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

Question

GMAT Club Tests' Fresh Question:

(1)  |x|^{|x|} = 4

(2)  |x^x| = x^2

M36-135

Puja priya · Accepted Answer

C in my opinion.
A gives -2,2
B gives 1,2
C gives only 2- sufficient

Bunuel · Answer

Official Solution: If x is a non-zero integer, is x a prime number? (1) |x|^{|x|} = 4 x=2 is an obvious solution but, because of the modulus, x=-2 will also work. In the first case x is a prime but in the second case it's not. Not sufficient. (2) |x^x| = x^2 Test numbers: If x=1 , then |1^1| = 1^2 . OK. If x=-1 , then |(-1)^{(-1)}| = (-1)^2 . OK. If x=2 , then |2^2| = 2^2 . OK. If x=-2 , then |(-2)^{(-2)}| =\frac{1}{4} but (-2)^2=4 . NOT OK. If x > 2 , then |x^x| > x^2 and if x < -2 , then |x^x| < x^2 ( |x^x| will be a fraction between 0 and 1, while x^2 will be positive integer). So, x=2=prime or x=1 eq prime or x=-1 eq prime . Not sufficient. (1)+(2) Only x=2 satisfies both statements, so x is a prime number. Not sufficient. Answer: C

US09 · Answer

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.

Puja priya · Answer

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

US09 · Answer

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

MathRevolution · Answer

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.

Bunuel · Answer

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

Archit3110 · Answer

#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

himanshu1105 · Answer

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

Archit3110 · Answer

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

Ypsychotic · Answer

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

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

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

GMATin · Answer

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

Archit3110 · Answer

#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

Vinayak013 · Answer

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

analytica233 · Answer

Regarding statement 2, Z can be -1.

dimri10 · Answer

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

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