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OG Point D is on AC.

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AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG Point D is on AC.

Post Tue Aug 22, 2017 7:27 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    ttps://postimg.org/image/5ychiodlh/" target="_blank">

    In the figure above, point D is on AC. What is the degree measure of ∠BAC?

    (1) The measure of ∠BDC is 60°
    (2) The degree measure of BAC is less than the degree measure of BCD.

    A

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    Post Tue Sep 12, 2017 9:18 am
    Hi AbeNeedsAnswers,

    This question asks us for the measure of ∠BAC. To answer it, we'll need to think about the 3 triangles in picture (the two 'smaller' triangle and the larger triangle that holds them).

    (1) The measure of ∠BDC is 60°

    With ∠BDC = 60, we can determine...
    ∠BDA = 120 (since lines sum to 180 degrees)
    ∠BAC = 40 (since triangles sum to 180 degrees and we have the other 2 angles in the triangle).
    Fact 1 is SUFFICIENT

    (2) The degree measure of ∠BAC is less than the degree measure of∠BCD.

    Fact 2 doesn't give us any numbers to work with, so there are LOTS of different possible values for
    ∠BAC.
    Fact 2 is INSUFFICIENT

    Final Answer: A

    GMAT assassins aren't born, they're made,
    Rich

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    GMAT/MBA Expert

    Post Fri Dec 08, 2017 10:22 am
    AbeNeedsAnswers wrote:
    ttps://postimg.org/image/5ychiodlh/" target="_blank">

    In the figure above, point D is on AC. What is the degree measure of ∠BAC?

    (1) The measure of ∠BDC is 60°
    (2) The degree measure of BAC is less than the degree measure of BCD.
    We are given the following diagram:



    We need to determine the degree measure of ∠BAC, which is also the degree measure of ∠BAD.

    Statement One Alone:

    The measure of ∠BDC is 60°.

    We can fill the above information into our diagram.



    Since ∠ADB and ∠BDC are supplementary, their total degree measurement is equal to 180.

    Thus, m∠ADB = 180 - 60 = 120 degrees.

    Since we have 2 of the 3 angles in triangle ABD, we can determine the measure of ∠BAC:

    m∠BAC = 180 - 120 - 20 = 40 degrees.

    Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

    Alternate solution:

    We can see that ∠ADB is an exterior angle of triangle ABD, and it is equal to the sum of the measures of ∠BAD and ∠ABD (recall that the measure of an exterior angle of a triangle is the sum of the measures of the two remote interior angles).

    Therefore, m∠BAD = m∠ADB - m∠ABD = 60 - 20 = 40 degrees.

    Statement Two Alone:

    The degree measure of ∠BAC is less than the degree measure of ∠BCD.

    Knowing that the measure of ∠BAC is less than the measure of ∠BCD does not allow us to determine the measure of ∠BAC. Statement two is not sufficient.

    Answer: A

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