byRituparna Nath Content Writer at Study Abroad Exams
Question: Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)?
(1) pq = -8
(2) -2 – p = q
- Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
- Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are not sufficient.
‘Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)?’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.
Solution and Explanation
Approach Solution 1:
There is only one approach to this problem.
Given in the question an equation y = (x-p)(x-q)
This is the equation of a line and it is asked whether it intercepts at the x-axis at the point (2,0) or not.
This is a question from coordinate geometry.
The point (2,0) lies on the x axis as the y value is 0.
Therefore we need to find the x-intercept of the given line.
The x-intercept of the given line will be when y = 0
(x - p)(x - q) = 0
There are two values of x for which this equation can be 0
Either x- p = 0
Or x-q = 0
This means either x = p or q
This line has x intercept either (p,0) or (q,0)
We are given two statements and we have to check if these equations are sufficient to get the answer or not.
In statement 1,
Given : pq = -8
This statement is not sufficient to say whether p = 2 or q = 2.
Coming to statement 2,
Given: -2 - p = q
This statement is also not sufficient to say whether p = 2 or q = 2.
Now taking both the statements into consideration we get,
Pq = -8
And -2 -p = q
Putting the value of q in equation 1
p(-2-p) = -8
-2p - \(p^2\)= -8
\(p^2\)+ 2p - 8 = 0
\(p^2\)- 2p + 4p - 8 = 0
p(p-2) + 4(p-2) = 0
(p-2)(p+4) = 0
P = 2 or -4
Putting p = 2 in statement 2 we get
-2-2 = q
Q = - 4
Putting p = -4 in statement 2 we get,
-2 + 4 = q
Q = 2
In either case one of the variables is 2 so y=(x−p)(x−q) intercepts the x-axis at the point (2,0).
Therefore the correct answer is option C
Correct Answer: C
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