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Is a positive integer x an odd number? 1) The smallest prime factor of

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Is a positive integer x an odd number? 1) The smallest prime factor of  [#permalink]

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New post 18 Aug 2017, 01:53
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Is a positive integer x an odd number?

1) The smallest prime factor of x is 7.
2) The greatest prime factor of x is 7.

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Re: Is a positive integer x an odd number? 1) The smallest prime factor of  [#permalink]

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New post 18 Aug 2017, 02:05
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MathRevolution wrote:
Is a positive integer x an odd number?

1) The smallest prime factor of x is 7.
2) The greatest prime factor of x is 7.


1) Smallest Prime Factor is 7
=> All prime factors greater than 7 would be odd. (2 is the only even prime number)
=> x is odd.
Sufficient.

2) Greatest Prime factor is 7
=> x could have 2,3,5 as prime factors as well -> Not Odd.
=> x could have 3,5,7 as prime factors -> Odd.
Insufficient.

A is the answer.
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Re: Is a positive integer x an odd number? 1) The smallest prime factor of  [#permalink]

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New post 18 Aug 2017, 04:44
MathRevolution wrote:
Is a positive integer x an odd number?

1) The smallest prime factor of x is 7.
2) The greatest prime factor of x is 7.


Statement 1 :
- X have factor of 7 X ... X ... X ....
- Since X doesn't have the 2 factor, thus the number cannot be EVEN (all of the prime numbers greater than 7 are ODD)
- X must be ODD
Sufficient.

Statement 2 :
- X can have a factor of : 3 X 5 X 7 : ODD
- X can have a factor of : 2 X 7 : EVEN.
INSUFFICIENT.

So the answer is B.
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Re: Is a positive integer x an odd number? 1) The smallest prime factor of  [#permalink]

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New post 20 Aug 2017, 19:09
=>Condition 1)
2 cannot be a factor of x, since the smallest prime factor of x is 7.

Condition 2)
Consider n = 2 and n =3.


Ans: A
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Re: Is a positive integer x an odd number? 1) The smallest prime factor of  [#permalink]

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New post 02 Sep 2017, 11:01
Answer is A. Statement 1 is sufficient to answer that the prime factorization would have 7 and above prime numbers hence it is an odd number

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Re: Is a positive integer x an odd number? 1) The smallest prime factor of   [#permalink] 17 Dec 2018, 11:04
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