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How many positive integers less than 50 are multiples of 4 but NOT mul

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How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 20 Dec 2015, 05:42
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 21 Dec 2015, 09:41
5
Bunuel wrote:
How many positive integers less than 50 are multiples of 4 but NOT multiples of 6?

A. 4
B. 6
C. 8
D. 10
E. 12


Think of it this way: Multiples of 4 but not of 6 will be integers divisible by 4 but not by 3.
The positive multiples of 4 will be from 4 to 48 i.e. 4*1 to 4*12 - in all 12 multiples.
Every third of these 12 multiples will be divisible by 3 so remove 1/3rd of these 12 multiples. 12 - (1/3)*12 = 8
You will be left with 8 multiples.

Answer (C)
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 20 Dec 2015, 07:56
How many positive integers less than 50 are multiples of 4 but NOT multiples of 6?

only 4, 8, 16, 20, 28, 32, 40 and 44. 8 total

12, 24, 36 and 48 are also multiples of 6


C. 8
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 21 Dec 2015, 03:22
IMO the answer is C (8 numbers)
The LCM of 4 and 6 is 12.
If x <50 and x is divisible by 4 not by 6 --> x is NOT divisible by 12.
From 1--> 50, we have 4 numbers which is divisible by 12: 12, 24, 36, 48.
From 1-->50, we have (48-4)/4 +1 =12 numbers divisible by 4.
Therefore, our answer is 12-4 = 8 numbers.
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 21 Dec 2015, 10:28
1
Bunuel wrote:
How many positive integers less than 50 are multiples of 4 but NOT multiples of 6?

A. 4
B. 6
C. 8
D. 10
E. 12


Positive Numbers less than 40 that are multiple of 4 = [50/4] = 12

Positive Numbers less than 40 that are multiple of 4 and 6 both i.e. multiple of LCM(4, 6) i.e. 12 = [50/12] = 4

i.e. Numbers that are multiple of 4 but not multiple of 6 = 12-4 = 8

Answer: option C
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 21 Dec 2015, 19:03
VeritasPrepKarishma wrote:
Bunuel wrote:
How many positive integers less than 50 are multiples of 4 but NOT multiples of 6?

A. 4
B. 6
C. 8
D. 10
E. 12


Think of it this way: Multiples of 4 but not of 6 will be integers divisible by 4 but not by 3.
The positive multiples of 4 will be from 4 to 48 i.e. 4*1 to 4*12 - in all 12 multiples.
Every third of these 12 multiples will be divisible by 3 so remove 1/3rd of these 12 multiples. 12 - (1/3)*12 = 8
You will be left with 8 multiples.

Answer (C)


Thanks Karishma, your approach is so simple and creative
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 22 Dec 2015, 15:59
VeritasPrepKarishma wrote:
Bunuel wrote:
How many positive integers less than 50 are multiples of 4 but NOT multiples of 6?

A. 4
B. 6
C. 8
D. 10
E. 12


Think of it this way: Multiples of 4 but not of 6 will be integers divisible by 4 but not by 3.
The positive multiples of 4 will be from 4 to 48 i.e. 4*1 to 4*12 - in all 12 multiples.
Every third of these 12 multiples will be divisible by 3 so remove 1/3rd of these 12 multiples. 12 - (1/3)*12 = 8
You will be left with 8 multiples.

Answer (C)


I'm sorry Karishma, can you please explain why every third of a set of multiples will be divisible by 3? Would this generally be the case?
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 22 Dec 2015, 22:11
daisuke123 wrote:
VeritasPrepKarishma wrote:
Bunuel wrote:
How many positive integers less than 50 are multiples of 4 but NOT multiples of 6?

A. 4
B. 6
C. 8
D. 10
E. 12


Think of it this way: Multiples of 4 but not of 6 will be integers divisible by 4 but not by 3.
The positive multiples of 4 will be from 4 to 48 i.e. 4*1 to 4*12 - in all 12 multiples.
Every third of these 12 multiples will be divisible by 3 so remove 1/3rd of these 12 multiples. 12 - (1/3)*12 = 8
You will be left with 8 multiples.

Answer (C)


I'm sorry Karishma, can you please explain why every third of a set of multiples will be divisible by 3? Would this generally be the case?


Multiples of 4 are:

4*1
4*2
4*3
4*4
4*5
4*6
4*7
etc

4 is not a multiple of 3 so 3 comes only from the second term. In 1, 2, 3, 4, 5, 6...etc, every third number will be a multiple of 3. Hence, every third number will be a multiple of 3.

Similarly, consider some multiples of 5:
15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65...

15 is divisible by 3. Then 30 is divisible by 3. Then 45 and so on... Again, starting from the first one, every third is divisible by 3.

Of course, if you look at multiples of 6, every multiple will be divisible by 3 because 6 itself is divisible by 3.
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 22 Dec 2015, 22:47
Thank you very much for the response. It makes sense, I'll keep it in mind going forward!
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 22 Dec 2015, 23:51
Multiples of 4 but not multiples of 3..
i.e. 4,8,16,20,28,32,40,44 = 8 multiles

Ans:C
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 23 Dec 2015, 01:43
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

How many positive integers less than 50 are multiples of 4 but NOT multiples of 6?

A. 4
B. 6
C. 8
D. 10
E. 12



The positive integers which are multiples of 4 have 4*K form for some positive integer K.
Since 4K <50, K<12.5 ---> K can be from 1 to 12.
Since they should not be multiples of 6 they are the multiples of 12 which is the least common multiple of 4 and 6.
Similarly with the case of the multiples of 4 there are positive integers T such as 12T<50 ---> T<4.17 ---> T can be form 1 to 4.
So the number of positive integers less than 50 which are multiples of 4 but not multiples of 6 is 12-4=8.


The answer is, therefore, (C).
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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New post 15 Oct 2016, 21:19
Bunuel wrote:
How many positive integers less than 50 are multiples of 4 but NOT multiples of 6?

A. 4
B. 6
C. 8
D. 10
E. 12



Multiples of 4 less than 50 = 50/4 = 12

Multiples of 4&6 i.e. 12 less than 50 = 50/12 = 4

Multiples of 4 but not multiples of 6 = 12-4 = 8

Answer: option C
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Re: How many positive integers less than 50 are multiples of 4 but NOT mul  [#permalink]

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