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# If x is a positive integer, is x divided by 5 an odd integer?

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Math Expert
Joined: 02 Sep 2009
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If x is a positive integer, is x divided by 5 an odd integer?  [#permalink]

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25 May 2016, 15:35
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35% (medium)

Question Stats:

63% (01:12) correct 37% (01:04) wrong based on 196 sessions

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If x is a positive integer, is x divided by 5 an odd integer?

(1) x contains only odd factors
(2) x is a multiple of 5

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Re: If x is a positive integer, is x divided by 5 an odd integer?  [#permalink]

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25 May 2016, 16:37
1) x contains only odd factors, so after dividing by 5, x will be a product of odd factors, so the result will be odd. Sufficient

2 ) x is multiple of 5, x could 10, so x/5 is even or x could be 15, so x/5 is odd. Not Sufficient.

IMO, A.
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Re: If x is a positive integer, is x divided by 5 an odd integer?  [#permalink]

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25 May 2016, 21:40
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Bunuel wrote:
If x is a positive integer, is x divided by 5 an odd integer?

(1) x contains only odd factors
(2) x is a multiple of 5

Given x>0

Statement 1
x contains only odd factors
If x = 5, then x divided by 5 will be an odd integer (yes)
If x = 3, then x divided by 5 will not even be an integer (no)
Hence, Insufficient

Statement 2
x is a multiple of 5
If x = 5, then x divided by 5 will be an odd integer (yes)
If x = 10, then x divided by 5 will be an even integer (no)
Insufficient

Statement 1 and 2
x is an odd multiple of 5, so x divided by 5 will always result in an odd integer.
Sufficient.
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Re: If x is a positive integer, is x divided by 5 an odd integer?  [#permalink]

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18 Apr 2017, 12:56
X is a positive integer. If X is divided by 5, will the result be odd?

Statement 1: X contains only odd factors
If X = 25 then the factors are 5 and 5. All factors are odd. X/5 is 5, which is odd.
If X = 27 then the factors are 3 and 9 (or 3-3-3). All factors are odd. X/5 is 27/5 though, which is not even and not odd.
Not sufficient.

Statement 2: X is divisible by 5
If X is 5 then it is divisible by 5. X/5 is 1 which is odd.
If X is 10 then it is divisible by 5. X/5 is 2 which is even.
Not sufficient.

Both: X is divisible by 5 and contains only odd factors.
If X is divisible by 5 and contains only odd factors, then it cannot end in zero. So it can be 5, 15, 25, 35, 45, 55, etc.
X cannot be 10 or 20 because those numbers are both divisible by 2, which is an even factor.
It looks like the formula for all the numbers that meet the requirements is X=5(2n+1), or all the odd numbers of 5n.
Since X will always be odd, and odd/odd is always odd, then x/5 will be odd.
This is sufficient, the answer is C.
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Re: If x is a positive integer, is x divided by 5 an odd integer?  [#permalink]

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19 Jul 2017, 21:42
Bunuel wrote:
If x is a positive integer, is x divided by 5 an odd integer?

(1) x contains only odd factors
(2) x is a multiple of 5

Very Simple

In order for x divided by 5 to be an odd integer x just has to be an odd multiple of 5- be careful- you need both statements in order to draw that conclusion
Re: If x is a positive integer, is x divided by 5 an odd integer?   [#permalink] 19 Jul 2017, 21:42
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