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The line in the xy-plane passes through

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The line in the xy-plane passes through [#permalink] New post 18 May 2016, 16:17
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Question Stats:

53% (00:41) correct 46% (00:35) wrong based on 39 sessions
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Quantity A
Quantity B
w + d
c + Z


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.




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Question: 7
Page: 82


[Reveal] Spoiler: image
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[Reveal] Spoiler: OA

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Re: The line in the xy-plane passes through [#permalink] New post 18 May 2016, 16:19
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Explanation

The line in the xy-plane passes through the origin and the point with coordinates (6, 6), so the equation of the line is y = x. Since the point with coordinates (c, d) is above the line, it follows that d > c, and since the point with coordinates (w, z) is below the line, it follows that w > z.

From the fact that d > c and w > z, you get w + d > c + z; that is, Quantity A is greater than Quantity B. Thus the correct answer is Choice A.
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Re: The line in the xy-plane passes through [#permalink] New post 03 Dec 2016, 01:32
Sandy-

If the question actually asked if quantity A (c + w) was greater than quantity B (d + z), would the answer then be D? or would we need to try and estimate values from the graph - and possibly arrive at C (as graphs and plots should be drawn to scale on the GRE)?
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Re: The line in the xy-plane passes through [#permalink] New post 03 Dec 2016, 02:17
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rsudhakar wrote:
Sandy-

If the question actually asked if quantity A (c + w) was greater than quantity B (d + z), would the answer then be D? or would we need to try and estimate values from the graph - and possibly arrive at C (as graphs and plots should be drawn to scale on the GRE)?


Yes then answer would be D.
Do not estimate value from graph usually the graphs are not drawn to scale.
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Re: The line in the xy-plane passes through [#permalink] New post 09 Dec 2016, 09:49
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sandy wrote:
Image

Quantity A
Quantity B
w + d
c + z




Notice that the line passing through (0,0) and (6,6) has the equation y = x.
That tells that, for every point ON the line, the x-coordinate is EQUAL to the y-coordinate.
For example, some points on the line include (1,1), (4,4), (18,18), etc

Also notice that the line divides the quadrant into TWO REGIONS: a region ABOVE the line, and a region BELOW the line.

ALL points that lie in the region ABOVE the line share an important characteristic: the x-coordinate is LESS THAN to the y-coordinate.
For example, some points in this region include (1,4), (3,9), (11,13), etc

ALL points that lie in the region BELOW the line share an important characteristic: the x-coordinate is GREATER THAN to the y-coordinate.
For example, some points in this region include (3,2), (7,1), (11,5), etc

Since the point, (c, d) lies in the region ABOVE the line, we can be certain that c < d
Since the point, (w, z) lies in the region BELOW the line, we can be certain that z < w

If we add the two inequalities, we get: c + z < d + w

Answer: A
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Re: The line in the xy-plane passes through   [#permalink] 09 Dec 2016, 09:49
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