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If |x|=|y|, which of the following must be true?
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24 Sep 2021, 03:11
24 Sep 2021, 03:11
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If |x|=|y|, which of the following must be true?
A x<y
B y>x
C x=y
D x^3=y^3
E x^4=y^4
Source: manhattanreview
A x<y
B y>x
C x=y
D x^3=y^3
E x^4=y^4
Source: manhattanreview
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Joined: 10 Apr 2015
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Re: If |x|=|y|, which of the following must be true?
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24 Sep 2021, 05:49
24 Sep 2021, 05:49
1
Carcass wrote:
If |x|=|y|, which of the following must be true?
A x < y
B y > x
C x = y
D x^3 = y^3
E x^4 = y^4
Source: manhattanreview
A x < y
B y > x
C x = y
D x^3 = y^3
E x^4 = y^4
Source: manhattanreview
A quick solution is to test values of x and y that satisfy the given equation |x|=|y|
For example, if |x|=|y|, then it could be the case that x = 1 and y = -1
When we plug x = 1 and y = -1 into each of the answer choices and evaluate, we get:
A 1 < -1 Not True. ELIMINATE
B -1 > 1 Not True. ELIMINATE
C 1 = -1 Not True. ELIMINATE
D 1 = -1 Not True. ELIMINATE
E 1 = 1 True
Answer: E
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If |x|=|y|, which of the following must be true?
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30 Dec 2021, 22:51
30 Dec 2021, 22:51
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Given that |x|=|y|
Now, |x| = |y| means that the Absolute value of x and y is same. There are multiple cases possible. Let's understand this using values
Case 1: x +ve, y +ve. Ex: x = 2, y = 2. Making |x| = |y| = |2| = 2
Case 2: x +ve, y- ve. Ex: x = 2, y = -2. Making |x| = |y| = |2|= |-2| = 2
Case 3: x -ve, y +ve. Ex: x = -2, y = 2. Making |x| = |y| = |-2| = |2| = 2
Case 4: x -ve, y- ve. Ex: x = -2, y = -2. Making |x| = |y| = |-2|= |-2| = 2
Now, in all of these cases if we square x and y then we will always have \(x^2\) = \(y^2\)
So, any even power of x and y will always be equal
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
Now, |x| = |y| means that the Absolute value of x and y is same. There are multiple cases possible. Let's understand this using values
Case 1: x +ve, y +ve. Ex: x = 2, y = 2. Making |x| = |y| = |2| = 2
Case 2: x +ve, y- ve. Ex: x = 2, y = -2. Making |x| = |y| = |2|= |-2| = 2
Case 3: x -ve, y +ve. Ex: x = -2, y = 2. Making |x| = |y| = |-2| = |2| = 2
Case 4: x -ve, y- ve. Ex: x = -2, y = -2. Making |x| = |y| = |-2|= |-2| = 2
Now, in all of these cases if we square x and y then we will always have \(x^2\) = \(y^2\)
So, any even power of x and y will always be equal
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
