The sides AC and BC of ∆ABC are parallel, respectively, to

Question

triangles.png The sides AC and BC of ∆ABC are parallel, respectively, to the lines L and M outside the triangle. What is the value of x ? (1) ∠B = 40° (2) ∠y = 100° What is the length of AB ? The sides AC and BC of triangle ABC are parallel, respectively, to the lines L and M outside the triangle. (1) < B = 40 (2) < y = 100

blueseas · Answer

clearly this is C

STATEMENT 1 AND 2 ALONE ARE INSUFFICIENT. AS WE KNOW ONLY ONE SIDE AND ONE ANGLE OF TRIANLE IN EACH CASE==>that will result in to various triangles hence length of AB will not be fixed.
hence insufficient.

combining both we know all 3 angles and one side length==>this gives a unique triangle and the length of which can be calculated.
hence sufficient

note: IN DS we dont need to calculate to end result ,only by knowing that whether the answer is definite or not we can answer the question.

cssk · Answer

Hi blueseas,

How can we conclude that knowing 3 angles and one side is sufficient to calculate the lengths of other sides.

I got confused with that. Kindly explain.

Thanks.

Bunuel · Answer

Because in this case a triangle is "fixed": only one such triangle can exist. For more check here: math-triangles-87197.html BTW: original question is different. Just edited.

WholeLottaLove · Answer

The sides AC and BC of ∆ABC are parallel, respectively, to the lines L and M outside the triangle. What is the value of x ?

(1) ∠B = 40°

Gives us angle B but we have no idea what the remaining two interior angles ad up to. Not Sufficient

(2) ∠y = 100°

We know that the interior angles B, C ad up to 100 but we don't know what their exact measures are. Not Sufficient.

1+2) We know that b+c = 100 and that b = 40 so c = 60. Because of alternate interior angles, and because the measures of x must = the measure of c, x = 60 degrees. SUFFICIENT

C

TooLong150 · Answer

Blueseas and Bunuel, why do the sides matter in this DS problem since we only need to calculate the value of an angle?

Bunuel · Answer

For the edited question the length of the sides does not matter.

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The sides AC and BC of ∆ABC are parallel, respectively, to

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GMAT Data Sufficiency (DS) Questions

The sides AC and BC of ∆ABC are parallel, respectively, to

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