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

Question

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.

Kudos for a correct  solution .

GMATinsight · Answer

In year 1996
Production of Line A = a
Production of Line B = b

In year 1997
Production of Line A = a+(5/100)a = 1.05a
Production of Line B = b+(10/100)b = 1.10b

Question : a = ?

Statement 1 : The two lines combined produced 100,000 units in 2006. 
a+b = 100000
Since b is unknown hence a can't be calculated
NOT SUFFICIENT

Statement 2 : The two lines combined produced 107,500 units total in 2007. 
1.05a+1.10b = 107500
Since b is unknown hence a can't be calculated
NOT SUFFICIENT

Combining the two statements  
a+b = 100000
1.05a+1.10b = 107500
Two equation in two variable can be simultaneously solved to get a unique value of a hence
SUFFICIENT

Answer: Option C

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Question Type: What Is the Value?  This question asks you for the number of units that line A produced in 2006.

Given information from the question stem: Production on line A increased by 5% from 2006 to 2007 and production on line B increased by 10%.

Statement 1 : This statement can be written as “A + B = 100,000 units.” This information is not sufficient since you do not know how many of the 100,000 units were produced by line A and how many by line B. Not sufficient. Eliminate answers A and D.

Statement 2 : This statement tells you the combined number of units in 2007. This can be written as 1.05A + 1.10B = 107,500. Similar to the above, this statement is not sufficient alone as you have two variables and one equation. Eliminate choice B as well.

Together : Now you have two distinct linear equations with two variables and you can solve. There is no need to actually solve for A since you are certain that you can. Together the statements are sufficient and  the answer is C .

MathRevolution · Answer

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

Attachment:

GCDS Bunuel If production on line A(20151007).jpg [ 23.25 KiB | Viewed 8480 times ]

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.

BrainLab · Answer

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) ?

KarishmaB · Answer

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/

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

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