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16 Sep 2014, 00:28
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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
(1) \(x\) is divisible by at least 2 prime numbers greater than 2
(2) \(\sqrt{x +1} - 1\) is prime
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
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
General Discussion
theeni03
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17 Jun 2019, 07:57
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I think this is a high-quality question.
