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OG A, B, C, and D are points on a line.

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OG A, B, C, and D are points on a line.

by AbeNeedsAnswers » Thu Aug 24, 2017 8:29 pm

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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

B
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Source: — Data Sufficiency |

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by [email protected] » Tue Sep 05, 2017 10:33 am

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Hi AbeNeedsAnswers,

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

Final Answer: B

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Re: OG A, B, C, and D are points on a line.

by AdityaBir » Sat Jan 25, 2020 5:17 am

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AbeNeedsAnswers wrote: ↑
Thu Aug 24, 2017 8:29 pm
 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

B
1) Length of AC is greater than 8.
DB =AC/2.
length of AC can be 9 or 11,12 etc. Not sufficient to determine whether DB>5.
Statement 1) alone is not sufficient.
2) since D is midpoint of CB, CD=DB, so using 2) we can conclude DB>6.
Statement 2) alone is sufficient.
Hence option B is correct.
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