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If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ? A. 97 B. 98 C. 99
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07 Jun 2022, 02:45
07 Jun 2022, 02:45
Expert Reply
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Question Stats:
90% (01:30) correct
9% (01:25) wrong based on 11 sessions
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If \(x - y = 2\) and \(x^2 - y^2\) = 16, then \(x^3 - y^3\) = ?
A. 97
B. 98
C. 99
D. 100
E. 152
A. 97
B. 98
C. 99
D. 100
E. 152
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Re: If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ? A. 97 B. 98 C. 99
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07 Jun 2022, 05:19
07 Jun 2022, 05:19
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Carcass wrote:
If \(x - y = 2\) and \(x^2 - y^2\) = 16, then \(x^3 - y^3\) = ?
A. 97
B. 98
C. 99
D. 100
E. 152
A. 97
B. 98
C. 99
D. 100
E. 152
Take: x² - y² = 16
Factor: (x + y)(x - y) = 16
Substitute to get: (x + y)(2) = 16
Divide both sides of the equation by 2 to get: x + y = 8
We now have the following system of equations:
x - y = 2
x + y = 8
Add the two equations to get: 2x = 10, which means x = 5
Once we know x = 5, we can plug this value into one of the two equations to learn that y = 3
Now that we know the values of x and y, x³ - y³ = 5³ - 3³ = 125 - 27 = 98
Answer: B
Re: If x - y = 2 and x^2 - y^2 = 16, then x^3 - y^3 = ? A. 97 B. 98 C. 99
[#permalink]
07 Jun 2022, 22:56
07 Jun 2022, 22:56
1
Since x-y=2, then x=y+2
We substitute for x in x^2 - y^2, we get (y+2)^2 - y^2=16
y^2+4y+4-y^2=16
y=3
x=y+2=5
Therefore x^3-y^3 = 125 - 9 = 98
The answer is (B)
We substitute for x in x^2 - y^2, we get (y+2)^2 - y^2=16
y^2+4y+4-y^2=16
y=3
x=y+2=5
Therefore x^3-y^3 = 125 - 9 = 98
The answer is (B)
