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.

_________________

Karishma

Veritas Prep GMAT Instructor

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