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When positive integer a is divided by positive integer b, yielding quotient q and remainder r, the result is 5.125. Which of the following must be true?
- a)r = 1
- b)q > r
- c)b = 8
- d)8r = b
- e)8b = r
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
When positive integer a is divided by positive integer b, yielding quo...
To solve this problem, we need to express the decimal 5.125 as a fraction. Since the remainder is always less than the divisor, the quotient in this case would be the whole number part, which is 5, and the remainder would be the fractional part, which is 0.125. Therefore, we have:
a/b = 5 + 0.125
Now, let's analyze each statement separately:
Statement (A): r = 1
Since the decimal part of the quotient is 0.125, the remainder cannot be 1. Therefore, statement (A) is not necessarily true.
Statement (B): q > r
In this case, q = 5 and r = 0.125. Since 5 is greater than 0.125, statement (B) is true.
Statement (C): b = 8
The value of the divisor, b, is not given in the problem. Therefore, we cannot determine its exact value based on the information provided. Statement (C) cannot be concluded.
Statement (D): 8r = b
The remainder, r, is 0.125. Multiplying this by 8 gives us 1, which matches the value of the divisor b (since 8 x 0.125 = 1). Therefore, statement (D) is true.
Statement (E): 8b = r
This statement suggests that the fractional part of the quotient (0.125) is equal to 8 times the divisor b. However, this is not true since 8 times any positive integer will result in a value greater than 1. Therefore, statement (E) is not true.
Based on the analysis above, the correct answer is D: 8r = b, which must be true.
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When positive integer a is divided by positive integer b, yielding quo...
Explanation:
Given Information:
When positive integer a is divided by positive integer b, yielding quotient q and remainder r, the result is 5.125.
Calculating the Quotient and Remainder:
Let's represent the division as:
a = bq + r
Given that a/b = 5.125, we can rewrite the equation as:
a = 5b + 0.125b
Identifying the Quotient and Remainder:
From the equation above, we can see that the quotient q = 5 and the remainder r = 0.125b.
Relationship between Remainder and Divisor:
In division, the remainder is always less than the divisor. Therefore, r < />
Checking the Options:
a) r = 1 - This is not necessarily true as r can be any value less than b.
b) q > r - This is true since q = 5 and r < />
c) b = 8 - This is not necessarily true as b can be any divisor that satisfies the given conditions.
d) 8r = b - This must be true based on the relationship between r and b in division.
e) 8b = r - This is not true as r is always less than b in division.
Therefore, the correct option is D) 8r = b.
Given Information:
When positive integer a is divided by positive integer b, yielding quotient q and remainder r, the result is 5.125.
Calculating the Quotient and Remainder:
Let's represent the division as:
a = bq + r
Given that a/b = 5.125, we can rewrite the equation as:
a = 5b + 0.125b
Identifying the Quotient and Remainder:
From the equation above, we can see that the quotient q = 5 and the remainder r = 0.125b.
Relationship between Remainder and Divisor:
In division, the remainder is always less than the divisor. Therefore, r < />
Checking the Options:
a) r = 1 - This is not necessarily true as r can be any value less than b.
b) q > r - This is true since q = 5 and r < />
c) b = 8 - This is not necessarily true as b can be any divisor that satisfies the given conditions.
d) 8r = b - This must be true based on the relationship between r and b in division.
e) 8b = r - This is not true as r is always less than b in division.
Therefore, the correct option is D) 8r = b.
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When positive integer a is divided by positive integer b, yielding quotient q and remainder r, the result is 5.125. Which of the following must be true?a)r = 1b)q > rc)b = 8d)8r = be)8b = rCorrect answer is option 'D'. Can you explain this answer?
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