number theory ques

[mani24]

unable to solve...por favor, el señor help

if X is a set of all positive multiples of 28 that are less than 300 and Y is a set of positive multiples of 16 less than 300 .How many elements of set X are also in Y .
a- 2
b- 5
c- 8
d- 10
e- 12

answer is 2

[mickgreen58]

Interesting question. Here is how I did it although I hope someone with a little bit more acumen can suggest another method.

A multiple of a number is found by multiplying N*0..N*1..N*2 etc etc

So you want to find multiples of 28 < 300 that are also in 16 < 300.

Don't actually divide everything, just reduce real fast and see that it won't divide evenly (you get a fraction):

16*0/28...bingo!
16*1/28...doesn't go evenly
16*2/28...doesn't go evenly
......
16*7/28...bingo!

You can stop at 10 because 28*11 > 300

Almost had me for a second until I realized I forgot about 0.

[skawal]

28*1/16
28*2/16
28*3/16
28*4/16
...........
...........
28*8/16
...........
28*10/16(28*11>300 so it cant be taken)

the problem ask u to find out the common multiple of both 16 and 28.
from the above we see find a common number, 28*P/16where p=1,2,3.....10

if u put the values of p then you would see that only p=4 and 8 gives you an integer number and those are the common multiples of 16 & 28.

[skawal]

for mick,
16*0/28....... not bingo!
16*14/28........bingo!