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(1) \(x!\) is not divisible by 5 --> \(x=0\), \(1\), \(2\), \(3\), or \(4\). Not sufficient. (2) \(|x|!\) is divisible by 6 --> \(|x|>2\). Not sufficient.

(1)+(2) \(x=3\) (prime) or \(x=4\) (not prime). Not sufficient.

Answer: E (Just noticed that OA is C, which I think is not correct).
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This is one of the common misunderstandings. If the question asked for the value of \(\sqrt{4}\), then it would surely be 2 and not -2 on GMAT. However, when it is stated that \(X^2=4\), you have two options, 2 and -2. There's nothing wrong in squaring a negative number. Does this explanation make any sense?

kl wrote:

Statement (2) - Should'nt we consider only the positive value for square root of 4 (and not -2)?

If that is true Stmt 2 would be sufficient, Am I missing something here?

Factorials of negative numbers are undefined on the GMAT. You won't encounter a negative number followed by a factorial sign on the GMAT.

gmatbull wrote:

Missed this because I assumed (wrongly) that -x can be a prime number. However, can we also have -x! -negative factorials. for example: (-4)! is it -4*-3.....*2*1?

It was such a dummy question anyway. from the basic explanation: 2! = 3!/3 = 2 1! = 2!/2 = 1 0! = 1!/1 = 1

-1! = 0!/0 => undefined similarly, for all negative numbers: (-x)! is undefined.
_________________

KUDOS me if you feel my contribution has helped you.

This question tricked me. Actually i though |X| is only positive integer.

Absolute value, |x| in our case, is never negative, |some expression|>=0. But the expression IN it (in ||) can be negative. So |x| >=0, but x can take ANY value, positive, zero, negative.

We are asked whether x is a prime number not absolute value of x (not |x|).

One more thing regarding this question: prime numbers are ONLY positive. 3 is prime, while -3 is not.

Hope it helps.

Bunuel Please clear my doubt here

Stmt 1 say that x can be 0,1,2,3,4 stmt 2 says -3>= x =>3 Both insufficient to make conclusion

Stmt 1 +Stmt 2 = x can be 3 or 4. Hence not sufficient Please explain if i am wrong or missing something here?????
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Prime number is a number that can be divided only by itself and the number one. For example, three and seven are prime numbers. So I think the correct answer is "E".

Statement (1): There are two possible values, +2 & -2 Statement (2): there are 2 possible values +2, -2

Prime number is a number that can be divided only by itself and the number one. For example, three and seven are prime numbers. So , shouldn't the answer be D cause we get the answer anyway that X is not a prime integer since both the answers are +2 & -2

+2 is a prime, -2 is not. Combining the two statements still doesn't give us more information. We can't be certain if \(X\) is prime (2) or not (-2) as both values of \(X\) are possible.

pdew wrote:

Is X a prime integer?

Statement (1): There are two possible values, +2 & -2 Statement (2): there are 2 possible values +2, -2

Prime number is a number that can be divided only by itself and the number one. For example, three and seven are prime numbers. So , shouldn't the answer be D cause we get the answer anyway that X is not a prime integer since both the answers are +2 & -2

seemed so simple...thanks for the question and the lesson learned story for the water cooler next week: "What'd ya do Thanksgiving?" response: "Learned that -2 is not prime."
_________________

This question tricked me. Actually i though |X| is only positive integer.

Absolute value, |x| in our case, is never negative, |some expression|>=0. But the expression IN it (in ||) can be negative. So |x| >=0, but x can take ANY value, positive, zero, negative.

We are asked whether x is a prime number not absolute value of x (not |x|).

One more thing regarding this question: prime numbers are ONLY positive. 3 is prime, while -3 is not.

This question tricked me. Actually i though |X| is only positive integer.

Absolute value, |x| in our case, is never negative, |some expression|>=0. But the expression IN it (in ||) can be negative. So |x| >=0, but x can take ANY value, positive, zero, negative.

We are asked whether x is a prime number not absolute value of x (not |x|).

One more thing regarding this question: prime numbers are ONLY positive. 3 is prime, while -3 is not.

Hope it helps.

since we're on the subject of prime numbers, one more addition to this would be that prime numbers are always odd. thus it becomes positive odd numbers, which can be divided by itself and 1

is it right that we go about handing absolute equations like this: for e.g. if we have |(any expression)| = 4 then that expression could mean either of these: (any expression) = 4 OR (any expression) = -4

we take one positive value of the number on the right hand side and one negative value?

is my understanding correct about absolute values?

This question tricked me. Actually i though |X| is only positive integer.

Absolute value, |x| in our case, is never negative, |some expression|>=0. But the expression IN it (in ||) can be negative. So |x| >=0, but x can take ANY value, positive, zero, negative.

We are asked whether x is a prime number not absolute value of x (not |x|).

One more thing regarding this question: prime numbers are ONLY positive. 3 is prime, while -3 is not.

Hope it helps.

since we're on the subject of prime numbers, one more addition to this would be that prime numbers are always odd. thus it becomes positive odd numbers, which can be divided by itself and 1

is it right that we go about handing absolute equations like this: for e.g. if we have |(any expression)| = 4 then that expression could mean either of these: (any expression) = 4 OR (any expression) = -4

we take one positive value of the number on the right hand side and one negative value?

is my understanding correct about absolute values?

Red part is not correct: 2 is even and is prime, it's also the only even prime and the smallest prime.

About the absolute value you are correct.

I'd suggest to check "Absolute value" and "Number theory" chapters in Math Book and also the topic "Inequalities" (links in my signature).
_________________

Missed this because I assumed (wrongly) that -x can be a prime number. However, can we also have -x! -negative factorials. for example: (-4)! is it -4*-3.....*2*1?
_________________

KUDOS me if you feel my contribution has helped you.

Factorials of negative numbers are undefined on the GMAT. You won't encounter a negative number followed by a factorial sign on the GMAT.

gmatbull wrote:

Missed this because I assumed (wrongly) that -x can be a prime number. However, can we also have -x! -negative factorials. for example: (-4)! is it -4*-3.....*2*1?