+0  
 
+1
84
2
avatar+502 

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

 Jun 5, 2021
 #1
avatar+179 
+2

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!

 Jun 5, 2021
edited by EnchantedLava68  Jun 5, 2021
 #2
avatar+502 
+1

it's ok thanks!

 Jun 8, 2021

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