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

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On a camping trip, x campers each paid y dollars for food. [#permalink]

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20 Mar 2004, 22:04
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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.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 11 Jan 2014, 04:58, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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20 Mar 2004, 22:14
Find xy/x

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

y = x -1

(2) xy - (xy/2) = 7x/2

y = 7

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Re: On a camping trip ,'x' campers each paid 'y' dollars for [#permalink]

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10 Jan 2014, 22:12
2
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IMO

Total Campers = x
Food cost per camper = y
Total food expenses = xy

Percent of the total food expenses that each camper have to pay = $$\frac{y}{xy}$$ ==> $$\frac{1}{x}$$

Thus, to answer the question, we need to find the value of x.

Stmt 1: $$xy = (x-1)(y-1)$$ - Not sufficient
Stmt 2: $$xy = \frac{x}{2}(y+7)$$ ==> $$y=7$$- Not Sufficient (we need value of x)

With Stmt 1 & 2 combined, we can find the value of x.

Hence C
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Re: On a camping trip, x campers each paid y dollars for food. [#permalink]

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04 Nov 2015, 11:02
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Re: On a camping trip, x campers each paid y dollars for food. [#permalink]

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08 Nov 2015, 06:14
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

If we modify the question, we want to know y/xy=1/x=? the conditions are sufficient if they have data about 'x' If we simplify the 2 conditions, the question asks 1/x=?
Condition 1) (x-1)(y+1)=xy, or xy-y+x-1=xy, or y=x-1
Condition 2) (x/2)(y+7)=xy, or (y+7)/2=y, y+7=2y, y=7.
There are 2 variables (x,y) and 2 equations are given from the 2 conditions so there is high chance (C) will be our answer, and (C) is , in fact, our answer.

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: On a camping trip, x campers each paid y dollars for food. [#permalink]

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23 Sep 2016, 03:54
According to the first statement I got an equation as follows,
(x-1)(y+1)/x-1,
Since the number of campers reduced by 1,I divided the total food cost by x-1.Because 1 member is reduced.
Where am I wrong.
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Re: On a camping trip, x campers each paid y dollars for food. [#permalink]

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23 Feb 2017, 06:05
Prompt analysis
There were x campers and total amount they paid for food is y.share per person is y/x

Superset
The value of x/y will be a positive rational number.

Translation
In order to find the value, we need:
1# exact value of x and y or x/y
2# two equations in x and y to find the value of x and y

Statement analysis

St 1: if x-1 produces y amount share per head will be y/x +1. Therefore (x-1)(y/x +1) = y. Two variables, 1 equation. INSUFFICIENT.

St 2: if there were x/2 campers, share per head will be y/x +7. Hence x/2 * (y/x +7 ) = y. Two variables, 1 equation. INSUFFICIENT.

St 1 & St 2: two variable and two equations. Hence x and y can be calculated and therefore y/x can be calculated.

Option C
Re: On a camping trip, x campers each paid y dollars for food.   [#permalink] 23 Feb 2017, 06:05
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