dtan5457 one year ago How many positive multiples of 4 less than 100 are not multiples of 6?

1. dtan5457

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

2. dtan5457

@mathstudent55 @satellite73 @sleepyjess

3. 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.

4. 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

5. dtan5457

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

6. dtan5457

something less time consuming

7. 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

8. UsukiDoll

which numbers are overlapping?

9. UsukiDoll

omg it's the cute purple owl!

10. 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

11. UsukiDoll

x) you're right

12. Kash_TheSmartGuy

"The Cute Purple Owl???"

13. 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

14. UsukiDoll

there are numbers that are overlapping here...

15. Kash_TheSmartGuy

16. 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.

17. dtan5457

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

18. UsukiDoll

?

19. UsukiDoll

oh yeah sorry I was in a conversation...

20. dtan5457

so is 17 right?

21. UsukiDoll

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

22. dtan5457

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

23. UsukiDoll

yup I got that too

24. dtan5457

im getting 17 as my answer but its not a choice

25. Zarkon

less than 100 not less than or equal to 100

26. dtan5457

ohh

27. dtan5457

good eyes

28. dtan5457

got it thanks

29. Zarkon

$\lfloor{99/4} \rfloor-\lfloor{99/12} \rfloor$

30. Zarkon

24-8=16

31. UsukiDoll

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