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In triangle ABC (not shown), is the range of the angles of the triangle greater than 90o?
(1) The median angle of triangle ABC is 70o
(2) The difference between the two larger angles of triangle ABC
is 10o
(1) The median angle of triangle ABC is 70o
(2) The difference between the two larger angles of triangle ABC
is 10o
- 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 'B'. Can you explain this answer?
Verified Answer
In triangle ABC (not shown), is the range of the angles of the triangl...
Step 1 & 2: Understand Question and Draw Inference
Given: A triangle ABC
- Let the angles of the triangle be x, y, z in increasing order of magnitude.
- We know x + y + z = 180o . . . (1)
To find: Is z – x > 90o ?
Step 3 : Analyze Statement 1 independent
(1) The median angle of triangle ABC is 70o.
But we do not know if x < 10o . So, Statement 1 alone is not sufficient.
Step 4 : Analyze Statement 2 independent
(2) The difference between the two larger angles of triangle ABC is 10o
But we do not know if 
So, Statement 2 alone is not sufficient.
So, Statement 2 alone is not sufficient.Step 5: Analyze Both Statements Together (if needed)
- From Statement 1: y = 70
- From Statement 2: z – y = 10
- By combining these two equations, we’ll get a unique value of z
- From (1), we’ll get a unique value of x
Since we now know the values of x, y and z, we’ll be able to answer the question on the range of the angles.
The two statements together are sufficient to answer the question.
The two statements together are sufficient to answer the question.
Answer: Option C
Most Upvoted Answer
In triangle ABC (not shown), is the range of the angles of the triangl...
Explanation:
The question asks whether the range of the angles in the triangle is greater than 90o. In other words, is the largest angle greater than 90o?
Statement 1:
The median angle of triangle ABC is 70o.
The median angle is the angle opposite the median, which is the line segment connecting the midpoint of one side to the opposite vertex. Since the median angle is 70o, we know that two of the angles in the triangle are less than 70o. However, we cannot determine whether the largest angle is greater than 90o based on this information alone.
Statement 1 is insufficient.
Statement 2:
The difference between the two larger angles of triangle ABC is 10o.
Let A be the largest angle, and B and C be the other two angles. Then we have two cases:
- Case 1: A is one of the two larger angles. Without loss of generality, let A = B + 10. Then C = 180 - 2B - 10 = 170 - 2B. Since A > B and A > C, we have B + 10 > 170 - 2B, which simplifies to 3B < 160,="" or="" b="" />< 53.33.="" therefore,="" a="" /> 63.33. In this case, the range of the angles is greater than 90o.
- Case 2: A is not one of the two larger angles. Without loss of generality, let B be the larger of the two angles. Then A = B + 10 and C = 180 - 2B - 10 = 170 - 2B. Since A > C, we have B + 10 > 170 - 2B, which simplifies to 3B < 160,="" or="" b="" />< 53.33.="" therefore,="" a="" /> 63.33. In this case, the range of the angles is also greater than 90o.
Therefore, statement 2 alone is sufficient to answer the question.
Answer:
Option B: Statement (2) alone is sufficient, but statement (1) alone is not sufficient to answer the question asked.
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In triangle ABC (not shown), is the range of the angles of the triangle greater than 90o?(1) The median angle of triangle ABC is 70o(2) The difference between the two larger angles of triangle ABCis 10oa)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 neededCorrect answer is option 'B'. Can you explain this answer?
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In triangle ABC (not shown), is the range of the angles of the triangle greater than 90o?(1) The median angle of triangle ABC is 70o(2) The difference between the two larger angles of triangle ABCis 10oa)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 neededCorrect answer is option 'B'. 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 triangle ABC (not shown), is the range of the angles of the triangle greater than 90o?(1) The median angle of triangle ABC is 70o(2) The difference between the two larger angles of triangle ABCis 10oa)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 neededCorrect answer is option 'B'. 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 triangle ABC (not shown), is the range of the angles of the triangle greater than 90o?(1) The median angle of triangle ABC is 70o(2) The difference between the two larger angles of triangle ABCis 10oa)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 neededCorrect answer is option 'B'. Can you explain this answer?.
In triangle ABC (not shown), is the range of the angles of the triangle greater than 90o?(1) The median angle of triangle ABC is 70o(2) The difference between the two larger angles of triangle ABCis 10oa)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 neededCorrect answer is option 'B'. 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 triangle ABC (not shown), is the range of the angles of the triangle greater than 90o?(1) The median angle of triangle ABC is 70o(2) The difference between the two larger angles of triangle ABCis 10oa)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 neededCorrect answer is option 'B'. 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 triangle ABC (not shown), is the range of the angles of the triangle greater than 90o?(1) The median angle of triangle ABC is 70o(2) The difference between the two larger angles of triangle ABCis 10oa)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 neededCorrect answer is option 'B'. Can you explain this answer?.
Solutions for In triangle ABC (not shown), is the range of the angles of the triangle greater than 90o?(1) The median angle of triangle ABC is 70o(2) The difference between the two larger angles of triangle ABCis 10oa)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 neededCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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