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A certain number when divided by 899 leaves the remainder 65. when the same number is divided by 31, the remainder is:
- a)2
- b)3
- c)4
- d)1
Correct answer is option 'B'. Can you explain this answer?
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A certain number when divided by 899 leaves the remainder 65. when the...
∵ 899 is divided by 31 and leaves 0.
∴ required remainder = remainder by 65/31 = 3
∴ required remainder = remainder by 65/31 = 3
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A certain number when divided by 899 leaves the remainder 65. when the...
To find the remainder when a certain number is divided by 31, we can use the concept of congruence.
Let's assume the given number is x.
x divided by 899 leaves the remainder 65:
x ≡ 65 (mod 899)
This equation tells us that x is congruent to 65 modulo 899, which means x and 65 have the same remainder when divided by 899.
Now we need to find the remainder when x is divided by 31. To do this, we can use the concept of congruence again.
We know that 31 is a factor of 899 (31 * 29 = 899), so any number that leaves a remainder of 65 when divided by 899 will also leave the same remainder when divided by 31.
x ≡ 65 (mod 31)
This equation tells us that x is congruent to 65 modulo 31, which means x and 65 have the same remainder when divided by 31.
Therefore, the remainder when the given number x is divided by 31 is also 65.
However, the correct answer provided is option 'B' which states that the remainder is 3. It seems there might be an error in the options provided or in the solution provided. The correct remainder should be 65, not 3.
Let's assume the given number is x.
x divided by 899 leaves the remainder 65:
x ≡ 65 (mod 899)
This equation tells us that x is congruent to 65 modulo 899, which means x and 65 have the same remainder when divided by 899.
Now we need to find the remainder when x is divided by 31. To do this, we can use the concept of congruence again.
We know that 31 is a factor of 899 (31 * 29 = 899), so any number that leaves a remainder of 65 when divided by 899 will also leave the same remainder when divided by 31.
x ≡ 65 (mod 31)
This equation tells us that x is congruent to 65 modulo 31, which means x and 65 have the same remainder when divided by 31.
Therefore, the remainder when the given number x is divided by 31 is also 65.
However, the correct answer provided is option 'B' which states that the remainder is 3. It seems there might be an error in the options provided or in the solution provided. The correct remainder should be 65, not 3.
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Community Answer
A certain number when divided by 899 leaves the remainder 65. when the...
899 is completely divisible by 31 hence remainder will be 65/31 = 3...
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A certain number when divided by 899 leaves the remainder 65. when the same number is divided by 31, the remainder is:a)2b)3c)4d)1Correct answer is option 'B'. Can you explain this answer?
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