Question Puzzle
Here is snippet of section D of the curious multiple-choice entrance exam into the exclusive BrainBashers puzzle club.
Q1. Which is the first question where c) is the correct answer?
a) Q3
b) Q4
c) Q1
d) Q2
Q2. Which is the first question where a) is the correct answer?
a) Q4
b) Q2
c) Q3
d) Q1
Q3. Which is the first question where d) is the correct answer?
a) Q1
b) Q2
c) Q4
d) Q3
Q4. Which is the first question where b) is the correct answer?
a) Q2
b) Q4
c) Q3
d) Q1
Solution (Previous Puzzle):
72 buses.
They have enough room for 60 of these, expanding the 60 capacity by 40% will give them enough room for 84, which we know is 12 more spaces than they currently need.
If they have B buses and S spaces before the expansion, they have enough room for:
S = B - 12 [1]
After the expansion they have more spaces, and enough room for:
S + 0.4 x S = B + 12 [2]
Rewriting [2] as:
1.4S = B + 12
and again as
B = 1.4S - 12 [3]
We can rewrite [1] as:
B = S + 12 [4]
Making [3] = [4] we have:
1.4S - 12 = S + 12
Subtracting S from both sides gives:
0.4S - 12 = 12
Adding 12 to both sides gives:
0.4S = 24
Multiplying by 10 and dividing by 4 on both sides gives:
S = 60
Using S = 60 in [4] gives B = 72.
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