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# Which of the following must be an integer if x is a positive integer

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Which of the following must be an integer if x is a positive integer  [#permalink]

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12 Mar 2018, 22:14
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35% (medium)

Question Stats:

66% (01:22) correct 34% (01:31) wrong based on 158 sessions

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Which of the following must be an integer if x is a positive integer and $$\frac{4}{x} + \frac{5}{x} + \frac{6}{x}$$ is an integer ?

A. x/5
B. 5/x
C. x/30
D. 30/x
E. x/120

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Re: Which of the following must be an integer if x is a positive integer  [#permalink]

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12 Mar 2018, 23:42
X can be 15,5 or 3 if take x=3 then only D follows .
if we take x=5 both A ,B and D follows
If x=15 then A and D follows so we can see that only D is correct
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Re: Which of the following must be an integer if x is a positive integer  [#permalink]

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13 Mar 2018, 00:02
arvind910619 wrote:
X can be 15,5 or 3 if take x=3 then only D follows .
if we take x=5 both A ,B and D follows
If x=15 then A and D follows so we can see that only D is correct

How did u count that 15,5 and 3?
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Re: Which of the following must be an integer if x is a positive integer  [#permalink]

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13 Mar 2018, 01:14
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Jahfors wrote:
arvind910619 wrote:
X can be 15,5 or 3 if take x=3 then only D follows .
if we take x=5 both A ,B and D follows
If x=15 then A and D follows so we can see that only D is correct

How did u count that 15,5 and 3?

HI 4/x+5/x+6/x is an integer 15/x = integer
So x can take values 15 ,3 , 5 and 1
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Re: Which of the following must be an integer if x is a positive integer  [#permalink]

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19 Feb 2019, 10:41
LCM of 2,3, and 5 is 30.

We can discard fastly A, C, and E because x can be 1.

B. 5/x
D. 30/x - (LCM of 2,3, and 5)

Hence, 30/x must be an integer.
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Re: Which of the following must be an integer if x is a positive integer  [#permalink]

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19 Feb 2019, 16:50
4/x + 5/x + 6/x is just equal to 15/x. If that's an integer, 30/x is clearly also an integer, since it's twice as big.
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Re: Which of the following must be an integer if x is a positive integer  [#permalink]

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20 Feb 2019, 20:40
3 consecutive integers will always be divisible by 3. So if 4, 5, and 6 over x are all integers, then x must be divisible by 3. 30 is divisible by 3, therefore option D.
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Re: Which of the following must be an integer if x is a positive integer  [#permalink]

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21 Feb 2019, 09:20
After solving the equation, we get 15/X.As 15 is divided by X, so 30/X also divided by X.

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Re: Which of the following must be an integer if x is a positive integer  [#permalink]

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21 Feb 2019, 18:01
Bunuel wrote:
Which of the following must be an integer if x is a positive integer and $$\frac{4}{x} + \frac{5}{x} + \frac{6}{x}$$ is an integer ?

A. x/5
B. 5/x
C. x/30
D. 30/x
E. x/120

Adding the fractions together, we have:

15/x = integer.

Thus, x must be a factor of 15. In that case, x must also be a factor of any multiple of 15, and thus 30/x will always be an integer.

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Re: Which of the following must be an integer if x is a positive integer  [#permalink]

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24 Feb 2019, 04:48
Adding up all the fractions we can clearly see that x must be a multiple of 3 or 5 or both. Considering all the possible cases:

A- if X were 3 this answer would not be an integer
B - same
C- x could not be bigger than 15 so this terms is not an integer
E - x cannot be bigger than 15, otherwise 15/x would not be an integer.

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Re: Which of the following must be an integer if x is a positive integer   [#permalink] 24 Feb 2019, 04:48
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