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# The line in the xy-plane passes through

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Joined: 07 Jun 2014
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The line in the xy-plane passes through [#permalink]  18 May 2016, 16:17
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00:00

Question Stats:

53% (00:41) correct 46% (00:35) wrong based on 39 sessions

 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.

Practice Questions
Question: 7
Page: 82

[Reveal] Spoiler: image
Attachment:

Quant.jpg [ 15.46 KiB | Viewed 4134 times ]
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1596 [2] , given: 373

Re: The line in the xy-plane passes through [#permalink]  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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Sandy
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Re: The line in the xy-plane passes through [#permalink]  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)?
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1596 [0], given: 373

Re: The line in the xy-plane passes through [#permalink]  03 Dec 2016, 02:17
Expert's post
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]  09 Dec 2016, 09:49
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sandy wrote:

 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

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