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A number when divided by 5 and 7 successively, leaves the remainder 2 and 4 respectively. Find the remainder when the same number is divided by 35?
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A number when divided by 5 and 7 successively, leaves the remainder 2 ...
Problem: A number when divided by 5 and 7 successively, leaves the remainder 2 and 4 respectively. Find the remainder when the same number is divided by 35?
Solution:
Given, when the number is divided by 5, the remainder is 2 and when the same number is divided by 7, the remainder is 4.
We need to find the remainder when the same number is divided by 35.
Method:
To find the remainder when the number is divided by 35, we need to find the number first.
We can use the Chinese Remainder Theorem to find the number.
Step 1:
Let the number be x.
x ≡ 2 (mod 5)
x ≡ 4 (mod 7)
Step 2:
We need to find a number y such that
5 × y ≡ 1 (mod 7)
We can see that y = 3 satisfies the above equation since
5 × 3 = 15 ≡ 1 (mod 7)
Step 3:
Using the above value of y, we can find the value of x as
x = (2 × 7 × 3 – 4 × 5 × 3) mod (5 × 7)
x = (42 – 60) mod 35
x = 17
Therefore, the number is 17.
Step 4:
To find the remainder when 17 is divided by 35, we can use the following formula:
Remainder = Number – (Divisor × Quotient)
Remainder = 17 – (35 × 0)
Remainder = 17
Therefore, the remainder when the number is divided by 35 is 17.
Answer: The remainder when the number is divided by 35 is 17.
Solution:
Given, when the number is divided by 5, the remainder is 2 and when the same number is divided by 7, the remainder is 4.
We need to find the remainder when the same number is divided by 35.
Method:
To find the remainder when the number is divided by 35, we need to find the number first.
We can use the Chinese Remainder Theorem to find the number.
Step 1:
Let the number be x.
x ≡ 2 (mod 5)
x ≡ 4 (mod 7)
Step 2:
We need to find a number y such that
5 × y ≡ 1 (mod 7)
We can see that y = 3 satisfies the above equation since
5 × 3 = 15 ≡ 1 (mod 7)
Step 3:
Using the above value of y, we can find the value of x as
x = (2 × 7 × 3 – 4 × 5 × 3) mod (5 × 7)
x = (42 – 60) mod 35
x = 17
Therefore, the number is 17.
Step 4:
To find the remainder when 17 is divided by 35, we can use the following formula:
Remainder = Number – (Divisor × Quotient)
Remainder = 17 – (35 × 0)
Remainder = 17
Therefore, the remainder when the number is divided by 35 is 17.
Answer: The remainder when the number is divided by 35 is 17.
Community Answer
A number when divided by 5 and 7 successively, leaves the remainder 2 ...
No can be represented as 5a+2 or 7b+4
put b=0,1,2,3,4 etc and saw that for b=4 we get 32 which also fits in 5a+2 category when a=6
326 will give 32
put b=0,1,2,3,4 etc and saw that for b=4 we get 32 which also fits in 5a+2 category when a=6
326 will give 32
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A number when divided by 5 and 7 successively, leaves the remainder 2 and 4 respectively. Find the remainder when the same number is divided by 35?
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A number when divided by 5 and 7 successively, leaves the remainder 2 and 4 respectively. Find the remainder when the same number is divided by 35? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A number when divided by 5 and 7 successively, leaves the remainder 2 and 4 respectively. Find the remainder when the same number is divided by 35? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided by 5 and 7 successively, leaves the remainder 2 and 4 respectively. Find the remainder when the same number is divided by 35?.
A number when divided by 5 and 7 successively, leaves the remainder 2 and 4 respectively. Find the remainder when the same number is divided by 35? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A number when divided by 5 and 7 successively, leaves the remainder 2 and 4 respectively. Find the remainder when the same number is divided by 35? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided by 5 and 7 successively, leaves the remainder 2 and 4 respectively. Find the remainder when the same number is divided by 35?.
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