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# If x = y + 4 and x = 20 - y, then x^2 - y^2 =

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Manager
Joined: 03 Jan 2015
Posts: 72
If x = y + 4 and x = 20 - y, then x^2 - y^2 =  [#permalink]

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23 May 2016, 00:49
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Difficulty:

5% (low)

Question Stats:

91% (01:00) correct 9% (01:55) wrong based on 93 sessions

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If $$x = y + 4$$ and $$x = 20 - y$$, then $$x^2 - y^2$$ =

(A) 16
(B) 80
(C) 144
(D) 256
(E) 384
Math Expert
Joined: 02 Sep 2009
Posts: 62352
Re: If x = y + 4 and x = 20 - y, then x^2 - y^2 =  [#permalink]

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23 May 2016, 01:03
2
1
saiesta wrote:
If $$x = y + 4$$ and $$x = 20 - y$$, then $$x^2 - y^2$$ =

(A) 16
(B) 80
(C) 144
(D) 256
(E) 384

$$x = y + 4$$ --> $$x-y=4$$;

$$x = 20 - y$$ --> $$x+y=20$$;

$$x^2 - y^2=(x-y)(x+y)=4*20=80$$.

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Math Expert
Joined: 02 Aug 2009
Posts: 8296
Re: If x = y + 4 and x = 20 - y, then x^2 - y^2 =  [#permalink]

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23 May 2016, 05:14
saiesta wrote:
If $$x = y + 4$$ and $$x = 20 - y$$, then $$x^2 - y^2$$ =

(A) 16
(B) 80
(C) 144
(D) 256
(E) 384

Hi
another method would be to equate terms...
$$x = y + 4$$ and $$x = 20 - y$$, so $$y+4 = 20-y....................2y=16 .....................y=8$$
so $$x=y+4=12$$...
$$x^2 - y^2$$ =$$12^2-8^2 = 144-64=80$$
B
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Re: If x = y + 4 and x = 20 - y, then x^2 - y^2 =  [#permalink]

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23 May 2016, 11:10
saiesta wrote:
If $$x = y + 4$$ and $$x = 20 - y$$, then $$x^2 - y^2$$ =

(A) 16
(B) 80
(C) 144
(D) 256
(E) 384

$$x = y + 4$$ => $$x - y = 4$$
$$x = 20 - y$$ => $$x + y = 20$$

$$x^2 - y^2$$ = ( $$x - y$$ )( $$x + y$$ )

$$x^2 - y^2$$ = ( $$4$$ )( $$20$$ )

$$x^2 - y^2$$ = $$80$$

Hence answer will be option (B) 80

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Thanks and Regards

Abhishek....

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Re: If x = y + 4 and x = 20 - y, then x^2 - y^2 =   [#permalink] 23 May 2016, 11:10
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