+514 In the expression 2013 & 2014 & 2015 & 2016 & 2017, the symbol & can be taken to mean either + or -, which of the following number cannot be obtained?
A. 2007
B. 2009
C. 2011
D. 2013
E. 2017
+179 2007 cannot be obtained
If we want to achieve a number near the 2015 range, 3 of the numbers will have plus signs, while two have minus signs.
Writing each of the terms relative to 2015, we have -2, -1, 0, 1, and 2. To obtain 2007, we must get a -8. However, regardless of the combination of + and -, it is impossible to achieve a negative 8, even when optimized (-2, -1, 0, -(1), -(2) sum = -6).
Thus, 2007 is impossible.
Just to double-check, I calculated each of the other answers using the strategy listed above.
2009 = 2013 + 2014 + 2015 - 2016 - 2017
2011 = 2013 + 2014 - 2015 + 2016 - 2017
2013 = 2013 + 2014 - 2015 - 2016 + 2017
2017 = 2013 - 2014 - 2015 + 2016 + 2017
Sorry for taking such a long time, I had to think about this for a bit before I could confidently post an answer.
Anyways, have a great day!
