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A number when divided by 296 leaves the remainder 75. What will be the remainder if the number is divided by 37?
- a)3
- b)4
- c)1
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A number when divided by 296 leaves the remainder 75. What will be the...
Let the Number be Y.
Then Y = 296 q + 75
= (37 x 8)q +( 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1
Most Upvoted Answer
A number when divided by 296 leaves the remainder 75. What will be the...
Given: A number when divided by 296 leaves the remainder 75.
Let the number be represented as N.
N = 296Q + 75 where Q is the quotient.
We need to find the remainder when N is divided by 37.
Approach:
We can use the property of remainders i.e., if a number is divided by a divisor and it leaves a remainder, then it can be written as divisor x quotient + remainder.
Using this property, we can write:
N = 296Q + 75 = (8 x 37 x Q) + 75
Now, we can see that 8 x 37 x Q is divisible by 37.
Therefore, the remainder when N is divided by 37 is the same as the remainder when 75 is divided by 37.
75 = 2 x 37 + 1
Hence, the remainder when N is divided by 37 is 1.
Answer: Option (c)
Let the number be represented as N.
N = 296Q + 75 where Q is the quotient.
We need to find the remainder when N is divided by 37.
Approach:
We can use the property of remainders i.e., if a number is divided by a divisor and it leaves a remainder, then it can be written as divisor x quotient + remainder.
Using this property, we can write:
N = 296Q + 75 = (8 x 37 x Q) + 75
Now, we can see that 8 x 37 x Q is divisible by 37.
Therefore, the remainder when N is divided by 37 is the same as the remainder when 75 is divided by 37.
75 = 2 x 37 + 1
Hence, the remainder when N is divided by 37 is 1.
Answer: Option (c)
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