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When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?
- a)9
- b)10
- c)11
- d)12
- e)13
Correct answer is option 'E'. Can you explain this answer?
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Most Upvoted Answer
When positive integer y is divided by 7, the remainder is 2. When y is...
The remainder when a positive integer y is divided by 7 is 2, resulting in possible values of y such as 2, 9, 16, 23, 30, 37, 44, 51, 58, and so on.
Similarly, when y is divided by 11, the remainder is 3, leading to possible values of y such as 3, 14, 25, 36, 47, 58, 69, 80, 91, 102, and so on.
The first common value between the two sets is 58.
To find the sum of its digits, we add 5 and 8, resulting in 13.
Therefore, the rephrased answer is: Option E.
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Community Answer
When positive integer y is divided by 7, the remainder is 2. When y is...
Given:
- When y is divided by 7, the remainder is 2.
- When y is divided by 11, the remainder is 3.
To find:
- The sum of the digits of the smallest possible value that meets the definition for y.
Solution:
To find the smallest value of y, we need to find the least common multiple (LCM) of 7 and 11.
Finding the LCM:
To find the LCM of 7 and 11, we can find the product of the two numbers and then divide it by their greatest common divisor (GCD).
- The product of 7 and 11 is 77.
- The GCD of 7 and 11 is 1 (since they are prime numbers).
So, the LCM of 7 and 11 is 77.
Finding the smallest possible value of y:
Since the remainder when y is divided by 7 is 2, the smallest possible value of y that satisfies this condition is 2.
To find the smallest possible value of y that satisfies the condition when y is divided by 11, we need to find the smallest multiple of 77 that leaves a remainder of 3 when divided by 11.
Finding the smallest multiple of 77 that leaves a remainder of 3 when divided by 11:
To find this, we can start by finding the multiples of 77 and checking if they leave a remainder of 3 when divided by 11.
77 x 1 = 77 (remainder = 0 when divided by 11)
77 x 2 = 154 (remainder = 3 when divided by 11)
Therefore, the smallest multiple of 77 that leaves a remainder of 3 when divided by 11 is 154.
Calculating the sum of the digits:
To find the sum of the digits of 154, we add the individual digits together.
1 + 5 + 4 = 10
So, the sum of the digits of the smallest possible value that meets the definition for y is 10.
Therefore, the correct answer is option B) 10.
- When y is divided by 7, the remainder is 2.
- When y is divided by 11, the remainder is 3.
To find:
- The sum of the digits of the smallest possible value that meets the definition for y.
Solution:
To find the smallest value of y, we need to find the least common multiple (LCM) of 7 and 11.
Finding the LCM:
To find the LCM of 7 and 11, we can find the product of the two numbers and then divide it by their greatest common divisor (GCD).
- The product of 7 and 11 is 77.
- The GCD of 7 and 11 is 1 (since they are prime numbers).
So, the LCM of 7 and 11 is 77.
Finding the smallest possible value of y:
Since the remainder when y is divided by 7 is 2, the smallest possible value of y that satisfies this condition is 2.
To find the smallest possible value of y that satisfies the condition when y is divided by 11, we need to find the smallest multiple of 77 that leaves a remainder of 3 when divided by 11.
Finding the smallest multiple of 77 that leaves a remainder of 3 when divided by 11:
To find this, we can start by finding the multiples of 77 and checking if they leave a remainder of 3 when divided by 11.
77 x 1 = 77 (remainder = 0 when divided by 11)
77 x 2 = 154 (remainder = 3 when divided by 11)
Therefore, the smallest multiple of 77 that leaves a remainder of 3 when divided by 11 is 154.
Calculating the sum of the digits:
To find the sum of the digits of 154, we add the individual digits together.
1 + 5 + 4 = 10
So, the sum of the digits of the smallest possible value that meets the definition for y is 10.
Therefore, the correct answer is option B) 10.
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When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?a)9b)10c)11d)12e)13Correct answer is option 'E'. Can you explain this answer?
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