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XXX Value

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by smclean23 » Thu Aug 07, 2008 7:05 pm
If 2x + 3y = 5, what is the value of x ?

(1) x + z = 3 + 2y + z
(2) y=-1/7




Answer is D.

2 is suff.
1. I cancelled z on both sides of the equation and got x=3+2y. This doesn't give me a value. How do I possibly get a value from this.
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Source: — Data Sufficiency |
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by parallel_chase » Thu Aug 07, 2008 8:27 pm
From the question stem we already know that 2x+3y=5

x=3+2y

2(3+2y) +3y =5

from this we can get the value of y=-1/7

Then insert this value in the equation x=3+2y to find the value of x.

Hence Sufficient.
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Re: XXX Value

by Stuart@KaplanGMAT » Thu Aug 07, 2008 8:57 pm
smclean23 wrote:If 2x + 3y = 5, what is the value of x ?

(1) x + z = 3 + 2y + z
(2) y=-1/7




Answer is D.

2 is suff.
1. I cancelled z on both sides of the equation and got x=3+2y. This doesn't give me a value. How do I possibly get a value from this.
Here's the MOST powerful rule in data sufficiency: to solve for a system of n variables, you need n distinct linear equations.

Know that rule; know the exceptions; love it and hug it and call it George.

From the original, we have 1 equation and 2 unknowns. If we can get 1 more equation with just Xs and Ys, we can solve for anything.

As you noted, you can reduce (1) to an x & y equation: sufficient.

(2) also gives us another equation that doesn't introduce any new variables: sufficient.

Remember, in data sufficiency we don't care what the answer is, we only need to determine if it's possible to find an exact value. Understanding the concepts behind the questions will save you a lot of time on test day.
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by pepeprepa » Fri Aug 08, 2008 12:57 am
Stuart when you state that
Here's the MOST powerful rule in data sufficiency: to solve for a system of n variables, you need n distinct linear equations.

Know that rule; know the exceptions; love it and hug it and call it George.
Do you either follow your rule during DS questions and tell you "it's impossible to solve" that because 3 unknowns and 2 equations, without any calculations or do you try to calculate any equations which seem impossible?

I was trapped 2 or 3 times by equations which indeed could been reduced and I spend more time on all of them now...
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by Stuart@KaplanGMAT » Fri Aug 08, 2008 11:56 am
pepeprepa wrote:Stuart when you state that
Here's the MOST powerful rule in data sufficiency: to solve for a system of n variables, you need n distinct linear equations.

Know that rule; know the exceptions; love it and hug it and call it George.
Do you either follow your rule during DS questions and tell you "it's impossible to solve" that because 3 unknowns and 2 equations, without any calculations or do you try to calculate any equations which seem impossible?

I was trapped 2 or 3 times by equations which indeed could been reduced and I spend more time on all of them now...
It's very important to know the exceptions to the rule as well. In fact, the better you're doing on the GMAT the more likely it is that you'll be tested on exceptions to rules.

Here's the most common exception to the "n linear equations" rule:

The rule only strictly applies when you're solving for an entire system of variables.

If you're only solving for 1 variable, then it's possible that 1 equation will be enough; if you're solving for 2 variables, then it's possible that 2 equations will be enough; and so on...

Further, if you're solving for a relationship between variables rather than the variables themselves, it's possible that 1 equation will be sufficient no matter how many variables are involved. Here's an example:

A certain restaurant only sells donuts and coffee. What's the cost of 2 donuts and a cup of coffee?

(1) one donut and one cup of cofee costs $2.00

(2) 4 donuts and 2 cups of cofee costs $6.00

At first glance, it may seem like we need both statements, since each one gives us 1 equation and we have a total of two unknowns. However, upon closer inspection statement (2) is sufficient alone, because we can reduce

4d + 2c = 6

to

2(2d + c) = 6

and

2d + c = 3

which is exactly the relationship that the question is asking us to find.
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