All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
GMAT Exam  >  GMAT Questions  >  Nonzero real numbers x, y, a, and b satisfy x... Start Learning for Free
Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How many of the following inequalities must be true?

(I) x + y < a + b
(II x - y < a - b
(III) xy < ab
(IV) x/y < a/b
  • a)
    0
  • b)
    1
  • c)
    2
  • d)
    3
  • e)
    4
Correct answer is option 'B'. Can you explain this answer?
Clear all your GMAT doubts with EduRev
Most Upvoted Answer
Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How...
Understanding the Problem
We have nonzero real numbers \(x, y, a,\) and \(b\) such that \(x < a\)="" and="" \(y="" />< b\).="" we="" need="" to="" analyze="" four="" inequalities="" to="" determine="" how="" many="" must="" be="" />
Analyzing Each Inequality
- (I) \(x + y < a="" +="" />
This inequality can be true. Since \(x < a\)="" and="" \(y="" />< b\),="" it="" follows="" that="" \(x="" +="" y="" />< a="" +="" b\)="" />
- (II) \(x - y < a="" -="" />
This inequality does not necessarily hold. For example, if \(x = 1, y = 2, a = 3, b = 2\), then \(x - y = -1\) and \(a - b = 1\), making the inequality true. However, if \(x = 2, y = 1, a = 3, b = 2\), then \(x - y = 1\) and \(a - b = 1\), which does not satisfy the inequality.
- (III) \(xy < />
This inequality does not necessarily hold either. For example, let \(x = 2, y = 3, a = 4, b = 6\). Here, \(xy = 6\) and \(ab = 24\), making it true. However, if \(x = 4, y = 3, a = 5, b = 6\), then \(xy = 12\) and \(ab = 30\), still making it true. There are cases where \(xy\) can be equal or larger than \(ab\).
- (IV) \(x/y < />
This inequality can also fail. Consider \(x = 2, y = 1, a = 3, b = 2\). Here, \(x/y = 2\) and \(a/b = 1.5\), so it does not hold.
Conclusion
From the analysis, only inequality (I) must always be true. Thus, the answer is option B: 1.
Explore Courses for GMAT exam

Similar GMAT Doubts

Comparable worth, as a standard applied to eliminate inequities in pay, insists that the values of certain tasks performed in dissimilar jobs can be compared. In the last decade, this approach has become a critical social policy issue, as large numbers of private-sector firms and industries as well as federal, state, and local governmental entities have adopted comparable worth policies or begun to consider doing so.This widespread institutional awareness of comparable worth indicates increased public awareness that pay inequities—that is, situations in which pay is not "fair" because it does not reflect the true value of a job—exist in the labor market. However, the question still remains: have the gains already made in pay equity under comparable worth principles been of a precedent-setting nature or are they mostly transitory, a function of concessions made by employers to mislead female employees into believing that they have made long-term pay equity gains?Comparable worth pay adjustments are indeed precedent-setting. Because of the principles driving them, other mandates that can be applied to reduce or eliminate unjustified pay gaps between male and female workers have not remedied perceived pay inequities satisfactorily for the litigants in cases in which men and women hold different jobs. But whenever comparable worth principles are applied to pay schedules, perceived unjustified pay differences are eliminated. In this sense then, comparable worth is more comprehensive than other mandates, such as the Equal Pay Act of 1963 and Title VII of the Civil Rights Act of 1964. Neither compares tasks in dissimilar jobs (that is, jobs across occupational categories) in an effort to determine whether or not what is necessary to perform these tasks—know-how, problem-solving, and accountability—can be quantified in terms of its dollar value to the employer. Comparable worth, on the other hand, takes as its premise that certain tasks in dissimilar jobs may require a similar amount of training, effort, and skill; may carry similar responsibility; may be carried on in an environment having a similar impact upon the worker; and may have a similar dollar value to the employer.According to the passage, which of the following is true of comparable worth as a policy?

Top Courses for GMATView all

Top Courses for GMAT

Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How many of the following inequalities must be true?(I) x + y < a + b(II x - y < a - b(III) xy < ab(IV) x/y < a/ba)0b)1c)2d)3e)4Correct answer is option 'B'. Can you explain this answer?
Question Description
Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How many of the following inequalities must be true?(I) x + y < a + b(II x - y < a - b(III) xy < ab(IV) x/y < a/ba)0b)1c)2d)3e)4Correct 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 Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How many of the following inequalities must be true?(I) x + y < a + b(II x - y < a - b(III) xy < ab(IV) x/y < a/ba)0b)1c)2d)3e)4Correct 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 Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How many of the following inequalities must be true?(I) x + y < a + b(II x - y < a - b(III) xy < ab(IV) x/y < a/ba)0b)1c)2d)3e)4Correct answer is option 'B'. Can you explain this answer?.
Solutions for Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How many of the following inequalities must be true?(I) x + y < a + b(II x - y < a - b(III) xy < ab(IV) x/y < a/ba)0b)1c)2d)3e)4Correct answer is option 'B'. 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 Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How many of the following inequalities must be true?(I) x + y < a + b(II x - y < a - b(III) xy < ab(IV) x/y < a/ba)0b)1c)2d)3e)4Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How many of the following inequalities must be true?(I) x + y < a + b(II x - y < a - b(III) xy < ab(IV) x/y < a/ba)0b)1c)2d)3e)4Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How many of the following inequalities must be true?(I) x + y < a + b(II x - y < a - b(III) xy < ab(IV) x/y < a/ba)0b)1c)2d)3e)4Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How many of the following inequalities must be true?(I) x + y < a + b(II x - y < a - b(III) xy < ab(IV) x/y < a/ba)0b)1c)2d)3e)4Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Nonzero real numbers x, y, a, and b satisfy x < a and y < b. How many of the following inequalities must be true?(I) x + y < a + b(II x - y < a - b(III) xy < ab(IV) x/y < a/ba)0b)1c)2d)3e)4Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
Explore Courses for GMAT exam

Top Courses for GMAT

Explore Courses
SaveJoin the Discussion on the App for FREE
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup