CAT Exam > CAT Questions > How many ordered pairs of natural numbers sat...
Start Learning for Free
How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?
- a)8
- b)12
- c)10
- d)15
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
How many ordered pairs of natural numbers satisfy the inequality 8x + ...
The inequality 8x - 2y < 40="" can="" be="" rewritten="" as="" 4x="" -="" y="" />< />
Let's consider the possible values for x and y.
When x = 1, the inequality becomes 4(1) - y < 20,="" which="" simplifies="" to="" -y="" />< 16.="" since="" y="" is="" a="" natural="" number,="" the="" only="" possible="" value="" is="" y="" />
When x = 2, the inequality becomes 4(2) - y < 20,="" which="" simplifies="" to="" 8="" -="" y="" />< 20.="" solving="" for="" y,="" we="" get="" y="" /> -12. Since y is a natural number, the possible values for y are 1, 2, 3, ..., 11, which is a total of 11 values.
Similarly, when x = 3, we have y > -8, giving us a total of 9 possible values for y.
Continuing this pattern, we find that when x = 1, there is 1 possible value for y. When x = 2, there are 11 possible values for y. When x = 3, there are 9 possible values for y. And so on.
Therefore, the total number of ordered pairs of natural numbers that satisfy the inequality is 1 + 11 + 9 + ... = 1 + 11 + 9 + 7 + 5 + 3 + 1 = 37.
Let's consider the possible values for x and y.
When x = 1, the inequality becomes 4(1) - y < 20,="" which="" simplifies="" to="" -y="" />< 16.="" since="" y="" is="" a="" natural="" number,="" the="" only="" possible="" value="" is="" y="" />
When x = 2, the inequality becomes 4(2) - y < 20,="" which="" simplifies="" to="" 8="" -="" y="" />< 20.="" solving="" for="" y,="" we="" get="" y="" /> -12. Since y is a natural number, the possible values for y are 1, 2, 3, ..., 11, which is a total of 11 values.
Similarly, when x = 3, we have y > -8, giving us a total of 9 possible values for y.
Continuing this pattern, we find that when x = 1, there is 1 possible value for y. When x = 2, there are 11 possible values for y. When x = 3, there are 9 possible values for y. And so on.
Therefore, the total number of ordered pairs of natural numbers that satisfy the inequality is 1 + 11 + 9 + ... = 1 + 11 + 9 + 7 + 5 + 3 + 1 = 37.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer?
Question Description
How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer?.
How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer?.
Solutions for How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer?, a detailed solution for How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup