*CD = (10-BC)(15-BC)
Solving gives BC as 6.

Sufficient.

C is the aswer.
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Re: What is the length of the line AD? (1) AC = 10, BD=15 (2) AB/BC=BC/CD   [#permalink] 17 Oct 2018, 19:16
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