If\(\sqrt{x}\) is a prime number, what is the value ofx?
\(\sqrt{x}=prime\)
\(x=prime^2\)
(1)\(-16<-3x+5<22\) ;
Subtract 5 from all three parts:\(-21<-3x<17\) ;
Divide by -3 and flip signs:\(-\frac{17}{3} <x<7\) ;
x can only be 4 (4 = 2^2 = ptime^2). S
Sufficient.
(2)\(x^{2}\) is a two-digit number.
This implies that x < 10. There are two prime^2 less than 10: 2^2 and 3^2.
Not sufficient.
Answer: A.
...
\(\sqrt{x}=prime\)
\(x=prime^2\)
(1)\(-16<-3x+5<22\) ;
Subtract 5 from all three parts:\(-21<-3x<17\) ;
Divide by -3 and flip signs:\(-\frac{17}{3} <x<7\) ;
x can only be 4 (4 = 2^2 = ptime^2). S
Sufficient.
(2)\(x^{2}\) is a two-digit number.
This implies that x < 10. There are two prime^2 less than 10: 2^2 and 3^2.
Not sufficient.
Answer: A.
...
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