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GMAT-MATHS-->View question

What is the length of DB if DA is perpendicular to AC? (GMAT-MATHS)

Circle 1 has the same radius as circle 2. A is the center of circle 1, and B is the center of
circle 2. Circle 1 and circle 2 meet only at C. ACB is a straight line segment of length 10.
What is the length of DB if DA is perpendicular to AC?
a. 10
b. 5^5
c. 11
d. 10^2
e. 15


Asked On2019-04-08 13:38:56 by:naikaumprakash

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We are given that A, B, C, D are points on a line. We also also given that C is the midpoint of line segment AB and D is the midpoint of line segment CB. We need to determine whether the length of line segment DB is greater than 5. Let’s denote the length of a line segment using the absolute value sign. Therefore, the question becomes: Is |DB| > 5? 

Since C is the midpoint of line segment AB, C must be between A and B. Furthermore, since D is the midpoint of line segment CB, D must be between C and B. Therefore, the points lie on the line in the following order: A, C, D, B.

Since D is the midpoint of line segment CB, we have |CD| = |DB|. Notice that |CB| = |CD| + |DB|. Since |CD| = |DB|, that means |CB| = 2|DB|. Moreover, since C is the midpoint of line segment AB, |AC| = |CB|. Since |CB| = 2|DB|, |AC| = 2|DB|.

Statement One Alone:

The length of line segment AC is greater than 8. 

Since we know |AC| = 2|DB|, we know that 2|DB| > 8 and thus|DB| > 4 However, knowing |DB| is greater than 4 does not mean it is greater than 5. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The length of line segment CD is greater than 6.

Recall that |CD| = |DB|. Therefore, if |CD| > 6, then |DB| > 6 and thus |DB| > 5. Statement two alone is sufficient to answer the question.

Answer: B 

Answerd on:2019-05-15 Answerd By:rishabhshukla

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We are given that A, B, C, D are points on a line. We also also given that C is the midpoint of line segment AB and D is the midpoint of line segment CB. We need to determine whether the length of line segment DB is greater than 5. Let’s denote the length of a line segment using the absolute value sign. Therefore, the question becomes: Is |DB| > 5? 

Since C is the midpoint of line segment AB, C must be between A and B. Furthermore, since D is the midpoint of line segment CB, D must be between C and B. Therefore, the points lie on the line in the following order: A, C, D, B.

Since D is the midpoint of line segment CB, we have |CD| = |DB|. Notice that |CB| = |CD| + |DB|. Since |CD| = |DB|, that means |CB| = 2|DB|. Moreover, since C is the midpoint of line segment AB, |AC| = |CB|. Since |CB| = 2|DB|, |AC| = 2|DB|.

Statement One Alone:

The length of line segment AC is greater than 8. 

Since we know |AC| = 2|DB|, we know that 2|DB| > 8 and thus|DB| > 4 However, knowing |DB| is greater than 4 does not mean it is greater than 5. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The length of line segment CD is greater than 6.

Recall that |CD| = |DB|. Therefore, if |CD| > 6, then |DB| > 6 and thus |DB| > 5. Statement two alone is sufficient to answer the question.

Answer: B 

Answerd on:2019-05-15 Answerd By:rishabhshukla

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