TANCET 2014 DS 70: Linear Equations
Directions for Data Sufficiency Question
The question is followed by two statements labeled (1) and (2) in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the problem plus your knowledge of mathematics and everyday facts, choose the answer as:
 Choice 1 if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
 Choice 2 if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
 Choice 3 if both the statements (1) and (2) TOGETHER are sufficient, but NEITHER statement alone is sufficient.
 Choice 4 if each statement ALONE is sufficient.
 Choice 5 if statements (1) and (2) TOGETHER are not sufficient, and additional data is needed.
Question
What is the sum of x, y and z?
 Statement 1: 2x + y + 3z = 45
 Statement 2: x + 2y = 30
Correct Answer Choice (3). Statements (1) and (2) TOGETHER are sufficient.
Explanatory Answer  step by step

What should we know from the Question Stem?
Before evaluating the two statements, answer the following questions to get clarity on when the data is sufficient.
What kind of an answer will the question fetch?
The question is "What is the sum of x, y and z?"
The answer to the question should be a number. For e.g., 65.
When is the data sufficient?
If we are able to come up with a UNIQUE value for the sum of x, y, and z, the data is sufficient.
If we are not able to come up with a UNIQUE value for (x + y + z), the data is NOT sufficient.
What is the approach?
Use the statements independently first and check whether by multiplying or dividing the equation by a number will result in (x + y + z). If it does, data is sufficient.
Else combine the two statements. Try and add, subtract or manipulate the equations in some way to arrive at x + y + z. If you could find a unique value data is sufficient. Else, data is NOT sufficient 
Statement (1) ALONE
2x + y + 3z = 45
We will not be able to get the value of x + y + z with the above equation.
Statement (1) ALONE is NOT sufficient.
If statement (1) ALONE is NOT sufficient, we can eliminate choices 1 and 4.
Choices narrow down to 2, 3, or 5.

Statement (2) ALONE
x + 2y = 30.
At least the first statement had all 3 variables in it. The second statement has only 2 variables in it.
No, we will not be able to find the value of x + y + z using statement 2
Statement (2) ALONE is NOT sufficient.
If statement (2) ALONE is NOT sufficient, we can eliminate choice 2 as well.
Choices narrow down to 3, or 5.

Statements Together
2x + y + 3z = 45
+
x + 2y = 30
Though at first sight it appears as if we have only two equations and 3 variables, a bit of tweaking is likely to give us the answer.
Add the two equations. {2x + y + 3z = 45} + {x + 2y = 30}
= 3x + 3y + 3z = 75.If 3x + 3y + 3z = 75, {x + y + z} = 25.
Using statements (1) and (2) together we were able to determine a unique value for the sum of x, y and z.
Hence, choice (3) is the answer.
Video Explanation
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 Number Theory
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 Pipes, Cisterns & Work, Time
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