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A, B, C, and D are points on a line. If C is the midpoint of line segm [#permalink]

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A, B, C, and D are points on a line. If C is the midpoint of line segment AB and if D is the midpoint of line segment CB, is the length of line segment DB greater than 5?

1) The length of line segment AC is greater than 8 2) The length of line segment CD is greater than 6

A, B, C, and D are points on a line. If C is the midpoint of line segment AB and if D is the midpoint of line segment CB, is the length of line segment DB greater than 5?

1) The length of line segment AC is greater than 8 2) The length of line segment CD is greater than 6

so from the given info.... AB is teh line..... C is the midpoint.....\(AC = BC = \frac{AB}{2}.....\) D is the midpoint of CB..............\(CD = BD = \frac{BC}{2} = \frac{AB}{4}..\)

lets see the statements-

1) The length of line segment AC is greater than 8 \(BD = \frac{BC}{2} = \frac{AC}{2}\) ..... so if AC>6, DB > 3..... DB can be 4, 5 ,6 etc Insuff

2) The length of line segment CD is greater than 6 \(BD = CD.\).. so if CD >6, BD>6.. Suff

A, B, C, and D are points on a line. If C is the midpoint of line segment AB and if D is the midpoint of line segment CB, is the length of line segment DB greater than 5?

1) The length of line segment AC is greater than 8 2) The length of line segment CD is greater than 6

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
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We're told that A, B, C, and D are points on a line, C is the midpoint of line segment AB and D is the midpoint of line segment CB. We're asked if the length of line segment DB is greater than 5. This is a YES/NO question.

You might find it useful to draw a picture (and it would likely help you to make the algebraic 'deductions' that are needed to answer this question).

< - - A - - - - - C - - D - - B - - >

In the above example, C is the midpoint of AB and D is the midpoint of CB, so... AC = CB = X CD = DB = Y X = 2Y

The question essentially asks if Y is greater than 5.

1) The length of line segment AC is greater than 8

With Fact 1, we know that X is greater than 8. This means that Y is greater than 4. IF... Y = 6, then the answer to the question is YES. IF... Y = 5, then the answer to the question is NO. Fact 1 is INSUFFICIENT

2) The length of line segment CD is greater than 6

With Fact 2, we know that Y is greater than 6. Thus, the answer to the question is ALWAYS YES. Fact 2 is SUFFICIENT