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09 Sep 2018, 08:51
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (02:15) correct
31%
(02:10)
wrong
based on 204
sessions
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A circle with center (1, 0) and radius 2 lies in the coordinate plane shown above. If point (x, y) lies on the circle, is (x, y) in quadrant II?
(1) |y| < 1
(2) |x| < 1
Attachment:
image001.jpg [ 1.42 KiB | Viewed 6539 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
09 Sep 2018, 10:02
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Bunuel
Target question: Is (x, y) in quadrant II?
Given: A circle with center (1, 0) and radius 2 lies in the coordinate plane
Let's sketch the circle along with some key points on the circle:
From here, let's jump to . . . .
Statements 1 and 2 combined
There are several points on the circles that satisfy BOTH statements. Here are two cases:
Case a: The point lies slightly above and to the right of (-1,0).
Notice that the x-coordinate is between -1 and 0, so we can be certain that |x| < 1
Likewise, the y-coordinate is slightly greater than 0, which means |y| < 1
In this case, the answer to the target question is YES, the point (x,y) IS in quadrant II
Case b: The point lies slightly below and to the right of (-1,0).
Notice that the x-coordinate is between -1 and 0, so we can be certain that |x| < 1
Likewise, the y-coordinate is slightly less than 0, which means |y| < 1
In this case, the answer to the target question is NO, the point (x,y) is NOT in quadrant II
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
KanishkM
Joined: 09 Mar 2018
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05 Feb 2019, 07:52
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Bunuel
Now when we plot the points on the co ordinate plane
We get a circle with 1,0 as center and crossing the points -1,0 & 3,0
from 1
|y| < 1
-1< y < 1, this tells nothing about x
from 2
|x| < 1
-1<x < 1, this tells nothing about y
Even when we combine both the statements, it wont be sufficient to answer the question.
E
15 Sep 2020, 08:40
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Bunuel
In second quadrant (Q2) \(x\) is negative and \(y\) is positive. Looking at the statements one of the value that we can use to prove and disprove each statement is \(0.5\) or \(\frac{1}{2}\)
Statement-I (|y| < 1, Insufficient)
Q1 - \(y = 0.5\) and \(x = 0.5\)
Q2 - \(y = 0.5\) and \(x = -0.5\)
Statement-II (|x| < 1, Insufficient)
Q1 - \(y = 0.5\) and \(x = 0.5\)
Q2 - \(y = 0.5\) and \(x = -0.5\)
Combined (|x| < 1 & |y| < 1, Insufficient)
Q1 - \(y = 0.5\) and \(x = 0.5\)
Q2 - \(y = 0.5\) and \(x = -0.5\)
Ans. E
