SAT Counter-Examples

For $p$ we can write,

$p = {2, 3, 5, 7, 11, 13, \dots}$

Here $p=2$ is an Even Number.

So, $[I]$ is wrong.

Again, $p = 7$ can divide by $7$

So, $[III]$ is wrong.

We know, $6$ is an even number and its mutiples will always be an even.

Hence, $p$ isn't divisible by $6$ .

Thus the right statement is $[II]$ and the answer is $B$

Correct Answer: B

Solution:

We analyze each of the options.

I. $p = 2$ is a prime number that is not odd. Hence option I need not be true.

II. A prime number has two factors: 1 and itself. If $p$ is divisible by 6, then it has at least four factors: 1, 2, 3 and 6. Hence, the prime number $p$ cannot be divisible by 6. Option II is true.

III. $p = 7$ is a prime number that is divisible by 7. Hence option III need not be true.

Because the only true statement is option II, the answer is (B).

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Incorrect Choices:

(A) , (C) , (D) , and (E)
The solution explains why these choices are wrong.

If you got this problem wrong, you should review SAT Factors, Divisibility, and Remainders .