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When a number is divided by 13, the remainder is 11. When the same number is divided by 17, the remainder is 9. What is the number?
- a)349
- b)546
- c)234
- d)179
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
When a number is divided by 13, the remainder is 11. When the same num...
From the given data
Let the number be x
We know that dividend = divisor × quotient + remainder
⇒ x = 13p + 11…eq 1
Also given that when the same number is divided by 17, the remainder is 9
⇒ x = 17q + 9...eq 2
From eq 1 and eq 2, we get
⇒ 13p + 11 = 17q + 9
⇒ 17q – 13p = 2
⇒ q = ( 2 + 13p)/17
The least value of p for which q = (2 + 13p)/17 is a whole number is p = 26
Substitute p = 26 in x = 13p + 11
⇒ x = 13× 26 + 11
⇒ x = 349
Let the number be x
We know that dividend = divisor × quotient + remainder
⇒ x = 13p + 11…eq 1
Also given that when the same number is divided by 17, the remainder is 9
⇒ x = 17q + 9...eq 2
From eq 1 and eq 2, we get
⇒ 13p + 11 = 17q + 9
⇒ 17q – 13p = 2
⇒ q = ( 2 + 13p)/17
The least value of p for which q = (2 + 13p)/17 is a whole number is p = 26
Substitute p = 26 in x = 13p + 11
⇒ x = 13× 26 + 11
⇒ x = 349
Most Upvoted Answer
When a number is divided by 13, the remainder is 11. When the same num...
To solve this problem, we need to find a number that satisfies the given conditions. Let's analyze the problem step by step.
Step 1: Understand the problem
We are given that when a certain number is divided by 13, the remainder is 11. This can be represented as:
Number = 13a + 11, where 'a' is an integer.
Similarly, when the same number is divided by 17, the remainder is 9. This can be represented as:
Number = 17b + 9, where 'b' is an integer.
Step 2: Set up the equations
We now have two equations based on the given conditions:
Equation 1: Number = 13a + 11
Equation 2: Number = 17b + 9
Step 3: Solve the equations
To find the value of the number, we can equate Equation 1 and Equation 2:
13a + 11 = 17b + 9
Step 4: Simplify the equation
Let's simplify the equation by rearranging the terms:
13a - 17b = 9 - 11
13a - 17b = -2
Step 5: Find a solution
To find a solution to this equation, we need to find values of 'a' and 'b' that satisfy it. We can do this by trial and error or by using the method of finding the least common multiple (LCM) of 13 and 17.
Step 6: Use LCM method
The LCM of 13 and 17 is 221. Therefore, we can rewrite the equation as:
17(13a) - 13(17b) = -2 * 221
Step 7: Simplify the equation further
221a - 221b = -442
Step 8: Find a solution
Dividing both sides of the equation by 221, we get:
a - b = -2
Step 9: Find the smallest positive solution
To find the smallest positive solution, we can substitute different values for 'a' and 'b' until we find a pair that satisfies the equation. In this case, the smallest positive solution is a = 1 and b = 3.
Step 10: Find the number
Substituting the values of 'a' and 'b' into Equation 1 or Equation 2, we can find the number:
Number = 13a + 11 = 13(1) + 11 = 24
Therefore, the number that satisfies the given conditions is 24.
However, the options provided in the question do not include 24. Hence, none of the given options is correct.
Step 1: Understand the problem
We are given that when a certain number is divided by 13, the remainder is 11. This can be represented as:
Number = 13a + 11, where 'a' is an integer.
Similarly, when the same number is divided by 17, the remainder is 9. This can be represented as:
Number = 17b + 9, where 'b' is an integer.
Step 2: Set up the equations
We now have two equations based on the given conditions:
Equation 1: Number = 13a + 11
Equation 2: Number = 17b + 9
Step 3: Solve the equations
To find the value of the number, we can equate Equation 1 and Equation 2:
13a + 11 = 17b + 9
Step 4: Simplify the equation
Let's simplify the equation by rearranging the terms:
13a - 17b = 9 - 11
13a - 17b = -2
Step 5: Find a solution
To find a solution to this equation, we need to find values of 'a' and 'b' that satisfy it. We can do this by trial and error or by using the method of finding the least common multiple (LCM) of 13 and 17.
Step 6: Use LCM method
The LCM of 13 and 17 is 221. Therefore, we can rewrite the equation as:
17(13a) - 13(17b) = -2 * 221
Step 7: Simplify the equation further
221a - 221b = -442
Step 8: Find a solution
Dividing both sides of the equation by 221, we get:
a - b = -2
Step 9: Find the smallest positive solution
To find the smallest positive solution, we can substitute different values for 'a' and 'b' until we find a pair that satisfies the equation. In this case, the smallest positive solution is a = 1 and b = 3.
Step 10: Find the number
Substituting the values of 'a' and 'b' into Equation 1 or Equation 2, we can find the number:
Number = 13a + 11 = 13(1) + 11 = 24
Therefore, the number that satisfies the given conditions is 24.
However, the options provided in the question do not include 24. Hence, none of the given options is correct.
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When a number is divided by 13, the remainder is 11. When the same number is divided by 17, the remainder is 9. What is the number?a)349b)546c)234d)179Correct answer is option 'A'. Can you explain this answer?
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