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rck1099
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16 Sep 2019, 06:24
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Is a < 2 ?
(1) In the xy-plane, the point (a,1) lies inside the circle whose equation is x^2 + y^2 = 3.
(2) In the xy-plane, the point (a,4) lies on the line whose equation is 2y + 4x = 10.
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.
This was on my GMAT prep practice exam. I had originally picked B as I could prove statement 2 by putting this in slope intercept form, factoring out the 2, and plugging in numbers. So for that I got y=2x+5, plugged in the numbers in the point and got 4=-2a+5, from there I did the algebra and got -1=-2a and a=1/2, which gives me a definitive yes for statement 2.
After reviewing this problem I did the same thing for equation 1 and got the y=sqrt2. I just want to make sure that this is in fact the way to go about solving this. If it is I made a careless mistake that is easily correctable. Thank you in advance for your help!
(1) In the xy-plane, the point (a,1) lies inside the circle whose equation is x^2 + y^2 = 3.
(2) In the xy-plane, the point (a,4) lies on the line whose equation is 2y + 4x = 10.
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.
This was on my GMAT prep practice exam. I had originally picked B as I could prove statement 2 by putting this in slope intercept form, factoring out the 2, and plugging in numbers. So for that I got y=2x+5, plugged in the numbers in the point and got 4=-2a+5, from there I did the algebra and got -1=-2a and a=1/2, which gives me a definitive yes for statement 2.
After reviewing this problem I did the same thing for equation 1 and got the y=sqrt2. I just want to make sure that this is in fact the way to go about solving this. If it is I made a careless mistake that is easily correctable. Thank you in advance for your help!
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
16 Sep 2019, 06:52
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rck1099
rck1099 - The equation given in Statement (1) is that of a circle, as stated. The general equation for a circle is \((x - h)^2 + (y - k)^2 = r^2\), in which r is the radius of the circle and point (h, k) is the center. You cannot alter a circle equation to turn it into a linear one, since a circle and a line, of course, are not the same geometric shape. However, there is no need to alter anything here, as the given equation lends itself to a simple substitution, as you had done on your own. You should understand, however, that if \(r^2 = 3\), then the radius of the circle must therefore be √3. This tells you that any point inside the circle must lie within that distance of the center of the circle. In Statement (1), given that y has a value of 1, we can substitute and solve for a:
\((a)^2 + (1)^2 = 3\)
\(a^2 + 1 = 3\)
\(a^2 = 2\)
\(a = \sqrt{2}\)
The question can now be reinterpreted as, "Is √2 < 2?" Whether we were to consider the positive or negative root, the answer would be "yes." Thus, Statement (1) is SUFFICIENT to answer the question, and choice (D) will be the correct answer.
I hope that helps. Please let me know if you have any questions. Good luck with your studies.
- Andrew
16 Sep 2019, 08:20
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Previously discussed here:
https://gmatclub.com/forum/is-a-161310.html
https://gmatclub.com/forum/is-a-161310.html
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
