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Word Problem

by heshamelaziry » Fri Dec 04, 2009 12:00 pm
At a business association conference, the registration fee for members of the association was $20 and the registration fee for nonmembers was $25. If the total receipts from registration were $5,500, did more members than nonmembers pay the registration fee?

(1) Registration receipts from members were $500 greater than receipts from nonmembers.
(2) A total of 250 people paid the registration fee.

OA D

Could you guys say what is the level of this question ?
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Source: — Data Sufficiency |
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by Stuart@KaplanGMAT » Sat Dec 05, 2009 10:53 am
heshamelaziry wrote:At a business association conference, the registration fee for members of the association was $20 and the registration fee for nonmembers was $25. If the total receipts from registration were $5,500, did more members than nonmembers pay the registration fee?

(1) Registration receipts from members were $500 greater than receipts from nonmembers.
(2) A total of 250 people paid the registration fee.

Could you guys say what is the level of this question ?
I'd estimate this as a low to mid-500s question.

The question takes 30 seconds tops if you use the bestest math rule ever: to solve for a system of n variables, you need n distinct linear equations (the # of equations vs # of unknowns rule).

From the original: 2 variables (# of members/# of non-members) and 1 equation. What do we need to solve? 1 more distinct linear equation.

1) a new linear equation with the same variables: sufficient
2) a new linear equation with the same variables: sufficient

Each statement is sufficient alone: choose D

The beauty of applying this rule in DS is that we don't actually have to translate the equations, we just have to know that they're there.
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by heshamelaziry » Sat Dec 05, 2009 2:42 pm
Stuart,

I didn't understand your response. I would appreciate it if you could elaborate, since this could save me lots of work.

Is my solution correct ?

From stem: 20M + 25N = 5500

Statement 2: M + N = 250 , with stem --> 20( 250-N) + 25N= 5500 ( Sufficient)

Statement 1: Total N + Total N + 500 = 5500 ------> Total N = 2500 --> total M = 5500 - 2500 = 3000 ---> # of nonmembers = 2500/ 25 = 100, # of members = 3000/20 = 150 (Suffficient)
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by Stuart@KaplanGMAT » Sat Dec 05, 2009 4:03 pm
heshamelaziry wrote:Stuart,

I didn't understand your response. I would appreciate it if you could elaborate, since this could save me lots of work.

Is my solution correct ?

From stem: 20M + 25N = 5500

Statement 2: M + N = 250 , with stem --> 20( 250-N) + 25N= 5500 ( Sufficient)

Statement 1: Total N + Total N + 500 = 5500 ------> Total N = 2500 --> total M = 5500 - 2500 = 3000 ---> # of nonmembers = 2500/ 25 = 100, # of members = 3000/20 = 150 (Suffficient)
If you would let me know which part of the response you didn't understand, I can address specific parts.

Basically, here's the most important rule to remember for data sufficiency:

to solve a system with n variables, you need n distinct linear equations.

In this question, we have two variables: M and N
From the stem, we can derive one equation (the one you posted).
Therefore, in order to answer ANY question about the system, we need one more equation.

(1) gives us another equation (as you translated). The only variables are still M and N and the equation is distinct (i.e. different) from the original equation. Equally important, it's linear (there are no exponents other than 1 attached to any variables).

Therefore, (1) is sufficient.

(2) same deal as (1) - also sufficient alone.

Remember, we don't care what the answer IS in data sufficiency; we just care whether we have enough information to get an answer. If you understand the principle, you rarely have to actually do all the math.
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