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In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle (a triangle each of whose angles measures less than 90∘)?
(1) NM = 10
(2) LM = 7
- 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 'D'. Can you explain this answer?
Verified Answer
In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a numb...
Given: Some number x
- ΔLMN with sides as shown below:
Find: Is ΔLMN an acute triangle?
Step 3: Analyze Statement 1 independently
- NM = 10
- That is, |x -4| = 10
- So, x is a number whose distance from 4 on the number line is 10
- So, x = -6 or 14
- Rejecting the negative value since x + 1, being the length of a geometric figure, must be positive.
- So, x = 14
- Therefore, the sides of the triangle are:
- 15, 10, 7
- The longest side is 15
- 102 + 72 < 152
- 15, 10, 7
- Therefore, the triangle is obtuse.
- (Note: An obtuse triangle is a triangle one of whose angles is greater than 90∘)
- So, the answer to the given question is NO.
- Since we’ve been able to arrive at a unique answer to the question, Statement 1 alone is sufficient.
Step 4: Analyze Statement 2 independently
- LM = 7
- |x-7| = 7
- So, x is a number whose distance from 7 on the number line is 7
- So, x = 0 or 14
- Case 1: x = 0
- The sides of the triangle are:
- 1, 4, 7
- The longest side is 7
- 1, 4, 7
- In this case, the sum of 2 sides of the triangle (1 + 4) is not greater than the 3rd side
- Therefore, this triangle is not possible
- So, this value of x is not possible.
- Case 2: x = 14
- So, the sides of the triangle are:
- 15, 10, 7
- The longest side is 15
- 102 + 72 < 152
- 15, 10, 7
- Therefore, the triangle is obtuse.
- So, the answer to the given question is NO.
- Since we’ve been able to arrive at a unique answer to the question, Statement 2 alone is sufficient
- Step 5: Analyze Both Statements Together (if needed)Since we’ve already arrived at a unique answer in each of Steps 3 and 4, this step is not requiredHence the correct answer is Option D .
Most Upvoted Answer
In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a numb...
Statement 1: NM = 10
Statement 2: LM = 7
To determine if LMN is an acute triangle, we need to compare the lengths of its sides.
Analysis of Statement 1:
NM = 10
Since we know the length of NM, we can find the difference between LM and NL by subtracting NM from MN.
MN - NM = |x-4| - 10 = |x-4|-10
Since we don't have any information about LM or NL, we cannot determine if LMN is an acute triangle based on this statement alone.
Analysis of Statement 2:
LM = 7
Since we know the length of LM, we can find the difference between LM and MN by subtracting LM from MN.
MN - LM = |x-4| - 7 = |x-4|-7
Again, since we don't have any information about NL or the value of x, we cannot determine if LMN is an acute triangle based on this statement alone.
Analysis of Statements 1 and 2 together:
Combining the information from both statements, we have:
NM = 10
LM = 7
Using these values, we can find the difference between LM and NL as well as the difference between LM and MN.
MN - NM = |x-4| - 10 = |x-4|-10
MN - LM = |x-4| - 7 = |x-4|-7
However, even with this additional information, we still cannot determine if LMN is an acute triangle because we do not know the value of x or have any constraints on its range.
Therefore, neither statement alone nor both statements together are sufficient to answer the question.
Hence, the correct answer is option D.
Statement 2: LM = 7
To determine if LMN is an acute triangle, we need to compare the lengths of its sides.
Analysis of Statement 1:
NM = 10
Since we know the length of NM, we can find the difference between LM and NL by subtracting NM from MN.
MN - NM = |x-4| - 10 = |x-4|-10
Since we don't have any information about LM or NL, we cannot determine if LMN is an acute triangle based on this statement alone.
Analysis of Statement 2:
LM = 7
Since we know the length of LM, we can find the difference between LM and MN by subtracting LM from MN.
MN - LM = |x-4| - 7 = |x-4|-7
Again, since we don't have any information about NL or the value of x, we cannot determine if LMN is an acute triangle based on this statement alone.
Analysis of Statements 1 and 2 together:
Combining the information from both statements, we have:
NM = 10
LM = 7
Using these values, we can find the difference between LM and NL as well as the difference between LM and MN.
MN - NM = |x-4| - 10 = |x-4|-10
MN - LM = |x-4| - 7 = |x-4|-7
However, even with this additional information, we still cannot determine if LMN is an acute triangle because we do not know the value of x or have any constraints on its range.
Therefore, neither statement alone nor both statements together are sufficient to answer the question.
Hence, the correct answer is option D.
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In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. Can you explain this answer?
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In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. 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 ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. 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 ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. Can you explain this answer?.
In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. 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 ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. 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 ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. Can you explain this answer?.
Solutions for In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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Here you can find the meaning of In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. Can you explain this answer?, a detailed solution for In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. Can you explain this answer? has been provided alongside types of In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In ΔLMN, LM = |x-7|, MN = |x-4| and NL = x + 1, where x is a number whose value is not known. Is ΔLMN an acute triangle(a triangle each of whose angles measures less than 90∘)?(1) NM = 10(2) LM = 7a)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 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
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