How many positive multiples of 4 less than 100 are not multiples of 6?

- dtan5457

How many positive multiples of 4 less than 100 are not multiples of 6?

- katieb

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- dtan5457

how would you solve this without listing out all 25 multiples?

- dtan5457

- UsukiDoll

multiples of 6 is basically the entire multiplication table of 6 x 1
6 x 2... so we list all of those numbers up to 100.

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## More answers

- UsukiDoll

and multiples of 4 is the entire multiplication table of 4 x 1 4 x 2.... so we list those numbers up to 100
and then we eliminate the digits that are multiples of 6

- dtan5457

for an SAT question with so little space i would think there is an easier way i hope

- dtan5457

something less time consuming

- UsukiDoll

hmmmmmm
multiples of 4 - 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80
multiples of 6 - 6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96

- UsukiDoll

which numbers are overlapping?

- UsukiDoll

omg it's the cute purple owl!

- Kash_TheSmartGuy

\(\color{pink}{\text{Originally Posted by}}\) @UsukiDoll
hmmmmmm
multiples of 4 - 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80
multiples of 6 - 6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96
\(\color{pink}{\text{End of Quote}}\)
Have to consider 84, 88, 92, 96 as it asks till 100

- UsukiDoll

x) you're right

- Kash_TheSmartGuy

"The Cute Purple Owl???"

- UsukiDoll

multiples of 4 - 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80 , 84, 88, 92, 96, 100
multiples of 6 - 6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96

- UsukiDoll

there are numbers that are overlapping here...

- Kash_TheSmartGuy

@dtan5457 , it's your question.. we want to help you and we can leave. You have to reply, not just sit there!

- UsukiDoll

Since the question asks for numbers for multiples of 4 less than 100 that's not a multiple of 6, we need to compare the multiples of 4 with the multiples of 6. any number appearing in multiple of 4 that's also in multiple of 6 needs to go.

- dtan5457

i'm getting 8 overlaps
25-8= 17 multiples of 4 that aren't of 6?

- UsukiDoll

?

- UsukiDoll

oh yeah sorry I was in a conversation...

- dtan5457

so is 17 right?

- UsukiDoll

let me check.. who is overlapping besides 12 and 96?

- dtan5457

12, 24, 46, 48, 60, 72, 84, 96

- UsukiDoll

yup I got that too

- dtan5457

im getting 17 as my answer but its not a choice

- Zarkon

less than 100 not less than or equal to 100

- dtan5457

ohh

- dtan5457

good eyes

- dtan5457

got it thanks

- Zarkon

\[\lfloor{99/4} \rfloor-\lfloor{99/12} \rfloor\]

- Zarkon

24-8=16

- UsukiDoll

x(! aahhhhhhhhhhhhhhhhhh! Well at least I tried... I didn't know that we can't have 100 involved

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