If production on line A increased 5% from 2006 to 2007, and if product

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.

If production on line A increased 5% from 2006 to 2007, and if production on line B increased 10% in the same period, how many units did line A produce in 2006?

(1) The two lines combined produced 100,000 units in 2006.
(2) The two lines combined produced 107,500 units total in 2007.

From the original condition and the question, we can obtain the below 2by2 table that is common in GMAT math test

In the above table, we have 2 variables (A,B), and 2 equations given from the 2 conditions, making it likely that (C) is going to be our answer as the number of variables and equations match;
Looking at the conditions together,
A+B=100,000
1.05A+1.1B=107,500.
The conditions are sufficient to solve for the variables, and the answer actually is (C).

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.

Hi, I've used the same method as mathrevolution to solve this one. By statement B, would it be appropriate to expect an unique combination (as by some tough DS questions, in which one equation with two variables can be solved because there is only one unique combination) ?

You are talking about unique integral solution to an equation in two variables. It is certainly good to ensure that the equation doesn't have a single solution but you don't have to worry about it in this case. Here is why:

1.05a + 1.1b = 107500
21a + 22b = 2150000

Note that the constant is much much greater than the co-efficients. There is obviously at least one solution to the equation. If there is one solution, there will be many more since a and b will be very large numbers and they will reduce/increase by much smaller numbers. So they will not become negative in a hurry.

e.g. a = 50,000 and b = 50,000 is a solution.
Another solution will be a = 50,000 - 22 = 49,978 and b = 50,000 + 21 = 50,021.
There will be many many such solutions. When the constant term is much greater than the co-efficients and we know that there exists at least one solution, we can be sure that there will be many solutions.

Here is a post on integral solutions: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/06 ... -of-thumb/

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.