On a camping trip, x campers each paid y dollars for food. What percen

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:
Total cost for food = x*y
Percent of total food expenses paid by each camper = (y/xy)*100 = 100/x

If we can find x, we'll be able to answer the question.

Statements:

(1) If there were one few camper, each camper would owe 1 dollar more.

New campers = x-1
New cost per camper = y+1

But the total cost of food remains the same. Equating that:

xy = (x-1)(y+1)
We get, x-y = 1 --- (A)

Can't find the value of x.
Insufficient

(2) If there were half as many campers, each camper would owe 7 dollars more.

New campers = x/2
New cost per camper = y+7

But the total cost of food remains the same. Equating that:

xy = (x/2)(y+7)

We get, either x = 0 or y = 7. Since the campers can't be 0. Hence, y=7. --- (B)
Still, we don't have x.
Insuffiient

Considering both (A) and (B), we get x= 8 and y=7.
Sufficient

Hence, Answer (C)

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:

• \( x = 1+y \)

From statement 2:

• \( y = 7\)

On combining both statements:

• \( x = 1+ 7 = 8\)
• Therefore, the required percentage \(= \frac{100}{8}\)

Thus, the correct answer is Option C.

We need to get the value of x.
Statement 1: Insufficient
Total food expenses = (x-1)*(y+1) = xy.
=> xy + x - y - 1 = xy
=> x - y = 1
We didn't get the value of x.
Statement 2: Insufficient
Total food expenses : (x/2)*(y+7) = xy.
=> xy + 7x = 2xy
=> xy = 7x
=> y = 7
But we didn't get the value of x.

Combining both,
y = 7 and x = 8

Hence, OA is (C).

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.

1) We can form this equation taking the original no of campers as n: ny/(n-1) - y = 1. or, ny - ny + y /n-1 = 1, or, y/ n-1 = 1. We can only infer the no of campers were 1 more than the dollar amount each paid. Not sufficient.

2) 2ny/n - y = 7, or, y = 7. So, each camper paid $7. But we don't have the no of campers. Hence, insufficient.

Together, there were 8 campers and each paid $7. So we can find the required percentage as 1/8 or, 12.5%. Sufficient.

C is the answer.

the 2 question seems to be incorrect or just insufficient. I hate such practical exercises as nowadays they are just too unrealistic, during the pandemic, I mean. However, perhaps, it's far better to go camping with the RV and be surrounded by nature, not by coughing people. Whilst staying at home, I have managed to fix all problems I had with my rv, the main was with the air conditioner. Really happy that this article from https://www.palmgear.com/best-rv-air-conditioner/ helped me to choose Domestic Brisk II. The guide and review there was pretty fair, you know.

Bunuel, the above Question is from Princeton Review Mock tests. You can add it to the tag if you'd like

_________________________
Added the tag. Thank you!

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