bmwhype2 wrote:
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
Source: GMAT Club Tests - hardest GMAT questions
Please show your work especially for 2. thanks
(1) \(x=3*5=15<53, \, x=5*7=35<53.\) No need to look for numbers that have 3 or more distinct prime factors.
Not sufficient.
(2) \(\sqrt{x +1} - 1=p,\) where \(p\) is some prime number.
Then \(\sqrt{x +1} =p+ 1\) or \(x+1=(p+1)^2\), and finally \(x=p(p+2).\)
We can have \(x=3*5=15<53,\, x=5*7=35<53,\) and that's it. \(7*9=63>53.\)
But still, more than one possibility.
Not sufficient.
(1) and (2) together won't help either, as can be seen from the above.
Answer E.
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