In the figure above, line segment \(CZ = 6.\) What is the length of line segment \(AB?\)

[Vincen]

In the figure above, line segment \(CZ = 6.\) What is the length of line segment \(AB?\)

(1) Line segment \(XY = 4.\)

(2) Line segment \(AZ >\) Line segment \(AY.\)

[spoiler]OA=A[/spoiler]

Source: Veritas Prep

[Jay@ManhattanReview]

Yaz.png

In the figure above, line segment \(CZ = 6.\) What is the length of line segment \(AB?\)

(1) Line segment \(XY = 4.\)

(2) Line segment \(AZ >\) Line segment \(AY.\)

[spoiler]OA=A[/spoiler]

Source: Veritas Prep

Let's take each statement one by one.

(1) Line segment \(XY = 4.\)

See the attached diagram. Note that the length of YZ has no bearing on the length of AB. I moved XY = 4 closer to CZ, you will notice that though AB changes its position to A'B', it's still AB, so it's length is constant.

This is a DS question and we need not necessarily calculate the value of AB if we are sure that it's unique. Here, we are sure that AB is determinable, so we would have its unique value. Sufficient.

(2) Line segment \(AZ >\) Line segment \(AY.\)

Insufficient.

Correct answer: A

Hope this helps!

-Jay
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