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How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?
- a)None
- b)One
- c)Two
- d)Three
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
How many two-digit whole numbers yield a remainder of 1 when divided b...
To find the two-digit whole numbers that satisfy the given conditions, we need to determine the numbers that leave a remainder of 1 when divided by both 10 and 6.
We can start by considering the multiples of 10. The multiples of 10 are numbers that end with a zero, such as 10, 20, 30, and so on. However, none of these numbers leaves a remainder of 1 when divided by 6. Therefore, we can conclude that none of the multiples of 10 are suitable solutions.
Next, let's consider the numbers that leave a remainder of 1 when divided by 6. Such numbers can be represented as 6n + 1, where n is an integer. To find the two-digit numbers that satisfy this condition, we can substitute values of n and check if the resulting number is within the range of two-digit numbers (10 to 99).
If we substitute n = 0, we get 6(0) + 1 = 1, which is not a two-digit number. Similarly, if we substitute n = 1, we get 6(1) + 1 = 7, which is also not a two-digit number. However, when we substitute n = 2, we get 6(2) + 1 = 13, which is a two-digit number.
Therefore, the number 13 satisfies the given conditions.
To check if there are any other two-digit numbers that satisfy the conditions, we can continue substituting larger values of n. If we substitute n = 3, we get 6(3) + 1 = 19, which is also a two-digit number. Finally, if we substitute n = 4, we get 6(4) + 1 = 25, which is not a two-digit number.
Thus, we have found two two-digit numbers (13 and 19) that satisfy the given conditions. Therefore, the correct answer is option D: Three.
We can start by considering the multiples of 10. The multiples of 10 are numbers that end with a zero, such as 10, 20, 30, and so on. However, none of these numbers leaves a remainder of 1 when divided by 6. Therefore, we can conclude that none of the multiples of 10 are suitable solutions.
Next, let's consider the numbers that leave a remainder of 1 when divided by 6. Such numbers can be represented as 6n + 1, where n is an integer. To find the two-digit numbers that satisfy this condition, we can substitute values of n and check if the resulting number is within the range of two-digit numbers (10 to 99).
If we substitute n = 0, we get 6(0) + 1 = 1, which is not a two-digit number. Similarly, if we substitute n = 1, we get 6(1) + 1 = 7, which is also not a two-digit number. However, when we substitute n = 2, we get 6(2) + 1 = 13, which is a two-digit number.
Therefore, the number 13 satisfies the given conditions.
To check if there are any other two-digit numbers that satisfy the conditions, we can continue substituting larger values of n. If we substitute n = 3, we get 6(3) + 1 = 19, which is also a two-digit number. Finally, if we substitute n = 4, we get 6(4) + 1 = 25, which is not a two-digit number.
Thus, we have found two two-digit numbers (13 and 19) that satisfy the given conditions. Therefore, the correct answer is option D: Three.
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How many two-digit whole numbers yield a remainder of 1 when divided b...
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How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?a)Noneb)Onec)Twod)ThreeCorrect answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?a)Noneb)Onec)Twod)ThreeCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?a)Noneb)Onec)Twod)ThreeCorrect answer is option 'D'. Can you explain this answer?.
How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?a)Noneb)Onec)Twod)ThreeCorrect answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?a)Noneb)Onec)Twod)ThreeCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?a)Noneb)Onec)Twod)ThreeCorrect answer is option 'D'. Can you explain this answer?.
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