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Manager  G
Joined: 26 Dec 2018
Posts: 142
Location: India
If a^3 + a^2 – a – 1 = 0, then which one of the following could be the  [#permalink]

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Difficulty:   5% (low)

Question Stats: 100% (00:42) correct 0% (00:00) wrong based on 21 sessions

### HideShow timer Statistics If a^3 + a^2 – a – 1 = 0, then which one of the following could be the value of a?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Source: Nova GMAT
Difficulty Level: 500

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GOOD LUCK!

Originally posted by UB001 on 04 Jan 2019, 10:06.
Last edited by SajjadAhmad on 15 Jul 2019, 01:07, edited 2 times in total.
VP  G
Joined: 09 Mar 2018
Posts: 1002
Location: India
Re: If a^3 + a^2 – a – 1 = 0, then which one of the following could be the  [#permalink]

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Manipulating the question to give

$$a^3 + a^2 – a – 1 = 0$$
$$a^2(a + 1) – 1(a + 1) = 0$$
$$(a^2 -1) (a + 1) = 0$$
$$a^2 = 1$$ or a = -1

So as you can see there are no -ive values present in the answer options.

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Originally posted by KanishkM on 04 Jan 2019, 11:05.
Last edited by KanishkM on 04 Jan 2019, 12:02, edited 1 time in total.
GMATH Teacher P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937
Re: If a^3 + a^2 – a – 1 = 0, then which one of the following could be the  [#permalink]

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1
UB001 wrote:
If a^3 + a^2 – a – 1 = 0, then which one of the following could be the value of a?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

$${a^3} + {a^2} = a + 1$$

$$?\,\,\,:\,\,\,{\rm{could}}\,\,{\rm{be}}\,\,a$$

Let´s do a trivial alternatives INSPECTION:

$$\left( A \right)\,\,0\mathop = \limits^? 1\,\,\,{\rm{no}}$$

$$\left( B \right)\,\,2\mathop = \limits^? 2\,\,\,{\rm{yes}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 1\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{B}} \right)$$

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net Re: If a^3 + a^2 – a – 1 = 0, then which one of the following could be the   [#permalink] 04 Jan 2019, 12:00
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