In ABC, point D lies on the side AB between vertices A and B.If CD = CB, is AD BC?(1) ADC = 110(2) ACD = 30a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?

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GMAT Exam > GMAT Questions > In ΔABC, point D lies on the side AB bet...

In ΔABC, point D lies on the side AB between vertices A and B.
If CD = CB, is AD > BC?
(1) ∠ADC = 110
(2) ∠ACD = 30

a)
Statement (1) ALONE is sufficient, but statement (2) alone is
not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is
not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to
answer the question asked, but NEITHER statement ALONE
is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question
asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to
answer the question asked, and additional data specific to the
problem are needed.

Correct answer is option 'C'. Can you explain this answer?

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In ΔABC, point D lies on the side AB between vertices A and B.If ...

step 1 & 2: Understand Question and Draw Inference
Given:

Representing the given information visually as below:

In triangle BCD, CD = CB
- So, angles opposite to these sides will be equal. Let these angles measure X^o
Let ∠ACD = y^∘
So, the different angles in this figure will be as under:

To find: If AD > BC

That is, if AD > CD (since BC = CD)
That is, if in triangle ADC,
- ∠ACD > ∠DAC (since sides opposite to greater angles are greater)
- That is, y^∘ > x^∘ − y^∘
- That is, 2y^∘ > x^∘
So, the answer to the question will be YES if
2y^∘ > x^∘

Step 3 : Analyze Statement 1 independent

Step 4 : Analyze Statement 2 independent

Step 5: Analyze Both Statements Together (if needed)

From Statement 1:x = 70^∘

From Statement 2: y = 30^∘

Since we now know the values of x^oand y^owe can determine if 2y^o> X^o

Thus, the 2 statements together are sufficient to answer the question.

Answer: Option C

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Most Upvoted Answer

In ΔABC, point D lies on the side AB between vertices A and B.If ...

Statement (1) alone:
- ADC = 110
- We know that CD = CB
- Since D lies on the side AB between A and B, we can infer that D is the midpoint of AB.
- Therefore, AD = DB
- Since ADC is an isosceles triangle with CD = CB, angle ADC = angle ACB = 110 degrees.
- By the Angle-Side-Angle (ASA) congruence criterion, triangles ADC and ACB are congruent.
- Therefore, AD = AB
- From this information alone, we can conclude that AD = BC.

Statement (2) alone:
- ACD = 30
- We know that CD = CB
- Since D lies on the side AB between A and B, we can infer that D is the midpoint of AB.
- Therefore, AD = DB
- Since ACD is a right triangle with ACD = 30 degrees, angle ADC = 90 - 30 = 60 degrees.
- By the Angle-Side-Angle (ASA) congruence criterion, triangles ADC and ACB are congruent.
- Therefore, AD = AB
- From this information alone, we can conclude that AD = BC.

Both statements together:
- Combining the information from both statements, we have:
- ADC = 110
- ACD = 30
- CD = CB
- Since D lies on the side AB between A and B, we can infer that D is the midpoint of AB.
- Therefore, AD = DB
- Since ADC is an isosceles triangle with CD = CB, angle ADC = angle ACB = 110 degrees.
- By the Angle-Side-Angle (ASA) congruence criterion, triangles ADC and ACB are congruent.
- Therefore, AD = AB = BC.

Conclusion:
- Both statements together are sufficient to conclude that AD = BC.
- The correct answer is option 'C'.

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In ΔABC, point D lies on the side AB between vertices A and B.If CD = CB, is AD > BC?(1) ∠ADC = 110(2) ∠ACD = 30a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?

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In ΔABC, point D lies on the side AB between vertices A and B.If CD = CB, is AD > BC?(1) ∠ADC = 110(2) ∠ACD = 30a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In ΔABC, point D lies on the side AB between vertices A and B.If CD = CB, is AD > BC?(1) ∠ADC = 110(2) ∠ACD = 30a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In ΔABC, point D lies on the side AB between vertices A and B.If CD = CB, is AD > BC?(1) ∠ADC = 110(2) ∠ACD = 30a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?.

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