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# What is x ? (1) x^2 - 1 = x + 1 (2) x + 3 is a prime number

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Math Expert
Joined: 02 Sep 2009
Posts: 54434
What is x ? (1) x^2 - 1 = x + 1 (2) x + 3 is a prime number  [#permalink]

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14 Aug 2017, 09:22
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Difficulty:

45% (medium)

Question Stats:

60% (01:12) correct 40% (01:14) wrong based on 119 sessions

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What is x ?

(1) x^2 - 1 = x + 1
(2) x + 3 is a prime number

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What is x ? (1) x^2 - 1 = x + 1 (2) x + 3 is a prime number  [#permalink]

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14 Aug 2017, 09:33
1
We have been asked to find the value of x.

1. x^2 - 1 = x + 1
x^2 - x - 2 = 0
(x-2)(x+1) = 0
x = 2 or -1 (Insufficient)

2. x + 3 is a prime number
x could be -1,0,2 and so on. (Insufficient)

On combining the information from both the statements,
x could be -1 or 2. (Insufficient) (Option E)
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Re: What is x ? (1) x^2 - 1 = x + 1 (2) x + 3 is a prime number  [#permalink]

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14 Aug 2017, 09:44
1st statement is insufficient as x can be -1 or 2.
2nd statement is definitely insufficient.

Combining 1 and 2, 2 and 5 are both prime numbers. Answer should be E
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Re: What is x ? (1) x^2 - 1 = x + 1 (2) x + 3 is a prime number  [#permalink]

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24 Aug 2017, 13:35
Bunuel wrote:
What is x ?

(1) x^2 - 1 = x + 1
(2) x + 3 is a prime number

Statement One Alone:

x^2 - 1 = x + 1

x^2 - 1 = x + 1

x^2 - x - 2 = 0

(x - 2)(x + 1) = 0

x = 2 or x = -1

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x + 3 is a prime number

x could have many values; for example, x could be 2 or x could be 0. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

From statement one, we know that x is either 2 or -1. From statement two, x + 3 is a prime number. If x = 2, x + 3 = 5 is a prime number. If x = -1, x + 3 = 2 is also a prime number. Thus, we still can’t determine the value of x. The two statements together are still not sufficient to answer the question.

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Re: What is x ? (1) x^2 - 1 = x + 1 (2) x + 3 is a prime number   [#permalink] 24 Aug 2017, 13:35
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