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

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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Please kudo me if you think my answer is good

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

Thanks Karishma, your approach is so simple and creative

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.

Thank you very much for the response. It makes sense, I'll keep it in mind going forward!

Multiples of 4 but not multiples of 3..
i.e. 4,8,16,20,28,32,40,44 = 8 multiles

Ans:C

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).

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

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
I solved it by forming a 2*2 matrix
No of Positive multiples of 4 under 50 = 12
No of positive multiples of 6 under 50 = 8
No of positive multiples under 50 that are multiples of both 6 & 4 = 4
Therefore total multiples of 4 But not 6 = 12 -4 =8
C
PS: I wanted to create the table with 4 variables multiples of 4,Not multiples of 4 on horizontal axis and multiples of 6 & Not multiples of 6 on the vertical axis, but the table comes out wayward every single time. when i try to attempt to draw the boxes.

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