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# If x^2 - 2x - 35 = 0 and x>0, which of the following must be equal to

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GMAT Forum Moderator
Joined: 28 May 2014
Posts: 528
GMAT 1: 730 Q49 V41
If x^2 - 2x - 35 = 0 and x>0, which of the following must be equal to [#permalink]

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06 Oct 2017, 07:41
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15% (low)

Question Stats:

82% (00:57) correct 18% (01:39) wrong based on 72 sessions

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If x^2 - 2x - 35 = 0 and x>0, which of the following must be equal to 0?

I. x^2 - 7x + 12
II. x^2 - 13x + 42
III. x^2 - 5x + 6

(a) I only
(b) II only
(c) III only
(d) II and III only
(e) I, II, and III

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Joined: 02 Sep 2009
Posts: 46283
Re: If x^2 - 2x - 35 = 0 and x>0, which of the following must be equal to [#permalink]

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06 Oct 2017, 07:44
saswata4s wrote:
If x^2 - 2x - 35 = 0 and x>0, which of the following must be equal to 0?

I. x^2 - 7x + 12
II. x^2 - 13x + 42
III. x^2 - 5x + 6

(a) I only
(b) II only
(c) III only
(d) II and III only
(e) I, II, and III

This is a copy of the following OG question: https://gmatclub.com/forum/if-x-2-2x-15 ... 67001.html
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Joined: 28 Dec 2010
Posts: 49
Re: If x^2 - 2x - 35 = 0 and x>0, which of the following must be equal to [#permalink]

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08 Oct 2017, 03:31
Lets first find valid values of x
$$(x-7)(x+5) = 0 , and x> 0$$

This means x=7

Now look at
1. (x-3) (x-4)
2. (x-6) (x-7)
3. (x-2) (x-3)

Only Statement 2 would be 0.
B.
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Joined: 22 May 2016
Posts: 1759
If x^2 - 2x - 35 = 0 and x>0, which of the following must be equal to [#permalink]

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08 Oct 2017, 04:31
saswata4s wrote:
If x^2 - 2x - 35 = 0 and x>0, which of the following must be equal to 0?

I. x^2 - 7x + 12
II. x^2 - 13x + 42
III. x^2 - 5x + 6

(a) I only
(b) II only
(c) III only
(d) II and III only
(e) I, II, and III

$$x^2 - 2x - 35 = 0$$
Find $$x$$

$$(x - 7)(x + 5)$$
$$x = 7$$ or $$x = -5$$
Prompt: $$x > 0$$, so $$x = 7$$

Either factor the expressions in the options, or plug $$x = 7$$ into them.

If you factor the expressions, one or both factors must be $$(x - 7)$$

Plugging in $$x = 7$$, looking for "which [option] must be equal to 0":

I. $$x^2 - 7x + 12$$
$$49 - 49 + 12 = 12$$ NO

II. $$x^2 - 13x + 42$$
$$49 - 91 + 42 = 0$$ YES

III. $$x^2 - 5x + 6$$
$$49 - 35 + 12 = 26$$ NO

Only Option II yields 0.

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If x^2 - 2x - 35 = 0 and x>0, which of the following must be equal to   [#permalink] 08 Oct 2017, 04:31
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