Bunuel wrote:
On a camping trip, x campers each paid y dollars for food. What percent of the total food expenses did each camper pay?
(1) If there were one few camper, each camper would owe 1 dollar more.
(2) If there were half as many campers, each camper would owe 7 dollars more.
Solution
Step 1: Analyse Question Stem
• There are \(x\) campers.
• Each camper paid \(y\) dollars for food.
o So, total food expense \(=x*y\) dollars
• We need to find out the percentage of the total food expenses that each camper paid.
o Or, we need to find out \(y\) is what percent of \(xy\)
o i.e. \(\frac{y*100}{xy}=\frac{100}{x}\)
So basically, we need to find the value of x.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: If there were one few camper, each camper would owe 1 dollar more.
• According to this statement: \((x-1)*(y+1) = xy\)
o \(⟹xy + x – y -1 = xy\)
o \(⟹x-y = 1\)
o \(⟹x = 1+ y\)
• However, we don’t know the value of y. So we cannot find x and hence the required percentage.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.
Statement 2: If there were half as many campers, each camper would owe 7 dollars more.
• According to this statement: \( \frac{x}{2}*(y+7) = xy\)
o \(⟹xy + 7x = 2xy\)
o \(⟹xy= 7x \)
o \(⟹y = 7\) [since x ≠0]
• But we don’t know the value of x. So we cannot find the required percentage.
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.
Step 3: Analyse Statements by combining.
From statement 1:
From statement 2:
On combining both statements:
• \( x = 1+ 7 = 8\)
• Therefore, the required percentage \(= \frac{100}{8}\)
Thus, the correct answer is
Option C.