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If x>100, what is the smallest value of x for which (3+x)/12 is an int

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If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

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New post 23 Feb 2017, 06:39
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Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

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New post 23 Feb 2017, 07:42
1
Bunuel wrote:
If x>100, what is the smallest value of x for which (3+x)/12 is an integer.

A. 102
B. 103
C. 104
D. 105
E. 106



means 3+x must be divisible by 3 &4 (since 3*4=12)

for divisible by 3 sum of all three digit of (3+x)should be divisible by 3
And for it tobe divisible by 4 ,last two digit of (3+x) must be divisible by 4

A) 102
3+x= 3+102=105....NO
B) 103
3+x= 3+103=106....NO
C) 104
3+x= 3+104=107....NO
D)105
3+x= 3+105=108....YES
E)106
3+x= 3+106=109....NO

Ans D
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Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

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New post 23 Feb 2017, 07:51
1
Bunuel wrote:
If x>100, what is the smallest value of x for which (3+x)/12 is an integer.

A. 102
B. 103
C. 104
D. 105
E. 106




For (3+x)/12 to be an integer (3+x) must be multiple of 12. We know x>100 so least multiple of 12 above 100 is 108. therefore we need to add 105 in order to make (3+x) a multiple of 12. so the ans is D.
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Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

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New post 23 Feb 2017, 08:25
Bunuel wrote:
If x>100, what is the smallest value of x for which (3+x)/12 is an integer.

A. 102
B. 103
C. 104
D. 105
E. 106


12*9 = 108

Now, to make the numerator 108 , we must add 105 to 3

Answer, must be (D) 105.
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Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

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New post 27 Feb 2017, 11:46
Bunuel wrote:
If x>100, what is the smallest value of x for which (3+x)/12 is an integer.

A. 102
B. 103
C. 104
D. 105
E. 106


Since (3 + x)/12 must be an integer and x >100, we must find the smallest value of x greater than 100 that makes 3 + x a multiple of 12.

Since (105 + 3)/12 = 108/12 = 9, 105 is the smallest possible value of x.

Answer: D
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Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

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New post 03 Apr 2017, 05:41
To be divisible by 12 (2^2*3), (3+x) should be even and therefore x must be odd (odd+odd=even).
105 fits all the requirements.

105+3= 108

It's divisible by 3 (1+0+8=9)
Also 108 is a multiple of 12.
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Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

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New post 08 Apr 2017, 07:34
Here's another way of looking at it :

(3+x)/12 => 3/12 + x/12

3/12 leaves a remainder of 3. Hence for the whole thing to be divisible by 12, the second part needs to leave a reminder 9.

105 leaves a remainder of 9 when divided by 12.
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Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

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New post 27 Jun 2017, 16:16
Bunuel wrote:
If x>100, what is the smallest value of x for which (3+x)/12 is an integer.

A. 102
B. 103
C. 104
D. 105
E. 106


Very simple- 12 x 9 = 108- this is the smallest number that satisfies x>100 so

3 + 105 /12 = 1

Thus
"D"
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Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

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New post 27 Jun 2017, 20:02
It's possible to use the following approaching:

You need the least multiple of 12 greater than 100.

You can get this quickly, using easy numbers:

12x5 = 60x2 = 120

120-12=108

3+x = 108
x = 105
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Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

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New post 03 Jul 2017, 12:33
It should be odd+odd=even to be divisible by an even so A,C,E eliminated now put values
Answer is: D is it right approach?
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Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int   [#permalink] 03 Jul 2017, 12:33
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