OG10 DS 215 multiple of 24

[mitzi]

Is the positive integer n a multiple of 24?
1) n is a multiple of 4
2) n is a multiple of 6

my approach to this question is as follows

step 1. multiples of 24 means 24, 48, 72 .....
step 2. 1) multiple of 4 : 4,8,12,16,20,24,28.....
among these number above, 24 and 48 are multiple of 24.
---> insufficient

step 3. 2) multiple of 6 : 6,12,18, 24,30, 36....
among these number above, 24 and 48 are multiple of 24
---> insufficient

taken together it is still insufficient.

gurus, I got an right answer. However how do gurus solve/approach to this question? my reasoning is acceptable?

Thank you for your help!

[nverma]

Originally Posted by mitzi

Is the positive integer n a multiple of 24?
1) n is a multiple of 4
2) n is a multiple of 6

my approach to this question is as follows

step 1. multiples of 24 means 24, 48, 72 .....
step 2. 1) multiple of 4 : 4,8,12,16,20,24,28.....
among these number above, 24 and 48 are multiple of 24.
---> insufficient

step 3. 2) multiple of 6 : 6,12,18, 24,30, 36....
among these number above, 24 and 48 are multiple of 24
---> insufficient

taken together it is still insufficient.

gurus, I got an right answer. However how do gurus solve/approach to this question? my reasoning is acceptable?

Thank you for your help!

I'm not a guru.. but still would like to answer..

Multiple of 6 are in the form of 2*3*k , where k is any integer

Multiple of 4 are in the form of 2*2*m , where m is any integer

Stat(1): 4, 8..are not multiple of 24 : insufficient.

Stat(2): 6, 12..are not multiple of 24 : insufficient.

Take both the statements together

Find the LCM(Least common multiple) of 6 (2*3) and 4(2*2)..

LCM is 12: >>> (highest power of 2 * highest power of 3) >>> 2^2 *3

And 12 is not the multiple of 24.. And we reach to thy answer..

[cristofer]

the key is that all multiples of 12 will occur in both lists (list of multiples of 4, and list of multiples of 6),
12, 24, 36, 48, 60, 72, ...

but not all multiples of 12 are necessarily multiples of 24, notice that every other number is not a multiple of 24. So that's why E is correct

[touche]

I believe in the factors approach....
Factors of 24 are 2,2,2,3
1) n is a multiple of 4.
factors are 2,2.... 2,3 still left to be divisible.. insuff
2) n is a multiple of 6
factors are 2,3....2,2 still left..insuff
1 and 2.
lcm 2*2*3
factor 2 still left out... insuff
E
I guess for easy numbers your approach is fine, but when numbers are large, this approach will be better to avoid doing unnecessary calculations.

[mitzi]

Thank you for clarification. I found that I need to practice and pick up more things from you guys.

I am very grateful for this.
Mitzi