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18 Sep 2025, 09:22
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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100% (00:53) correct
0% (00:00) wrong based on 1 sessions
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The circle at left above is tangent to the x- and y-axes, and has radius equal to 3. The circle at right above is tangent to the x-axis and to the other circle and has radius equal to 4.
Quantity A
The slope of the line containing the centers of the two circles.
Quantity B
\(\frac{1}{7}\)
Attachment:
GMAT-Club-Forum-p86ebz59.png [ 9.43 KiB | Viewed 125 times ]
28 Sep 2025, 04:49
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Official Explanation
The segment whose endpoints are the centers of the two circles will have a length of 3 + 4 = 7, because the segment consists of the radii of the two circles meeting endpoint to endpoint on a straight line. Since the circles are tangent to the x-axis (intersecting at exactly one point), the radius of each circle, when drawn to the x-axis, will be perpendicular to the x-axis and will determine the center ’s y-coordinate. That is, one circle’s center is 3 units above the x-axis, and one center is 4 units above the x–axis. Then for some constants, c and d, we can think of the coordinates of the two centers as (c,3) and (d,4). To find the slope of the segment, find change in y over change in x, or
We can infer that d – c is less than 7, because it represents the length of the horizontal leg of the right triangle depicted, which must be less than the length of the triangle’s hypotenuse, 7.
Then
so (A) is greater. For positive values, a larger number in the denominator makes the fraction smaller.
Answer: A
GMAT-Club-Forum-67vnos98.png [ 123.31 KiB | Viewed 92 times ]
GMAT-Club-Forum-qx2uzm4l.png [ 17.71 KiB | Viewed 92 times ]
GMAT-Club-Forum-w7tfhe18.png [ 14.19 KiB | Viewed 94 times ]
GMAT-Club-Forum-ifd8dh39.png [ 6.87 KiB | Viewed 93 times ]
The segment whose endpoints are the centers of the two circles will have a length of 3 + 4 = 7, because the segment consists of the radii of the two circles meeting endpoint to endpoint on a straight line. Since the circles are tangent to the x-axis (intersecting at exactly one point), the radius of each circle, when drawn to the x-axis, will be perpendicular to the x-axis and will determine the center ’s y-coordinate. That is, one circle’s center is 3 units above the x-axis, and one center is 4 units above the x–axis. Then for some constants, c and d, we can think of the coordinates of the two centers as (c,3) and (d,4). To find the slope of the segment, find change in y over change in x, or
We can infer that d – c is less than 7, because it represents the length of the horizontal leg of the right triangle depicted, which must be less than the length of the triangle’s hypotenuse, 7.
Then
so (A) is greater. For positive values, a larger number in the denominator makes the fraction smaller.
Answer: A
Attachment:
GMAT-Club-Forum-67vnos98.png [ 123.31 KiB | Viewed 92 times ]
Attachment:
GMAT-Club-Forum-qx2uzm4l.png [ 17.71 KiB | Viewed 92 times ]
Attachment:
GMAT-Club-Forum-w7tfhe18.png [ 14.19 KiB | Viewed 94 times ]
Attachment:
GMAT-Club-Forum-ifd8dh39.png [ 6.87 KiB | Viewed 93 times ]
