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

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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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15 Jun 2016, 02:20
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Question Stats:

80% (01:27) correct 20% (01:30) wrong based on 1468 sessions

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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
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Posts: 8792
Re: A, B, C, and D are points on a line. If C is the midpoint of line segm  [#permalink]

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15 Jun 2016, 05:14
1
AbdurRakib wrote:
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

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

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06 Dec 2016, 07:21
2
AbdurRakib wrote:
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.

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

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12 Dec 2017, 10:36
1
Hi All,

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

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

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13 Apr 2020, 06:15
2
Top Contributor
AbdurRakib wrote:
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

Given: 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
When we sketch this information we get the following:

Notice that the two blue bars of equal length represent AC = CB, and the two red bars of equal length represent CD = DB.

Aside: The 4 points could also be arranged as B..D..C......A, but that doesn't change the answer to the question

Target question: Is the length of line segment DB greater than 5?

Statement 1: The length of line segment AC is greater than 8
There are several scenarios that satisfy statement 1. Here are two:
Case a: AC = 9.

In this case, the answer to the target question is NO, line segment DB is NOT greater than 5

Case b: AC = 14.

In this case, the answer to the target question is YES, line segment DB IS greater than 5

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The length of line segment CD is greater than 6

Since CD = DB, we can conclude that line segment DB IS greater than 6, which means line segment DB IS greater than 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: A, B, C, and D are points on a line. If C is the midpoint of line segm   [#permalink] 13 Apr 2020, 06:15