number property

[sacx]

If n is a prime number, does n = 17?

a. n-1 = m^4, where m is an integer
b. n^2 < 300

[scoobydooby]

stmnt 1: n-1 = m^4
if m=1, n=1+1=2 a prime , n not equal to 17
if m=2, n=16+1=17
not sufficient, gives both yes and no

stmnt 2: n^2 < 300
n can be 17, 17^2=289<300
n can be any other prime, say 2, 3, 5. doesnt give definite yes or no
not suff

combining,
again for m=1 we get n=2
m=2 we get n=17 (square of both <300)
no definite yes or no

E

[DanaJ]

1 has at least two answers:
2 - 1 = 1 = 1^4
17 - 1 = 16 = 2^4
Both 2 and 17 are prime numbers, so we can't tell if n is actually 2 or 17.
2 has a lot of answers: it's basically any prime number from 2 to 17.

Put them together and it's still not enough, since both 2 and 17 have sqares (4 and 289) smaller than 300.
So it's E

[ramyaravindran]

I think the answer should be E.

Statement I

n-1 = m^4 has many solutions not just 17. For example 257 is a prime number that satisfies this equation and so is prime number 2.

So statement 1 is clearly not sufficient.

Statement 2
n^2 < 300
This narrows n to prime numbers less than or equal to 17. Still we have 2 and 17 that both satisfy this condition.

So Statement 2 is clearly not sufficient.

Combining both the statements we still have 2 values for n - 2 and 17. So the answer should be E.

[sacx]

yes the OA is E

made such a silly mistake