Does the equation y = ( x – p)( x – q) intercept the x-axis at the point (2,0)?
(1) pq = -8
(2) -2 – p = q
The answer is
My analysis tells me that (1) should be sufficient based on these steps:
Plug in (2,0) in the equation and expand:
0 = (2 - p)(2 - q)
0 = 2^2 - 2q - 2p + pq
Now, sub in (1) pq = -8
0 = 4 - 2q - 2p -8
4 = -2q - 2p
-2 = q + pHence: -2 - p = q
--> same as statement (2)... so if I'm able to derive statement (2) just using information in (1), can't I plug "-2 = q + p" into pq = -8 and solve? Isn't this the same as using both statements except you can only use the first one to get the info in the second, thus making (1) sufficient?
What am I missing here?
Kudos for any help please!
For Data Sufficiency questions, you are not required to find answers. You just have to tell whether the statements given are sufficient to
answer the questions or not.
At first you have to treat each statements independently. You should not
take any information from statement 2 when you are trying to
figure out if statement 1 alone is sufficient and vice versa. (Basically you have to assume the other statement is not there when you are solving
for one statement alone.)
If each statement alone does not give you answer then you have to combine both and check.
Please look at the answer choices:
A. Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
B. Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
C. Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
D. Each statement alone is sufficient
E. Statements 1 and 2 together are not sufficient.
What is the question here?
Does the equation y = ( x – p)( x – q) intercept the x-axis at the point (2,0)? You are required to tell if the statements given are sufficient to answer the questions.
i.e. y = x^2 - x(p+q) + pq . You need information about both 'p+q' and 'pq' to solve for this.
Take statement 1 alone. Are you able to answer the above question just by taking statement 1 alone.?
No. Because you know pq = -8.But you don't know what is p+q. When you are checking for statement 1 alone you should not take any info from statement 2.
Take statement 2 alone. Are you able to answer the above question just by taking statement 2 alone.?
No.Because you know p+ q = -2 But you don't know what is pq. When you are checking for statement 2 alone you should not take any info from statement 1.
When each statement alone is not giving you any answer. You have to combine both.
Now you will see that there is information about p+q AND pq which is sufficient to answer the question.
Hope you understood.
Kindly press Kudos if the explanation is clear.