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12 Nov 2021, 09:02
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If x and y are positive integers, then what is the value of \((–1)^x + (–1)^y + (–1)^x*(–1)^y\) ?
(1) \(x\) does not have a prime factor greater than 1.
(2) \(y\) is a common factor of all prime numbers between 101 to 202
(1) \(x\) does not have a prime factor greater than 1.
(2) \(y\) is a common factor of all prime numbers between 101 to 202
12 Nov 2021, 09:02
Kudos
Bookmarks
Official Solution:
If x and y are positive integers, then what is the value of \((–1)^x + (–1)^y + (–1)^x*(–1)^y\) ?
(1) \(x\) does not have a prime factor greater than 1.
The above means that \(x\) must be 1. All other numbers are either composite or prime.
In this case: \((–1)^x + (–1)^y + (–1)^x*(–1)^y=(–1)^{1} + (–1)^{y} + (–1)^{1}*(–1)^{y}=-1+(–1)^{y}-(–1)^{y}=-1\). Sufficient.
(2) \(y\) is a common factor of all prime numbers between 101 to 202
The only common factor those integer have is 1, so \(y=1\).
In this case: \((–1)^x + (–1)^y + (–1)^x*(–1)^y=(–1)^{x} + (–1)^{1} + (–1)^{x}*(–1)^{1}=(–1)^{x}-1-(–1)^{x}=-1\). Sufficient.
Answer: D
If x and y are positive integers, then what is the value of \((–1)^x + (–1)^y + (–1)^x*(–1)^y\) ?
(1) \(x\) does not have a prime factor greater than 1.
The above means that \(x\) must be 1. All other numbers are either composite or prime.
In this case: \((–1)^x + (–1)^y + (–1)^x*(–1)^y=(–1)^{1} + (–1)^{y} + (–1)^{1}*(–1)^{y}=-1+(–1)^{y}-(–1)^{y}=-1\). Sufficient.
(2) \(y\) is a common factor of all prime numbers between 101 to 202
The only common factor those integer have is 1, so \(y=1\).
In this case: \((–1)^x + (–1)^y + (–1)^x*(–1)^y=(–1)^{x} + (–1)^{1} + (–1)^{x}*(–1)^{1}=(–1)^{x}-1-(–1)^{x}=-1\). Sufficient.
Answer: D
