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A number when divided by 192 gives a remainder of 54. What remainder would be obtained on dividing the same number by 16?
- a)2
- b)4
- c)6
- d)8
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A number when divided by 192 gives a remainder of 54. What remainder w...
When a number x is divided by y and it leaves a remainder z,
the number (x + z) is always divisible by y
When number is divided by 192 and a remainder of 54 is obtained, the number can be written as
(192x + 54) where x is a natural number.
Now this number is divided by 16, both the sum of numbers can be individually divided by 16.
192x is divisible by 16 as 192 is divisible by 16
54 = (16 × 3) + 6
54 when divided by 16 leaves a remainder of 6 and quotient of 3 so when the sum is divided by
16, a remainder of 6 is obtained
Most Upvoted Answer
A number when divided by 192 gives a remainder of 54. What remainder w...
Given: A number when divided by 192 gives a remainder of 54.
To find: Remainder obtained on dividing the same number by 16.
Solution:
Let the number be x.
When x is divided by 192, the remainder is 54.
So, we can write,
x = 192a + 54 ----(1)
where a is some integer.
Now, we need to find the remainder when x is divided by 16.
We can use the fact that if a number is divisible by 16, then it is also divisible by 2^4 = 16.
So, let's divide both sides of equation (1) by 16,
x/16 = (192a + 54)/16
x/16 = 12a + 3 + 6/16
x/16 = 12a + 3 + 3/8
So, the remainder when x is divided by 16 is 3.
Therefore, the correct answer is option (c) 6.
To find: Remainder obtained on dividing the same number by 16.
Solution:
Let the number be x.
When x is divided by 192, the remainder is 54.
So, we can write,
x = 192a + 54 ----(1)
where a is some integer.
Now, we need to find the remainder when x is divided by 16.
We can use the fact that if a number is divisible by 16, then it is also divisible by 2^4 = 16.
So, let's divide both sides of equation (1) by 16,
x/16 = (192a + 54)/16
x/16 = 12a + 3 + 6/16
x/16 = 12a + 3 + 3/8
So, the remainder when x is divided by 16 is 3.
Therefore, the correct answer is option (c) 6.
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A number when divided by 192 gives a remainder of 54. What remainder would be obtained on dividing the same number by 16?a)2b)4c)6d)8Correct answer is option 'C'. Can you explain this answer?
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