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M06-31

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Bunuel
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M06-31 [#permalink] New post   16 Sep 2014, 00:28
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Question Stats:

58% (02:14) correct 42% (02:20) wrong based on 716 sessions
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If \(0 \lt x \lt 53\), what is the value of integer \(x\)?


(1) \(x\) is divisible by at least 2 prime numbers greater than 2

(2) \(\sqrt{x +1} - 1\) is prime
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Bunuel
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Re M06-31 [#permalink] New post   16 Sep 2014, 00:28
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Official Solution:


If \(0 \lt x \lt 53\), what is the value of integer \(x\)?

(1) \(x\) is divisible by at least 2 prime numbers greater than 2.

Multiple value of \(x\) satisfy the above condition. For example, \(x = 3*5=15\) or \(x = 3*7=21\) or \(x = 5*7=35\). Not sufficient.

(2) \(\sqrt{x +1} - 1\) is prime.

\(\sqrt{x +1} - 1=prime\)

\(\sqrt{x +1} =prime+1\)

\(x +1 = (prime+1)^2\)

\(x = (prime+1)^2 - 1\)

If \(prime =2\), then \(x = (prime+1)^2 - 1=8\)

If \(prime =3\), then \(x = (prime+1)^2 - 1=15\)

If \(prime =5\), then \(x = (prime+1)^2 - 1=35\)

...

Not sufficient.

(1)+(2) \(x\) can still take more than one value. For instance, \(x\) can be 15 or 35. Not sufficient.


Answer: E
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theeni03
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Re: M06-31 [#permalink] New post   17 Jun 2019, 07:57
I think this is a high-quality question.
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Re: M06-31 [#permalink] New post   09 Aug 2023, 06:24
I think this is a high-quality question and I agree with explanation.
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Re: M06-31 [#permalink] New post   13 Aug 2023, 04:29
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M06-31 [#permalink]
13 Aug 2023, 04:29
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