CAT Exam > CAT Questions > x is the smallest positive integer such that ...
Start Learning for Free
x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.
(2015)
- a)49
- b)76
- c)94
- d)15
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
x is the smallest positive integer such that when it is divided by 7, ...
x = L.C.M. of (7, 8, 9) – 3 = 504 – 3 = 501
x3 + 2x2 + x – 3 = (x – 1) (x + 1) (x + 2) –1
= 500 × 502 × 503 – 1
Remainder when 500 × 502 × 503 – 1 is divided by:
11 = 4
3 = 0
4 = 3
Required remainder = least possible number which when divided by 11, 3 and 4 leavs remainder 4, 0 and 3 respectively.
Such least no. is 15.
x3 + 2x2 + x – 3 = (x – 1) (x + 1) (x + 2) –1
= 500 × 502 × 503 – 1
Remainder when 500 × 502 × 503 – 1 is divided by:
11 = 4
3 = 0
4 = 3
Required remainder = least possible number which when divided by 11, 3 and 4 leavs remainder 4, 0 and 3 respectively.
Such least no. is 15.
Most Upvoted Answer
x is the smallest positive integer such that when it is divided by 7, ...
To find the remainder when $x^{3}-2x^{2}$ is divided by $7,8,$ and $9,$ we can find the remainders of $x^{3}$ and $2x^{2}$ when divided by $7,8,$ and $9,$ and then subtract.
$x\equiv4\pmod7$ implies $x^{2}\equiv2\pmod7$ and $x^{3}\equiv8\equiv1\pmod7.$
$x\equiv5\pmod8$ implies $x^{2}\equiv1\pmod8$ and $x^{3}\equiv5\pmod8.$
$x\equiv6\pmod9$ implies $x^{2}\equiv0\pmod9$ and $x^{3}\equiv0\pmod9.$
Thus, $x^{3}-2x^{2}\equiv1-2(5)\equiv\boxed{3}\pmod8.$
$x\equiv4\pmod7$ implies $x^{2}\equiv2\pmod7$ and $x^{3}\equiv8\equiv1\pmod7.$
$x\equiv5\pmod8$ implies $x^{2}\equiv1\pmod8$ and $x^{3}\equiv5\pmod8.$
$x\equiv6\pmod9$ implies $x^{2}\equiv0\pmod9$ and $x^{3}\equiv0\pmod9.$
Thus, $x^{3}-2x^{2}\equiv1-2(5)\equiv\boxed{3}\pmod8.$
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
x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. Can you explain this answer?
Question Description
x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. 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 x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. Can you explain this answer?.
x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. 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 x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. Can you explain this answer?.
Solutions for x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. 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 x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. Can you explain this answer?, a detailed solution for x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice x is the smallest positive integer such that when it is divided by 7, 8 and 9 leaves remainder as 4, 5 and 6 respectively. Find the remainder when x3 + 2x2 – x – 3 is divided by 132.(2015)a)49b)76c)94d)15Correct answer is option 'D'. 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