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When a number is divided by 125, the remainder is 82, when the same number is divided by 25, the remainder will be ____.
- a)8
- b)9
- c)6
- d)7
Correct answer is option 'D'. Can you explain this answer?
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When a number is divided by 125, the remainder is 82, when the same nu...
**Given Information:**
- When a number is divided by 125, the remainder is 82.
**To Find:**
- The remainder when the same number is divided by 25.
**Solution:**
When a number is divided by 125, the remainder is 82. This means that the number can be expressed in the form:
Number = 125 * Q + 82, where Q is the quotient.
Now, we need to find the remainder when the same number is divided by 25. Let's substitute the value of the number from the given equation into this expression:
Number = 125 * Q + 82
Dividing both sides by 25:
Number / 25 = (125 * Q + 82) / 25
Simplifying the expression:
Number / 25 = 5 * Q + 82 / 25
Since we know that the remainder when a number is divided by another number is the same as the remainder when their difference is divided by that number, we can rewrite the expression as:
Number / 25 = 5 * Q + (82 - 5 * 25) / 25
Number / 25 = 5 * Q + (82 - 125) / 25
Number / 25 = 5 * Q - 43 / 25
From the equation, we can see that the remainder when the number is divided by 25 is -43 (since 43 is greater than 25). However, we need to find the positive remainder.
To obtain the positive remainder, we can add 25 to the negative remainder:
Remainder = -43 + 25 = -18
But the remainder cannot be negative. Therefore, we add 25 again until we get a positive remainder:
Remainder = -18 + 25 = 7
Therefore, the remainder when the same number is divided by 25 is 7.
Hence, the correct answer is option D) 7.
- When a number is divided by 125, the remainder is 82.
**To Find:**
- The remainder when the same number is divided by 25.
**Solution:**
When a number is divided by 125, the remainder is 82. This means that the number can be expressed in the form:
Number = 125 * Q + 82, where Q is the quotient.
Now, we need to find the remainder when the same number is divided by 25. Let's substitute the value of the number from the given equation into this expression:
Number = 125 * Q + 82
Dividing both sides by 25:
Number / 25 = (125 * Q + 82) / 25
Simplifying the expression:
Number / 25 = 5 * Q + 82 / 25
Since we know that the remainder when a number is divided by another number is the same as the remainder when their difference is divided by that number, we can rewrite the expression as:
Number / 25 = 5 * Q + (82 - 5 * 25) / 25
Number / 25 = 5 * Q + (82 - 125) / 25
Number / 25 = 5 * Q - 43 / 25
From the equation, we can see that the remainder when the number is divided by 25 is -43 (since 43 is greater than 25). However, we need to find the positive remainder.
To obtain the positive remainder, we can add 25 to the negative remainder:
Remainder = -43 + 25 = -18
But the remainder cannot be negative. Therefore, we add 25 again until we get a positive remainder:
Remainder = -18 + 25 = 7
Therefore, the remainder when the same number is divided by 25 is 7.
Hence, the correct answer is option D) 7.
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When a number is divided by 125, the remainder is 82, when the same nu...
Option (d) 7
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