If x is a non-zero integer, is x a prime number?

IMO B

The question asks to check if x is prime (and obviously positive).

1)|x|^|x|=4. Possible values of x=2,-2. Therefore, not sufficient.

2)|x^x|=x^2. Possible values of x=2. Sufficient.

Hence, B.

But 1 also fits in the second statement. Isn't it? Plz correct me if I am wrong.

Yes, you are right. The answer should be C. Possible values for 2) can be -1,1 and 2. Thanks for correcting!

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
\(|x|^{|x|} = 4\) implies \(x = 2\) or \(x = -2\).
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
\(|x^x| = x^2\) implies \(x = 2\), \(-1\) or \(1\).
Since we don't have a unique solution, condition 1) is not sufficient.

Conditions 1) & 2)
The solution for both conditions together is \(2\) only.
Since we have a unique solution, both conditions together are sufficient.

Therefore, C is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

Par of GMAT CLUB'S New Year's Quantitative Challenge Set

#1: it can be either +/-2 not sufficeint

#2: x^x=x^2
x can be either +/-1 or +2not sufficeint

from 1 & 2:
x = 2 sufficient C

Can you please explain how come the solution is 2 ? It is because 2 is common in both the conditions ??

himanshu1105

it would be +2 not -2 .. because its common and only valid option..

#1: it can be either +/-2 not sufficeint

#2: x^x=x^2
x can be either +/-1 or +2not sufficient

from 1 & 2:
x = 2 sufficient C

Statement 1) x can 2 or -2. Insufficient.

Statement 2) x can be -1, 1 or 2. Insufficient.

(1)+(2)
x=2. Sufficient.

The trick to this question is in statement 2

Statement 1 is easy. It gives us two values for x, 2 and -2. Since, 2 is a prime number here and -2 is not (prime numbers can only be positive integer), this statement is insufficient

Lets talk about statement 2 now.

It is tempting to assume that since \(|x^x| = x^2\), x=2 and hence this statement is sufficient. Although, x can definitely be 2, but it can also take the values 1 and -1. Idea is to always look at the expression as a whole and check for a few cornerstone values such as -1, 0, 1, 2 etc (depends on the case of course)

If x=1, then \(|x^x| = |1^1| = 1 = 1^2\)
and
If X=-1, then \(|x^x| = |-1^-1| = |-1| = 1= 1^2\)

So, statement 2 is also insufficient

Combining these two statements, we find only one common value i.e. 2 and 2 is a prime number. Hence, sufficient

Correct Answer is C

#1
\(|Z|^{|Z|} = 4\)
x=+/-2
insufficient
#2
\(|Z^Z| = Z^2\)
Z=1 or 2
insufficient
from 1&2
Z=+2 sufficient
IMO C

Can someone please provide a detailed explanation? Unable to understand.

Regarding statement 2, Z can be -1.

From statement 1 z can be -2 or 2. Yet, 2 is prime and -2 is not ( only positive numbers are primes). NS
From statement 2, z is either 1 or 2 . 2 is prime, 1 is not .NS
From both statements :2 is the only value that is common to both statement 1 and 2 . So answer is C

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