Quant Exam > Quant Questions > A certain number when successively divided by...
Start Learning for Free
A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.
- a)190
- b)112
- c)156
- d)138
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A certain number when successively divided by 4, 5 and 7 leaves remain...
See Diference between Divisor and remaider
4-2=2 = k
5-3=2 = k
7-5=2 = k
this difference is same
so answer will be LCM(4,5,7) - k
140 - 2
138
4-2=2 = k
5-3=2 = k
7-5=2 = k
this difference is same
so answer will be LCM(4,5,7) - k
140 - 2
138
Most Upvoted Answer
A certain number when successively divided by 4, 5 and 7 leaves remain...
U can do this by hit and trial
divide each option by 9,7,5 and when u will get 8 ,5,1 as remainder that will be ur answer
divide each option by 9,7,5 and when u will get 8 ,5,1 as remainder that will be ur answer
Free Test
FREE
| Start Free Test |
Community Answer
A certain number when successively divided by 4, 5 and 7 leaves remain...
Given: Number when divided by 9, 7, and 5 leaves remainders 8, 5, and 1 respectively.
To find: Smallest 4-digit number satisfying the given conditions.
Solution:
Let the number be x.
x ≡ 8 (mod 9)
x ≡ 5 (mod 7)
x ≡ 1 (mod 5)
We can use the Chinese Remainder Theorem (CRT) to solve the above system of congruences.
Step 1: Find the product of the moduli of the given congruences.
M = 9 x 7 x 5 = 315
Step 2: Find the values of Mi such that Mi ≡ M/mi (mod mi), where mi is the modulus of each congruence.
M1 = 315/9 = 35
M2 = 315/7 = 45
M3 = 315/5 = 63
Step 3: Find the solutions of the given congruences with respect to each modulus using the extended Euclidean algorithm.
x1 ≡ 1 (mod 9) => x1 = 8 + 9k1, where k1 is an integer.
x2 ≡ 1 (mod 7) => x2 = 5 + 7k2, where k2 is an integer.
x3 ≡ 1 (mod 5) => x3 = 1 + 5k3, where k3 is an integer.
Step 4: Find the solution of the system of congruences using CRT.
x ≡ Σ(xiMiMi^-1) (mod M), where xi = MiMi^-1 (mod mi) and Mi^-1 is the inverse of Mi modulo mi.
x ≡ (8 x 45 x 4) + (5 x 35 x 2) + (1 x 63 x 1) (mod 315)
x ≡ 1440 (mod 315)
The smallest 4-digit number satisfying the given conditions is 1061, which is the smallest number greater than or equal to 1440 that leaves a remainder of 8 when divided by 9, a remainder of 5 when divided by 7, and a remainder of 1 when divided by 5.
Therefore, the correct answer is option (D) 1061.
To find: Smallest 4-digit number satisfying the given conditions.
Solution:
Let the number be x.
x ≡ 8 (mod 9)
x ≡ 5 (mod 7)
x ≡ 1 (mod 5)
We can use the Chinese Remainder Theorem (CRT) to solve the above system of congruences.
Step 1: Find the product of the moduli of the given congruences.
M = 9 x 7 x 5 = 315
Step 2: Find the values of Mi such that Mi ≡ M/mi (mod mi), where mi is the modulus of each congruence.
M1 = 315/9 = 35
M2 = 315/7 = 45
M3 = 315/5 = 63
Step 3: Find the solutions of the given congruences with respect to each modulus using the extended Euclidean algorithm.
x1 ≡ 1 (mod 9) => x1 = 8 + 9k1, where k1 is an integer.
x2 ≡ 1 (mod 7) => x2 = 5 + 7k2, where k2 is an integer.
x3 ≡ 1 (mod 5) => x3 = 1 + 5k3, where k3 is an integer.
Step 4: Find the solution of the system of congruences using CRT.
x ≡ Σ(xiMiMi^-1) (mod M), where xi = MiMi^-1 (mod mi) and Mi^-1 is the inverse of Mi modulo mi.
x ≡ (8 x 45 x 4) + (5 x 35 x 2) + (1 x 63 x 1) (mod 315)
x ≡ 1440 (mod 315)
The smallest 4-digit number satisfying the given conditions is 1061, which is the smallest number greater than or equal to 1440 that leaves a remainder of 8 when divided by 9, a remainder of 5 when divided by 7, and a remainder of 1 when divided by 5.
Therefore, the correct answer is option (D) 1061.
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer?
Question Description
A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer?.
A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer?.
Solutions for A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A certain number when successively divided by 4, 5 and 7 leaves remainders 2, 3 and 5 respectively. Find such a least number.a)190b)112c)156d)138Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup