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

Question

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.

RaghavKhanna · Answer

Campers = x
Amount paid by each camper = y

=>  Total amount paid = xy

% payment by each camper = (y/xy)*100 = 100/x

Statement 1:  
Campers = (x+1)
Money paid by each camper = (y-1)

(x+1)(y-1) = xy
y - x = 1

Cannot find values of x and y from this.

Statement 1 is insufficient.

Statement 2:  
Campers = x/2
Money paid by each camper = (y+7)

x/2 * (y+7) = xy
xy + 7x = 2xy
xy = 7x
x(y-7) = 0
=> y = 7

Cannot find x from this.

Statement 2 is insufficient.

Statement 1 and Statement 2:  
From statement 2, we have, y = 7
From statement 1, we have, x = 6

=>  % payment by each camper = 100/6 = 16.67%

Statement 1 and Statement 2 are together sufficient.

Answer: C

nkme2007 · Answer

From Statement 1, Total food expenses : (x-1)*(y+1) = xy.
Solving the above gives x-y = 1

From Statement 2, Total food expenses : (x/2)*(y+7) = xy.
Solving the above gives y = 7 and no value for x.

Combining both, y = 7 and x = 6.

Hence, OA: C

KaramveerBakshi · Answer

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)

GMATWhizTeam · Answer

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    
• 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.

v12345 · Answer

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).

minustark · Answer

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.

atova01 · Answer

Hello - why can't we plug 7 in for y for equation 2? Why is statement 2 not enough?

Bunuel · Answer

Yes, from (2) we can determine that y = 7. However, we need to find the value of y/(xy)*100, which simplifies to 1/x*100. This means we require the value of x to answer the question, not the value of y.

bumpbot · Answer

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

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