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

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New post 06 Oct 2017, 07:41
2
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A
B
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E

Difficulty:

  15% (low)

Question Stats:

84% (01:34) correct 16% (02:24) wrong based on 73 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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Re: If x^2 - 2x - 35 = 0 and x>0, which of the following must be equal to  [#permalink]

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New post 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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Re: If x^2 - 2x - 35 = 0 and x>0, which of the following must be equal to  [#permalink]

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

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New post 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.

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