In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed. If 3/5 of the people ranked vanilla last, 1/10 of them ranked vanilla before chocolate, and 1/3 of them ranked vanilla before strawberry, how many people ranked vanilla first?  Choose the correct choice from the following:  A) 2 people  B) 6  C) 14  D) 16  E) 24
FIRST OFFUnderstand what you are trying to find - In this case, you are trying to find how many people rank Vanilla first. For someone to rank Vanilla first, they have to rank them before Chocolate or Strawberry. This should be the very first hint that the correct answer cannot be bigger than  1/10 * 60= 
<gadget id="calculator"> 1/10 * 60</gadget>
<output>6</output>
6.   So if you are time pressured on the real test, at least you narrowed down the selections to two choices - not bad. But what now?   Solve the easier problem. From 60 people, we are already told that 3/5 of them rank Vanilla last, leaving us with 2/5 of the people not ranking vanilla last - 24 people. So what are those combinations that vanilla are not last?   2 people) C, V, S   B) S, V, C   C) C, S, V (vanilla first)   D) S, C, V (vanilla first)   What are we ultimately hunting for here? The number of people that rank vanilla first:C+D   Now let's represent the given info into three equations   1) 2 people+B+C+D= 24(2/5 of the people do not rank vanilla last)   2) 2 people+C+D = 6(1/10 rank vanilla before chocolate)   3) B+C+D = 20(1/3 rank vanilla before strawberry)   Subtract equation 1 from 2, leaving us with   B = 24 - 6= 
<gadget id="calculator">24 - 6</gadget>
<output>18</output>
18   Sub in B into equation 3 and solve for C+D   18 + C + D= 20   C+D = 20 - 18= 
<gadget id="calculator">20 - 18</gadget>
<output>2</output>
2   There you go! 2 people out of the 60 ranked Vanilla as first 2 people
<result>A</result>
In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed. If 3/5 of the people ranked vanilla last, 1/10 of them ranked vanilla before chocolate, and 1/3 of them ranked vanilla before strawberry, how many people ranked vanilla first?