Is x a prime number? (1) x is an even number. (2) x cannot be divided

Question

Is x a prime number?

(1) x is an even number.
(2) x cannot be divided evenly by an odd number other than 1.

Marcab · Answer

Statement 2 states that x is not evenly divisible by an odd number other than 1.
It talks, IMO, about numbers such as 2, 4, 8, 10 etc i.e. multiples of 2 that are not divisible by ANY odd number but 1.

Bunuel · Answer

10 is divisible by 5 so x cannot be 10.

Is x a prime number?

(1) x is an even number. If x=2 then the answer is YES but if x is any other even number then the answer is NO. Not sufficient.

(2) x can not be divided evenly by an odd number other than 1. This statement implies that x is some power of 2: 2, 4, 8, 16, ... Not sufficient.

(1)+(2) Still not sufficient. Consider x=2 and x=4.

Answer: E.

Marcab · Answer

yeah right.
missed it completely.

unceldolan · Answer

This is more of a "don't overthink too much question" than anything else.
is x prime?

(1) x is even. X could be 2, hence prime. But also 4,6,8,...IS
(2) x can not be divided evenly by an odd number other than 1. This is tempting but the statement says nothing about even numbers. So x could be even! (I see what you did there).

Together it basically stays the same. From (2), x could be be even and from (1) we only get that x is even, hence still IS.

E.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is x a prime number?

(1) x is an even number.
(2) x can not be divided evenly by an odd number other than 1. 
 
In the original condition, there is 1 variable(x), which should match with the number equation. So you need 1 more equation. However, for 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. 
In 1), x=2 -> yes and x=4 -> no, which is not sufficient. 
In 2), x=2 -> yes and x=4 -> no, which is not sufficient. Even when 1) & 2), ), x=2 -> yes and x=4 -> no, which is not sufficient. Therefore, the answer is E.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

unverifiedvoracity · Answer

1) x could be 2, which is a prime or x could be 4 which is not a prime. Not Sufficient.

2) This statement tells us that x has no odd factors other than 1, so x is even (In fact, we may also conclude that x is a power of 2). This statement provides same info as statement 1. Not Sufficient.

Statement 1 and 2 give the same information, so combined together these statements are not sufficient.

my answer would be E.

nalinnair · Answer

Statement 1
x is an even number
If x = 2, then x is a prime (yes)
If x = 4, then x is not a prime (no)
Insufficient

Statement 2
x can not be divided evenly by an odd number other than 1
Same cases as statement 1 above - Insufficient.

Statement 1 and 2
Same cases as statement 1 above - Insufficient.

Answer - E

Yash26 · Answer

Bunuel,

When we say - divide "evenly"- do we mean that the number should be divided in even factors? for example 9 (an odd) number can be divided by 3 bit there is no even factor. so, can we say that 3 divides 9 evenly? or only when a number has an even factor then we can say that number is "evenly" divided? Answer to this question will play a major role in solving above question.

Regards
Yash

Bunuel · Answer

Divide evenly simply means divides without a remainder, so we can say that 3 divides 9 evenly because 9/3 = 3, no remainder.

bumpbot · Answer

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Is x a prime number? (1) x is an even number. (2) x cannot be divided

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GMAT Data Sufficiency (DS) Questions

Is x a prime number? (1) x is an even number. (2) x cannot be divided

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