By Lisasimpson (Lisasimpson) on Friday, April 30, 2004 - 05:39 pm: Edit

hey, this question is #25 on section 3 of the sat bulletin:

chairs ready for shipment at the northern chair factory come down a ramp in single file. Inspector a checks every thrid chair, beginning with the third. inspector b checks every fifth char, beginning with the fifth. if 98 chairs came down the ramp while both inspectors were working on monday, how many of these chairs were NOT checked by either of these two inspectors?

i have no clue how to solve this except by drawing out all the chairs and counting, and i know that there has to be a shortcut..please help if you know how to do it

thanks

 By Paradox (Paradox) on Friday, April 30, 2004 - 06:02 pm: Edit

The number counted is those that are the "third" plus those that are "fifth" minus those that are both (to avoid overcounting). Floor(98/3) gives 32 positive multiples of 3 less than or equal to 98. Floor(98/5) gives 19 positive multiples of 5 less than or equal to 98. Floor(98/15) gives 6 positive multiples of 15 less than or equal to 98. So the answer is 98 - (32 + 19 - 6) = 53 chairs not checked.

Floor(r) being the function giving the greatest integer not greater than r, you can verify for yourself that Floor(a/b) gives the number of positive multiples of b less than or equal to a.

 By Lisasimpson (Lisasimpson) on Friday, April 30, 2004 - 06:12 pm: Edit

whoaaa that was waaay over my head. what does floor mean? thats not anything i learned in algebra or geometry or arithmetic. can anyone explain this simpler?

btw paradox, the answers 53, not 52..but i have no clue how or why

 By Paradox (Paradox) on Friday, April 30, 2004 - 06:35 pm: Edit

Floor is the same as the greatest integer function -- if the number is in decimal form, the function just removes the decimal point and all digits to the right of it.

And though the method is correct, I can't do arithmetic: the answer is in fact 53.

 By Neophyte31 (Neophyte31) on Friday, April 30, 2004 - 06:55 pm: Edit

I would think get all the multiples of 3 and 5 then subtract 99 from it. watch out for the chairs that both inspectors check and make sure you don't count those as two chairs..