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A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder is
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A number when divided by 6 leaves remainder 3. When the square of the ...
Let the number be ‘x’
x = 6y + 3
x2 = (6y + 3)2
x2 = 36y2 + 36y + 9
x2 = 6 × (6y2 + 6y + 1) + 3
∴ When the square of the same number is divided by 6, the remainder will be 3.
x = 6y + 3
x2 = (6y + 3)2
x2 = 36y2 + 36y + 9
x2 = 6 × (6y2 + 6y + 1) + 3
∴ When the square of the same number is divided by 6, the remainder will be 3.
Most Upvoted Answer
A number when divided by 6 leaves remainder 3. When the square of the ...
To solve this problem, we need to use the concept of remainders when dividing by a number. Let's break down the problem step by step:
Step 1: Given that a number, when divided by 6, leaves a remainder of 3. We can represent this as:
Number = 6n + 3, where n is an integer.
Step 2: We need to find the remainder when the square of the number is divided by 6. Let's square the expression we obtained in Step 1:
Number^2 = (6n + 3)^2
= 36n^2 + 36n + 9
Step 3: Now, let's divide the squared number by 6 and find the remainder. We can express this as:
Number^2 = 6m + remainder, where m is an integer.
So, substituting the expression from Step 2:
36n^2 + 36n + 9 = 6m + remainder
Step 4: To find the remainder, we can simplify the equation:
36n^2 + 36n + 9 = 6m + remainder
(6n + 3)(6n + 3) = 6m + remainder
(6n + 3)^2 = 6m + remainder
Step 5: From Step 1, we know that (6n + 3) is the number. So, we can substitute it in Step 4:
(6n + 3)^2 = 6m + remainder
Number^2 = 6m + remainder
Step 6: From Step 5, we can conclude that the remainder when the square of the number is divided by 6 is the same as the remainder when the number itself is divided by 6. Therefore, the remainder is 3 (option D).
In summary, when a number is divided by 6 and leaves a remainder of 3, the remainder when the square of the number is divided by 6 will also be 3.
Step 1: Given that a number, when divided by 6, leaves a remainder of 3. We can represent this as:
Number = 6n + 3, where n is an integer.
Step 2: We need to find the remainder when the square of the number is divided by 6. Let's square the expression we obtained in Step 1:
Number^2 = (6n + 3)^2
= 36n^2 + 36n + 9
Step 3: Now, let's divide the squared number by 6 and find the remainder. We can express this as:
Number^2 = 6m + remainder, where m is an integer.
So, substituting the expression from Step 2:
36n^2 + 36n + 9 = 6m + remainder
Step 4: To find the remainder, we can simplify the equation:
36n^2 + 36n + 9 = 6m + remainder
(6n + 3)(6n + 3) = 6m + remainder
(6n + 3)^2 = 6m + remainder
Step 5: From Step 1, we know that (6n + 3) is the number. So, we can substitute it in Step 4:
(6n + 3)^2 = 6m + remainder
Number^2 = 6m + remainder
Step 6: From Step 5, we can conclude that the remainder when the square of the number is divided by 6 is the same as the remainder when the number itself is divided by 6. Therefore, the remainder is 3 (option D).
In summary, when a number is divided by 6 and leaves a remainder of 3, the remainder when the square of the number is divided by 6 will also be 3.
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A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder isa)0b)1c)2d)3Correct answer is option 'D'. Can you explain this answer?
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A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder isa)0b)1c)2d)3Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder isa)0b)1c)2d)3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder isa)0b)1c)2d)3Correct answer is option 'D'. Can you explain this answer?.
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