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On a camping trip, x campers each paid y dollars for food. What percen 10 Jul 2020, 02:47
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

59% (02:06) correct 41% (02:25) wrong based on 380 sessions

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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.

 
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C
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On a camping trip, x campers each paid y dollars for food. What percen 10 Jul 2020, 03:02
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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
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On a camping trip, x campers each paid y dollars for food. What percen 10 Jul 2020, 03:10
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Bunuel
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.
 
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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
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On a camping trip, x campers each paid y dollars for food. What percen 10 Jul 2020, 04:04
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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)
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On a camping trip, x campers each paid y dollars for food. What percen 10 Jul 2020, 04:28
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Bunuel
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.

Show 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:
    • \( x = 1+y \)
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.
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On a camping trip, x campers each paid y dollars for food. What percen 10 Jul 2020, 08:09
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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).
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On a camping trip, x campers each paid y dollars for food. What percen 10 Jul 2020, 08:54
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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.
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On a camping trip, x campers each paid y dollars for food. What percen 17 Jun 2024, 08:15
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nkme2007

Bunuel
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.

 
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
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­Hello - why can't we plug 7 in for y for equation 2? Why is statement 2 not enough?
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atova01

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Bunuel
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.

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