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Is x a prime number?

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Is x a prime number? [#permalink]

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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.

can someone please explain statement 2
[Reveal] Spoiler: OA

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Re: Is x a prime number? [#permalink]

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New post 20 Dec 2012, 01:34
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.
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Re: Is x a prime number? [#permalink]

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New post 20 Dec 2012, 02:14
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Marcab wrote:
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.


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.
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Re: Is x a prime number? [#permalink]

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Re: Is x a prime number? [#permalink]

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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.

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Re: Is x a prime number? [#permalink]

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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.
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Re: Is x a prime number? [#permalink]

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New post 01 Sep 2016, 03:20
Bunuel wrote:
Marcab wrote:
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.


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.


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

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Re: Is x a prime number? [#permalink]

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New post 01 Sep 2016, 03:25
Yash26 wrote:
Bunuel wrote:
Marcab wrote:
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.


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.


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


Divide evenly simply means divides without a remainder, so we can say that 3 divides 9 evenly because 9/3 = 3, no remainder.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is x a prime number?   [#permalink] 01 Sep 2016, 03:25
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