35 kids, not all dance, rows of 2,3 or,4 one has no partner. rows of 5 all have partners. how many danced?

Question

this is supposed to be 5th grade math but it is blowing my mind.

Answer 1

Assuming you have to have a partner to dance, then the answer is 30.

 

If one kid from each row of 2, 3, or 4 doesn't dance, then that leaves 1, 2, and 3.  All rows of 5 are dancing.

 

The LCM of 1,2,3, and 5 is 30.

Answer 2

Hi Stephen,

 

I am guessing the solution has something to do with the common multiple of 2,3 &4 but less than 35. The information about 5 rows will eliminate some options. 

If X ( <35) are the number of kids who dance, then X-1 is a multiple of 2,3 & 4 because one has no partner.

 

Is this in the direction you were thinking ? ( I am not very clear about the meaning 'rows of 2,3 or 4 has no partner)