How many positive integers less than 250 are there such that they are multiples of 15 or multiples of 14?
Choose the most appropriate option:  A) 30  B) 31  C) 32  D) 33  E) 34
250/15 = 16 (plus remainder) so there are 16 multiples of 15   250/14 = 17 (plus remainder) so there are 17 multiples of 14   We need to subtract 1 because 15*14 is a multiple of both so it was counted twice.   The total is  16+17-1= 
<gadget id="calculator"> 16+17-1</gadget>
<output>32</output>
32   The answer is 32.
<result>C</result>
How many positive integers less than 250 are there such that they are multiples of 15 or multiples of 14?