In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?(1) If the slope of m is y and the slope of n is z, then andndash;yz = 1.(2) m has a slope of andndash;1, and n passes through the point (andndash;x, andndash;x).a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > In the rectangular coordinate system, lines m...

Join the Discussion on the App

In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?

(1) If the slope of m is y and the slope of n is z, then –yz = 1.
(2) m has a slope of –1, and n passes through the point (–x, –x).

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
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 are needed

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

FREE This question is part of

Test: Coordinate Geometry

Attempt Test

Attempt this Test

Most Upvoted Answer

In the rectangular coordinate system, lines m and n cross at the origi...

To determine whether line m is perpendicular to line n, we need to analyze the given statements.

Statement (1) states that if the slope of line m is represented by y and the slope of line n is represented by z, then –yz = 1. From this statement, we can conclude that the product of the slopes of lines m and n is equal to -1. In the rectangular coordinate system, two lines are perpendicular if and only if the product of their slopes is -1. Therefore, statement (1) alone is sufficient to answer the question, and the answer cannot be E or C.

Statement (2) tells us that line m has a slope of -1, and line n passes through the point (-x, -x). While this information provides the slope of line m, it does not provide any direct information about the slope of line n. Without the slope of line n, we cannot definitively determine whether line m is perpendicular to line n. Thus, statement (2) alone is not sufficient to answer the question.

Considering the statements together, we have the slope of line m (-1) from statement (2) and the relationship between the slopes of lines m and n (-yz = 1) from statement (1). Combining these two pieces of information, we can conclude that line m is perpendicular to line n. Therefore, each statement alone is sufficient to answer the question.

Hence, the answer is D: EACH statement ALONE is sufficient to answer the question asked.

Answered by Talent Skill Learning · View profile

Attention GMAT Students!

To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for GMAT exam

Similar GMAT Doubts

In the rectangular coordinate system, lines L1 and L2 intersect at point C. Are the lines L1 and L2 perpendicular to each other?(1) The product of the slopes of lines L1 and L2 is at a distance of 1 unit from 0 on the number line.(2) Lines x = 0 and y = 0 are the perpendicular bisectors of lines L1 and L2 respectively.

View answer

In the rectangular plane, point A has coordinates (a,0), point B has coordinates (0, b), and point O is at the origin. What is the measure of angle BAO?(1) a = 4(2) b =α√3

View answer

Directions: Each GMAT Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.For integers w, x, y, and z, is wxyz = -1?(1) wx / yz = -1(2) w = -1/x and y = 1/z

View answer

Directions: Each Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.A codebreaking device is made up of a rectangular box filled with x cylinders of ball bearings placed together such that the diameter of the bearings and the cylinders are equal, and the cylinders line up evenly, touching, with no extra room inside the device. If the cylinders are the same height as the box, and the box is 18 inches long and 10 inches wide, what’s the value of x?(1) 9 cylinders can line up along the length of the box.(2) Each ball bearing has a radius of 1.

View answer

Directions: Each GMAT Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.How many integers are there between m and n, exclusive, if m and n are themselves integers?(1) m − n = 8(2) There are 5 integers between, but not including, m − 1 and n − 1.

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

100 RCs for GMAT

Top Courses for GMAT

View all

In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?(1) If the slope of m is y and the slope of n is z, then –yz = 1.(2) m has a slope of –1, and n passes through the point (–x, –x).a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?(1) If the slope of m is y and the slope of n is z, then –yz = 1.(2) m has a slope of –1, and n passes through the point (–x, –x).a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?(1) If the slope of m is y and the slope of n is z, then –yz = 1.(2) m has a slope of –1, and n passes through the point (–x, –x).a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?(1) If the slope of m is y and the slope of n is z, then –yz = 1.(2) m has a slope of –1, and n passes through the point (–x, –x).a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?.

Solutions for In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?(1) If the slope of m is y and the slope of n is z, then –yz = 1.(2) m has a slope of –1, and n passes through the point (–x, –x).a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?(1) If the slope of m is y and the slope of n is z, then –yz = 1.(2) m has a slope of –1, and n passes through the point (–x, –x).a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?(1) If the slope of m is y and the slope of n is z, then –yz = 1.(2) m has a slope of –1, and n passes through the point (–x, –x).a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?(1) If the slope of m is y and the slope of n is z, then –yz = 1.(2) m has a slope of –1, and n passes through the point (–x, –x).a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?(1) If the slope of m is y and the slope of n is z, then –yz = 1.(2) m has a slope of –1, and n passes through the point (–x, –x).a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?(1) If the slope of m is y and the slope of n is z, then –yz = 1.(2) m has a slope of –1, and n passes through the point (–x, –x).a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam