A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 7/17. What was the number erased?  Choose the correct choice
A) SEVEN 7 B) 8 C) 9 D) 15 E) 17
2) The average of the new group of numbers is 35 7/17. The denominator of THAT fraction tells us that the total number of terms in the new list MUST be a multiple of 17:   17, 34, 51, 68, 85, etc.   3) Since we're removing 1 number from a list of consecutive positive integers, we could quickly limit down the possible number of terms in the ORIGINAL list:   If new = 17, old = 18, but the numbers from 1 to 18 would NOT have an average in the mid-30s (it would be much smaller). ELIMINATE this option.   If new = 34, old = 35, but we run into the same problem. The average won't match here either. ELIMINATE this option.   If new = 51, old = 52, same problem here. ELIMINATE this option.   If new = 68, old = 69....HERE we have a group of numbers that might just be what we're looking for.   In theold group, the average is themiddle term= 35, which is REALLY close to the new average once we remove a number.   Now, we just have to figure out which of the 5 answers was removed (and that changed the new average to 35 7/17). There are a couple of ways to do this math, but I'm going to use the answers to save myself some steps:   Sum of 1 to 69, inclusive = 69(35) = 2415   Remove Answer B....2415 - 8 = 2407   New average = 2407/68 = 35 27/68   Now, we can compare 27/68 to 7/17   27/68 and 28/68   This is REALLY close, but is not the answer. Eliminate B. The answer is either A or C.   Since 28/68 is a BIGGER fraction than 27/68, we need the sum (of the 68 integers) to be BIGGER...which means we need to remove a SMALLER number.   Final SEVEN 7nswer:   SEVEN 7
<result>A</result>
A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 7/17. What was the number erased?