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When a number is divided by 527 gives the remainder as 21. When the same number is divided by 17, the remainder will be?
- a)2
- b)3
- c)4
- d)7
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
When a number is divided by 527 gives the remainder as 21. When the sa...
Let the number be 527a + 21
when divided by 17, 527a is divisible by 17 and leaves remainder as 4 when 21 is divided by 17
when divided by 17, 527a is divisible by 17 and leaves remainder as 4 when 21 is divided by 17
Most Upvoted Answer
When a number is divided by 527 gives the remainder as 21. When the sa...
527 os divisible by 17 hence no remainder
when 21 is devided by 17
remainder is 4
when 21 is devided by 17
remainder is 4
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Community Answer
When a number is divided by 527 gives the remainder as 21. When the sa...
Solution:
Let the number be x.
When x is divided by 527, the remainder is 21.
So, x = 527k + 21, where k is a positive integer.
We need to find the remainder when x is divided by 17.
Let's try to express x in terms of 17.
527 can be written as 17 x 31.
So, x = (17 x 31 x k) + 21
We can write (17 x 31 x k) as 527k - 10k.
So, x = 527k - 10k + 21
Now, we can see that x leaves a remainder of 21 when divided by 17 if and only if 10k leaves a remainder of 4 when divided by 17.
Let's try to find such a value of k.
10k leaves a remainder of 4 when divided by 17 means: 10k = 17n + 4, where n is a positive integer.
Solving for k, we get:
k = (17n + 4)/10
We can see that k is an integer only when n leaves a remainder of 8 when divided by 10.
Let n = 10m + 8, where m is a positive integer.
Substituting in the above equation, we get:
k = (17 x (10m + 8) + 4)/10
Simplifying, we get:
k = 17m + 14
So, for any positive integer m, k leaves a remainder of 14 when divided by 17.
Substituting in the equation for x, we get:
x = 527k - 10k + 21
x = (527 - 10)k + 21
x = 517k + 21
x leaves a remainder of 4 when divided by 17.
Therefore, the correct answer is option C (4).
Let the number be x.
When x is divided by 527, the remainder is 21.
So, x = 527k + 21, where k is a positive integer.
We need to find the remainder when x is divided by 17.
Let's try to express x in terms of 17.
527 can be written as 17 x 31.
So, x = (17 x 31 x k) + 21
We can write (17 x 31 x k) as 527k - 10k.
So, x = 527k - 10k + 21
Now, we can see that x leaves a remainder of 21 when divided by 17 if and only if 10k leaves a remainder of 4 when divided by 17.
Let's try to find such a value of k.
10k leaves a remainder of 4 when divided by 17 means: 10k = 17n + 4, where n is a positive integer.
Solving for k, we get:
k = (17n + 4)/10
We can see that k is an integer only when n leaves a remainder of 8 when divided by 10.
Let n = 10m + 8, where m is a positive integer.
Substituting in the above equation, we get:
k = (17 x (10m + 8) + 4)/10
Simplifying, we get:
k = 17m + 14
So, for any positive integer m, k leaves a remainder of 14 when divided by 17.
Substituting in the equation for x, we get:
x = 527k - 10k + 21
x = (527 - 10)k + 21
x = 517k + 21
x leaves a remainder of 4 when divided by 17.
Therefore, the correct answer is option C (4).
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When a number is divided by 527 gives the remainder as 21. When the same number is divided by 17, the remainder will be?a)2b)3c)4d)7e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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