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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal

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Math Expert V
Joined: 02 Sep 2009
Posts: 58310
If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal  [#permalink]

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Difficulty:   15% (low)

Question Stats: 88% (01:17) correct 12% (02:15) wrong based on 26 sessions

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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

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GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4978
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal  [#permalink]

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Bunuel 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

$$x^2 + y^2 = 25$$
solve with x+y=7
we get y=4,3 and x= 3,4
x^3+y^3 = 27+64 ; 91
IMO E
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Manager  B
Joined: 31 Dec 2018
Posts: 115
Location: India
Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal  [#permalink]

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the smart method is stated above by archit.
However, solving algebraically:
(x+y)²=x²+y²+2xy
xy=12.

(x+y)³=x³+y³+3xy(x+y)
substitute the values to get
7³=x³+y³+3*12*7
x³+y³=91

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Manager  S
Joined: 19 Jan 2019
Posts: 88
Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal  [#permalink]

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X^3 + y^3 = (X+y)(x^2+y^2-xy) --(1)

(X+y)^2 = x^2+y^2+2xy
49-25=2xy
2xy = 24
Xy=12

Substitute xy=12.
7(25-12)
7*13 = 91..

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Manager  G
Joined: 21 Feb 2019
Posts: 125
Location: Italy
Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal  [#permalink]

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$$x + y = 7$$
$$x^2 + y^2 = 25$$

$$7$$ as sum of two numbers is given by: 4+3; 6+1; 5+2 ...

If the second equation is verified, pick them; otherwise, reject them.

$$4^2 + 3^2 = 16$$? Yes. Pick them.

$$4^3 + 3^3 = 64 + 27 = 91$$. Correct answer: E.
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Joined: 12 Sep 2015
Posts: 3991
Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal  [#permalink]

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Top Contributor
Bunuel 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

----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

Cheers,
Brent
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Target Test Prep Representative D
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Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal  [#permalink]

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Bunuel 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

Since x + y = 7, (x + y)^2 = 7^2 → x^2 + 2xy + y^2 = 49. Since x^2 + y^2 = 25, we have 25 + 2xy = 49 → 2xy = 24 → xy = 12.

Recall that x^3 + y^3 factored as (x + y)(x^2 - xy + y^2), so we have:

x^3 + y^3 = (7)(25 - 12) = 7(13) = 91

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal   [#permalink] 10 Apr 2019, 17:48
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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal

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