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# M11-23

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Math Expert
Joined: 02 Sep 2009
Posts: 48037

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16 Sep 2014, 00:45
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Difficulty:

25% (medium)

Question Stats:

79% (00:38) correct 21% (00:57) wrong based on 81 sessions

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What is the value of $$x$$?

(1) $$x^2+24=8(x+1)$$

(2) $$x^2+24=44-x$$

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Math Expert
Joined: 02 Sep 2009
Posts: 48037

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16 Sep 2014, 00:45
Official Solution:

(1) $$x^2+24=8(x+1)$$.

$$x^2-8x+16=0$$;

$$(x-4)^2=0$$, so $$x=4$$. Sufficient.

(2) $$x^2+24=44-x$$.

$$x^2+x-20$$;

$$(x-4)(x+5)$$, so $$x=4$$ or $$x=-5$$. Not sufficient.

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Intern
Joined: 02 Aug 2017
Posts: 1

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18 Sep 2017, 20:23
This question is confusing. I solved each part correctly. In the end I chose C because I recall a test prep book saying when you receive mixed answers for the two solutions you should check if they both match. When I chose C, both answers resulted in 4. Can someone help me understand why the correct answer is A?
Math Expert
Joined: 02 Sep 2009
Posts: 48037

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18 Sep 2017, 21:25
cfyan wrote:
This question is confusing. I solved each part correctly. In the end I chose C because I recall a test prep book saying when you receive mixed answers for the two solutions you should check if they both match. When I chose C, both answers resulted in 4. Can someone help me understand why the correct answer is A?

The first statement gives a single numerical value of x:

(1) $$x^2+24=8(x+1)$$.

$$x^2-8x+16=0$$;

$$(x-4)^2=0$$, so $$x=4$$. Sufficient.
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Re: M11-23 &nbs [#permalink] 18 Sep 2017, 21:25
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# M11-23

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