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X and y are 2 non-negative integers and 5x+4y when divided by 9 leaves remainder of 2. What will be the remainder when x-y is divided by 9?
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X and y are 2 non-negative integers and 5x+4y when divided by 9 leaves...
Given:
To find:
Explanation:
We know that 5x 4y when divided by 9 leaves remainder of 2. So, we can write the equation as:
5x 4y = 9a + 2
where a is some integer.
Now we need to find the remainder when x-y is divided by 9. So, let's subtract y from both sides of the above equation:
5x 4y - y = 9a + 2 - y
5x - 3y = 9a + (2-y)
Since we need to find the remainder when x-y is divided by 9, let's subtract (2-y) from both sides:
5x - 3y - (2-y) = 9a
5x - 4y + 2 = 9a
Now we can see that the left-hand side of the equation is the same as the given equation, which leaves a remainder of 2 when divided by 9. So, we can write:
5x - 4y = 9b + 2
where b is some integer.
Now let's add y to both sides:
5x = 4y + 9b + 2 + y
5x = 9c + y + 2
where c = b + (y+2)/9 is some integer.
We can see that the right-hand side of the equation leaves a remainder of (y+2) when divided by 9. Since we know that 5x 4y leaves a remainder of 2 when divided by 9, it follows that x leaves a remainder of (y+4) when divided by 9.
So, the remainder when x-y is divided by 9 is the same as the remainder when (y+4)-y is divided by 9, which is 4.
Answer: The remainder when x-y is divided by 9 is 4.
- Two non-negative integers x and y
- 5x 4y when divided by 9 leaves remainder of 2.
To find:
- The remainder when x-y is divided by 9.
Explanation:
We know that 5x 4y when divided by 9 leaves remainder of 2. So, we can write the equation as:
5x 4y = 9a + 2
where a is some integer.
Now we need to find the remainder when x-y is divided by 9. So, let's subtract y from both sides of the above equation:
5x 4y - y = 9a + 2 - y
5x - 3y = 9a + (2-y)
Since we need to find the remainder when x-y is divided by 9, let's subtract (2-y) from both sides:
5x - 3y - (2-y) = 9a
5x - 4y + 2 = 9a
Now we can see that the left-hand side of the equation is the same as the given equation, which leaves a remainder of 2 when divided by 9. So, we can write:
5x - 4y = 9b + 2
where b is some integer.
Now let's add y to both sides:
5x = 4y + 9b + 2 + y
5x = 9c + y + 2
where c = b + (y+2)/9 is some integer.
We can see that the right-hand side of the equation leaves a remainder of (y+2) when divided by 9. Since we know that 5x 4y leaves a remainder of 2 when divided by 9, it follows that x leaves a remainder of (y+4) when divided by 9.
So, the remainder when x-y is divided by 9 is the same as the remainder when (y+4)-y is divided by 9, which is 4.
Answer: The remainder when x-y is divided by 9 is 4.
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X and y are 2 non-negative integers and 5x+4y when divided by 9 leaves remainder of 2. What will be the remainder when x-y is divided by 9?
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X and y are 2 non-negative integers and 5x+4y when divided by 9 leaves remainder of 2. What will be the remainder when x-y is divided by 9? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about X and y are 2 non-negative integers and 5x+4y when divided by 9 leaves remainder of 2. What will be the remainder when x-y is divided by 9? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X and y are 2 non-negative integers and 5x+4y when divided by 9 leaves remainder of 2. What will be the remainder when x-y is divided by 9?.
X and y are 2 non-negative integers and 5x+4y when divided by 9 leaves remainder of 2. What will be the remainder when x-y is divided by 9? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about X and y are 2 non-negative integers and 5x+4y when divided by 9 leaves remainder of 2. What will be the remainder when x-y is divided by 9? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X and y are 2 non-negative integers and 5x+4y when divided by 9 leaves remainder of 2. What will be the remainder when x-y is divided by 9?.
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