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# What is the value of x^2 - 2x - 14 ? (1) x < 0 (2) (x - 5)(x + 3) = 0

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What is the value of x^2 - 2x - 14 ? (1) x < 0 (2) (x - 5)(x + 3) = 0  [#permalink]

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19 Nov 2019, 01:56
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55% (hard)

Question Stats:

55% (01:14) correct 45% (01:13) wrong based on 38 sessions

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What is the value of $$x^2 - 2x - 14$$?

(1) $$x < 0$$

(2) $$(x-5)(x+3) = 0$$

Are You Up For the Challenge: 700 Level Questions

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Re: What is the value of x^2 - 2x - 14 ? (1) x < 0 (2) (x - 5)(x + 3) = 0  [#permalink]

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19 Nov 2019, 02:04
IMO C
1) X is negative. Not enough to give us a numerical value of the equation.
2) X = 5 or -3. Insufficient.

Both x can be only 5. and equation can be solved.
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What is the value of x^2 - 2x - 14 ? (1) x < 0 (2) (x - 5)(x + 3) = 0  [#permalink]

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Updated on: 19 Nov 2019, 09:59
Bunuel wrote:
What is the value of $$x^2 - 2x - 14$$?

(1) $$x < 0$$

(2) $$(x-5)(x+3) = 0$$

Are You Up For the Challenge: 700 Level Questions

Explanation:
In statement 1; X<0, So we don't know whether the value is an integer or not. X can be -1, -1/2.. or any negative value. Not Sufficient.
In statement 2; Solving equation, We get 2 values of x, i.e. x=5,-3
by putting both values in equation {x^2 - 2x - 14}, we get same value. i.e. 1 So sufficient.

Please give kudos, if you find my explanation good enough

Originally posted by rajatchopra1994 on 19 Nov 2019, 03:56.
Last edited by rajatchopra1994 on 19 Nov 2019, 09:59, edited 1 time in total.
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Re: What is the value of x^2 - 2x - 14 ? (1) x < 0 (2) (x - 5)(x + 3) = 0  [#permalink]

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19 Nov 2019, 04:39
Bunuel wrote:
What is the value of $$x^2 - 2x - 14$$?

(1) $$x < 0$$

(2) $$(x-5)(x+3) = 0$$

(1) $$x < 0$$ insufic

(2) $$(x-5)(x+3) = 0$$ sufic
$$x=5: x^2 - 2x - 14=25-10-14=1$$
$$x=-3: x^2 - 2x - 14=9-2(-3)-14=15-14=1$$

Ans (B)
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What is the value of x^2 - 2x - 14 ? (1) x < 0 (2) (x - 5)(x + 3) = 0  [#permalink]

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19 Nov 2019, 05:18
What is the value of $$x^{2}—2x—14= (x—1)^{2}—15?$$

(Statement1): x <0
Clearly insufficient

(Statement2): (x—5)(x+3) =0
—>$$x=5: (x—1)^{2}—15= 16–15=1$$
—> $$x=—3: (x—1)^{2}—15=16–15=1$$

We got the same value from both entities.
Sufficient

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What is the value of x^2 - 2x - 14 ? (1) x < 0 (2) (x - 5)(x + 3) = 0  [#permalink]

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19 Nov 2019, 07:33
Bunuel wrote:
What is the value of $$x^2 - 2x - 14$$?

(1) $$x < 0$$

(2) $$(x-5)(x+3) = 0$$

Are You Up For the Challenge: 700 Level Questions

$$x^2 - 2x - 14$$

(1) $$x < 0$$
x=-1......$$x^2 - 2x - 14=(-1)^2-2(-1)-14=1+2-14=-11$$
x=-2......$$x^2 - 2x - 14=(-2)^2-2(-2)-14=4+4-14=-6$$
Insuff

(2) $$(x-5)(x+3) = 0...$$..
$$x^2-2x-15=0$$..
Add 1 to each side....$$x^2-2x-15+(1)=0+(1)....x^2-2x-14=1$$

B
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What is the value of x^2 - 2x - 14 ? (1) x < 0 (2) (x - 5)(x + 3) = 0   [#permalink] 19 Nov 2019, 07:33
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