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Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaningthroughout the question.
Q. r and t are consecutive integers and p = r2 + t
Quantity A : (-1)p
Quantity B : -1
- a)Quantity A is greater.
- b)Quantity B is greater.
- c)The two quantities are equal.
- d)The relationship cannot be determined from the information given.
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Directions: Compare Quantity A and Quantity B, using additional infor...
Recall that
Since p = r2 + t, the value of (−1)p depends on whether r2 + t is odd or even.
If r is an odd integer, then r2 is an odd integer and, since r and t are consecutive integers, t is an even integer. In this case, p is the sum of an odd integer and an even integer and is therefore an odd integer.
Similarly, if r is an even integer, then r2 is an even integer and t is an odd integer. In this case, p is the sum of an even integer and an odd integer and is therefore an odd integer.
In both cases, p is an odd integer. It follows that (−1)p = −1, and the correct answer is Choice C.
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Community Answer
Directions: Compare Quantity A and Quantity B, using additional infor...
Given:
- r and t are consecutive integers
- p = r^2 - t
To find:
Compare Quantity A: (-1)^p and Quantity B: -1
Solution:
Let's first calculate the value of p using the given information.
Since r and t are consecutive integers, we can write t = r + 1.
Substituting this value of t in the expression for p, we get:
p = r^2 - (r + 1)
Expanding the equation, we have:
p = r^2 - r - 1
Now, let's calculate the value of (-1)^p and -1.
Quantity A: (-1)^p
Substituting the value of p in (-1)^p:
(-1)^p = (-1)^(r^2 - r - 1)
Since the base (-1) is negative, the exponent r^2 - r - 1 will alternate between positive and negative values depending on whether r is even or odd.
If r is even, then r^2 - r - 1 will be odd.
If r is odd, then r^2 - r - 1 will be even.
In both cases, (-1) raised to an odd or even power will always be -1.
Therefore, Quantity A can be simplified to -1.
Quantity B: -1
Since Quantity B is a constant -1, its value is always -1.
Comparison:
Quantity A: (-1)^p = -1
Quantity B: -1
Since both Quantity A and Quantity B have the same value of -1, the answer is option (c) The two quantities are equal.
Conclusion:
The two quantities, Quantity A and Quantity B, are equal.
- r and t are consecutive integers
- p = r^2 - t
To find:
Compare Quantity A: (-1)^p and Quantity B: -1
Solution:
Let's first calculate the value of p using the given information.
Since r and t are consecutive integers, we can write t = r + 1.
Substituting this value of t in the expression for p, we get:
p = r^2 - (r + 1)
Expanding the equation, we have:
p = r^2 - r - 1
Now, let's calculate the value of (-1)^p and -1.
Quantity A: (-1)^p
Substituting the value of p in (-1)^p:
(-1)^p = (-1)^(r^2 - r - 1)
Since the base (-1) is negative, the exponent r^2 - r - 1 will alternate between positive and negative values depending on whether r is even or odd.
If r is even, then r^2 - r - 1 will be odd.
If r is odd, then r^2 - r - 1 will be even.
In both cases, (-1) raised to an odd or even power will always be -1.
Therefore, Quantity A can be simplified to -1.
Quantity B: -1
Since Quantity B is a constant -1, its value is always -1.
Comparison:
Quantity A: (-1)^p = -1
Quantity B: -1
Since both Quantity A and Quantity B have the same value of -1, the answer is option (c) The two quantities are equal.
Conclusion:
The two quantities, Quantity A and Quantity B, are equal.
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Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaningthroughout the question.Q. r and t are consecutive integers and p = r2 + tQuantity A : (-1)pQuantity B : -1a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'C'. Can you explain this answer?
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Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaningthroughout the question.Q. r and t are consecutive integers and p = r2 + tQuantity A : (-1)pQuantity B : -1a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'C'. Can you explain this answer? for GRE 2024 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaningthroughout the question.Q. r and t are consecutive integers and p = r2 + tQuantity A : (-1)pQuantity B : -1a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GRE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaningthroughout the question.Q. r and t are consecutive integers and p = r2 + tQuantity A : (-1)pQuantity B : -1a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'C'. Can you explain this answer?.
Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaningthroughout the question.Q. r and t are consecutive integers and p = r2 + tQuantity A : (-1)pQuantity B : -1a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'C'. Can you explain this answer? for GRE 2024 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaningthroughout the question.Q. r and t are consecutive integers and p = r2 + tQuantity A : (-1)pQuantity B : -1a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GRE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaningthroughout the question.Q. r and t are consecutive integers and p = r2 + tQuantity A : (-1)pQuantity B : -1a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'C'. Can you explain this answer?.
Solutions for Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaningthroughout the question.Q. r and t are consecutive integers and p = r2 + tQuantity A : (-1)pQuantity B : -1a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GRE.
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