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If x + y = 7 and x^2 + y^2 = 25, then which one of the
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07 Apr 2019, 06:26
07 Apr 2019, 06:26
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If \(x + y = 7\) and \(x^2 + y^2 = 25\), then which one of the following equals the value of \(x^3 + y^3\) ?
(A) 7
(B) 25
(C) 35
(D) 65
(E) 91
(A) 7
(B) 25
(C) 35
(D) 65
(E) 91
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the
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07 Apr 2019, 07:35
07 Apr 2019, 07:35
1
Carcass wrote:
If \(x + y = 7\) and \(x^2 + y^2 = 25\), then which one of the following equals the value of \(x^3 + y^3\) ?
(A) 7
(B) 25
(C) 35
(D) 65
(E) 91
(A) 7
(B) 25
(C) 35
(D) 65
(E) 91
----ASIDE---------------
We COULD use some algebra to solve the question.
First rewrite the first equation as x = 7 - y
Then take second equation and replace x with 7 - y to get: (7 - y)² + y² = 25
When we eventually solve the system, we get two possible solutions:
Solution #1: x = 3 and y = 4
Solution #2: x = 4 and y = 3
-----------------------------
Solving the question is the above way takes time. So, before resorting to algebra, we might first see if we can solve the question through inspection.
If we do so, we might quickly realize that one value must be 3 and the other must be 4.
So, x³ + y³ = 3³ + 4³
= 27 + 64
= 91
Answer: E
Cheers,
Brent
Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the
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17 Jul 2022, 06:04
17 Jul 2022, 06:04
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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