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A number when divided by 296 leaves the remainder 75. If the same number is divided by 37, then what will be the remainder?
- a)1
- b)4
- c)8
- d)11
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A number when divided by 296 leaves the remainder 75. If the same numb...
Let x be the number.
Given: x = 296n + 75 [where n is the quotient]
x = 37(8n + 2) + 1
Hence, when x is divided by 37, it gives 1 as the remainder.
Given: x = 296n + 75 [where n is the quotient]
x = 37(8n + 2) + 1
Hence, when x is divided by 37, it gives 1 as the remainder.
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Community Answer
A number when divided by 296 leaves the remainder 75. If the same numb...
Understanding the Problem
We have a number that, when divided by 296, leaves a remainder of 75. We need to determine what the remainder would be if the same number is divided by 37.
Setting up the Equation
Let's represent the number as:
- N = 296k + 75 (where k is an integer)
This equation shows that N is equal to 296 multiplied by some integer k, plus the remainder 75.
Finding the Remainder When Divided by 37
Next, we need to find N mod 37:
- First, calculate 296 mod 37.
- 296 divided by 37 gives a quotient of 8 and a remainder of 0 (since 296 is exactly 8 times 37).
Thus,
- 296 ≡ 0 (mod 37)
Now, we can express N mod 37:
- N = 296k + 75
- N mod 37 = (296k mod 37) + (75 mod 37)
Since 296 mod 37 is 0:
- N mod 37 = 0 + (75 mod 37)
Calculating 75 mod 37
Now, we need to find the remainder when 75 is divided by 37:
- 75 divided by 37 gives a quotient of 2 and a remainder of 1.
So, we have:
- 75 ≡ 1 (mod 37)
Final Calculation
Now substituting back into our equation:
- N mod 37 = 0 + 1 = 1
Thus, the remainder when the number is divided by 37 is:
Remainder = 1
Therefore, the correct answer is option 'A'.
We have a number that, when divided by 296, leaves a remainder of 75. We need to determine what the remainder would be if the same number is divided by 37.
Setting up the Equation
Let's represent the number as:
- N = 296k + 75 (where k is an integer)
This equation shows that N is equal to 296 multiplied by some integer k, plus the remainder 75.
Finding the Remainder When Divided by 37
Next, we need to find N mod 37:
- First, calculate 296 mod 37.
- 296 divided by 37 gives a quotient of 8 and a remainder of 0 (since 296 is exactly 8 times 37).
Thus,
- 296 ≡ 0 (mod 37)
Now, we can express N mod 37:
- N = 296k + 75
- N mod 37 = (296k mod 37) + (75 mod 37)
Since 296 mod 37 is 0:
- N mod 37 = 0 + (75 mod 37)
Calculating 75 mod 37
Now, we need to find the remainder when 75 is divided by 37:
- 75 divided by 37 gives a quotient of 2 and a remainder of 1.
So, we have:
- 75 ≡ 1 (mod 37)
Final Calculation
Now substituting back into our equation:
- N mod 37 = 0 + 1 = 1
Thus, the remainder when the number is divided by 37 is:
Remainder = 1
Therefore, the correct answer is option 'A'.
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A number when divided by 296 leaves the remainder 75. If the same number is divided by 37, then what will be the remainder?a)1b)4c)8d)11Correct answer is option 'A'. Can you explain this answer?
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