The slope of the line ax+by+c=0 is 2/3. b=? 1) a=3 2) c=-6 GMAT data sufficiency

Question: The slope of the line ax + by + c = 0 is 2/3. b = ?

1) a = 3
2) c = -6

              A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient
              B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient
              C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
              D) EACH statement ALONE is sufficient
              E) Statements (1) and (2) TOGETHER are not sufficient

Approach Solution 1

Given that the slope of the line ax + by + c = 0 is ⅔
It has asked to find out the value of b.
From the theory of straight line we know that the slope of a line having equation ax + by + c = 0 is -b/c
We are given that,
-b/a = ⅔
Now,
Statement 1:
Given a = 3
Putting a in equation
-b / 3 = ⅔
We get b = -2
Statement 2: given c = -6
Even after getting the value of c we have 2 variables and one equation.
We cannot find the value of b.

Hence, A is the correct answer.

Approach Solution 2

The task is to determine the value of "b" from the given equation of a line, ax + by + c = 0, with a known slope of ⅔. The slope of the line is represented by -b/a in this equation.
Given that -b/a = ⅔, we can rearrange the equation to solve for "b":
-b/a = ⅔
Multiplying both sides by "a":
-b = (⅔) * a
Now, let's consider the two statements provided:
Statement 1:
Given a = 3
Substituting the value of "a" in the equation:
-b = (⅔) * 3
Solving for "b":
-b = 2
Thus, the value of "b" is -2.
Statement 2:
Given c = -6
Even after obtaining the value of "c," there are still two variables (a and b) and only one equation. Therefore, we cannot determine the value of "b" with this information alone.
Hence, Statement 1 is sufficient to find the value of "b," and the answer is A.

Approach Solution 3

To find the value of "b" in the equation ax + by + c = 0 with a slope of ⅔, we use the fact that the slope is represented by -b/a. Given -b/a = ⅔:
If a = 3, then b = -2.
If c = -6, we cannot determine "b" with this information alone.

Hence, the answer is A

“ The slope of the line ax+by+c=0 is 2/3. b=? 1) a=3 2) c=-6 " - is a topic of the GMAT data sufficiency section of the GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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