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x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
- a)24
- b)21
- c)20
- d)17
- e)15
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
x, y, a, and b are positive integers. When x is divided by y, the rema...
The problem states that when x is divided by y the remainder is 6. In general, the divisor (y in this case) will always be greater than the remainder. To illustrate this concept, let's look at a few examples:
15/4 gives 3 remainder 3 (the divisor 4 is greater than the remainder 3)
25/3 gives 8 remainder 1 (the divisor 3 is greater than the remainder 1)
46/7 gives 6 remainder 4 (the divisor 7 is greater than the remainder 4)
In the case at hand, we can therefore conclude that y must be greater than 6.
The problem also states that when a is divided by b the remainder is 9. Therefore, we can conclude that b must be greater than 9.
If y > 6 and b > 9, then y + b > 6 + 9 > 15. Thus, 15 cannot be the sum of y and b.
The correct answer is E.
15/4 gives 3 remainder 3 (the divisor 4 is greater than the remainder 3)
25/3 gives 8 remainder 1 (the divisor 3 is greater than the remainder 1)
46/7 gives 6 remainder 4 (the divisor 7 is greater than the remainder 4)
In the case at hand, we can therefore conclude that y must be greater than 6.
The problem also states that when a is divided by b the remainder is 9. Therefore, we can conclude that b must be greater than 9.
If y > 6 and b > 9, then y + b > 6 + 9 > 15. Thus, 15 cannot be the sum of y and b.
The correct answer is E.
Most Upvoted Answer
x, y, a, and b are positive integers. When x is divided by y, the rema...
To find the value that is not a possible value for y * b, we need to understand the concept of remainders when dividing integers.
When x is divided by y, the remainder is 6. This can be written as x = q1 * y + 6, where q1 is the quotient when x is divided by y.
Similarly, when a is divided by b, the remainder is 9. This can be written as a = q2 * b + 9, where q2 is the quotient when a is divided by b.
We can rewrite these equations as x - 6 = q1 * y and a - 9 = q2 * b.
To find a value that is not possible for y * b, we need to find a common factor of (x - 6) and (a - 9) that is not a factor of 6 or 9. This is because if y * b is divisible by a common factor of (x - 6) and (a - 9), then it would be a possible value for y * b.
Let's consider the answer choices:
a) 24: If y * b = 24, then y and b must have factors of 2 and/or 3. However, since 6 and 9 are also factors of 24, it is a possible value for y * b.
b) 21: If y * b = 21, then y and b must have a factor of 3. However, since 6 and 9 are also factors of 21, it is a possible value for y * b.
c) 20: If y * b = 20, then y and b must have factors of 2 and/or 5. However, since 6 and 9 are also factors of 20, it is a possible value for y * b.
d) 17: If y * b = 17, then y and b must be factors of 17. However, since 6 and 9 are not factors of 17, it is not a possible value for y * b.
e) 15: If y * b = 15, then y and b must have factors of 3 and/or 5. However, since 6 and 9 are not factors of 15, it is not a possible value for y * b.
Therefore, the answer is e) 15.
When x is divided by y, the remainder is 6. This can be written as x = q1 * y + 6, where q1 is the quotient when x is divided by y.
Similarly, when a is divided by b, the remainder is 9. This can be written as a = q2 * b + 9, where q2 is the quotient when a is divided by b.
We can rewrite these equations as x - 6 = q1 * y and a - 9 = q2 * b.
To find a value that is not possible for y * b, we need to find a common factor of (x - 6) and (a - 9) that is not a factor of 6 or 9. This is because if y * b is divisible by a common factor of (x - 6) and (a - 9), then it would be a possible value for y * b.
Let's consider the answer choices:
a) 24: If y * b = 24, then y and b must have factors of 2 and/or 3. However, since 6 and 9 are also factors of 24, it is a possible value for y * b.
b) 21: If y * b = 21, then y and b must have a factor of 3. However, since 6 and 9 are also factors of 21, it is a possible value for y * b.
c) 20: If y * b = 20, then y and b must have factors of 2 and/or 5. However, since 6 and 9 are also factors of 20, it is a possible value for y * b.
d) 17: If y * b = 17, then y and b must be factors of 17. However, since 6 and 9 are not factors of 17, it is not a possible value for y * b.
e) 15: If y * b = 15, then y and b must have factors of 3 and/or 5. However, since 6 and 9 are not factors of 15, it is not a possible value for y * b.
Therefore, the answer is e) 15.
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x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?a)24b)21c)20d)17e)15Correct answer is option 'E'. Can you explain this answer?
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x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?a)24b)21c)20d)17e)15Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?a)24b)21c)20d)17e)15Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?a)24b)21c)20d)17e)15Correct answer is option 'E'. Can you explain this answer?.
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