The line at Ice Cream Parlor stretches down the block. there is one more person in line behind James than there is in front of him. There are two times as many people in the entire line as there are behind him. How many people are in line?
Possible answers 56, 44, 10, 100 and none of the above.
Here is what I came out:
People behind James is X+1
Two times as many people in the entire line as behind him is 2(X+1)
2x+2=56
x=27
2x+2=44
x=21
2x+2=10
x=4
2x+2=100
x=49
My question is? Is my answer none of the above?
number of people in front of James --- x
number of people behind James ----- x+1
entire line = james + in front + behind
= 1 + x + x+1
= 2x+2
2x+2 = 2(x+1)
0=0 ----> true for all x's
There is an infinite number of solutions,
just plug in any value of x
e.g.
x = 20
number in front of him = 20
number behind him = 21
total = 1+20+21 = 42
x = 45
total = 92
Since the total is 2x+2, and 2x+2 is always an even number,
any even number for the total will work
e.g. total = 246
in front = 122
behind = 123
James = 1
total = 246
All of the given choices are possible, however, if the trick part is to eliminate those that would not "reach down the block", we get into a different argument.
Certainly 100 could reach down the block, but probably 10 wouldn't.