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Math Expert V
Joined: 02 Sep 2009
Posts: 58364
In the figure above, lines k1 and k2 are parallel to each other, lines  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 41% (02:55) correct 59% (02:53) wrong based on 142 sessions

HideShow timer Statistics In the figure above, lines k1 and k2 are parallel to each other, lines l1 and l2 are parallel to each other, and line m passes through the intersection points of k1 with l1 and k2 with l2. What is the value of x?

(1) x = 3z – y
(2) (y – z)^2 = 225

Attachment: 2015-06-02_1757.png [ 24.92 KiB | Viewed 4171 times ]

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In the figure above, lines k1 and k2 are parallel to each other, lines  [#permalink]

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[quote="Bunuel"] In the figure above, lines k1 and k2 are parallel to each other, lines l1 and l2 are parallel to each other, and line m passes through the intersection points of k1 with l1 and k2 with l2. What is the value of x?

(1) x = 3z – y
(2) (y – z)^2 = 225

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File comment: www.GMATinsight.com sol.jpg [ 260.43 KiB | Viewed 3502 times ]

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Originally posted by GMATinsight on 02 Jun 2015, 07:27.
Last edited by GMATinsight on 04 Jun 2015, 06:54, edited 1 time in total.
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Re: In the figure above, lines k1 and k2 are parallel to each other, lines  [#permalink]

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I think the answer is C. We can combine the parallel lines and will have X+Y+Z = 180
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Re: In the figure above, lines k1 and k2 are parallel to each other, lines  [#permalink]

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GMATinsight wrote:
Bunuel wrote: In the figure above, lines k1 and k2 are parallel to each other, lines l1 and l2 are parallel to each other, and line m passes through the intersection points of k1 with l1 and k2 with l2. What is the value of x?

(1) x = 3z – y
(2) (y – z)^2 = 225

Attachment:
2015-06-02_1757.png

GMAT Insight,

you mentioned (y-z)^2 = 225 => y-z = 15, I guess this is not correct, it should be y -z = 15 or y-z = -15

therefore after combining st 1 and st2 ,we will have two answers, So final answer is E.
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Re: In the figure above, lines k1 and k2 are parallel to each other, lines  [#permalink]

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viksingh15 wrote:
GMATinsight wrote:
Bunuel wrote: In the figure above, lines k1 and k2 are parallel to each other, lines l1 and l2 are parallel to each other, and line m passes through the intersection points of k1 with l1 and k2 with l2. What is the value of x?

(1) x = 3z – y
(2) (y – z)^2 = 225

Attachment:
2015-06-02_1757.png

GMAT Insight,

you mentioned (y-z)^2 = 225 => y-z = 15, I guess this is not correct, it should be y -z = 15 or y-z = -15

therefore after combining st 1 and st2 ,we will have two answers, So final answer is E.

You are right. Correction Done. Thank you!
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Math Expert V
Joined: 02 Sep 2009
Posts: 58364
Re: In the figure above, lines k1 and k2 are parallel to each other, lines  [#permalink]

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1
1
Bunuel wrote: In the figure above, lines k1 and k2 are parallel to each other, lines l1 and l2 are parallel to each other, and line m passes through the intersection points of k1 with l1 and k2 with l2. What is the value of x?

(1) x = 3z – y
(2) (y – z)^2 = 225

Attachment:
The attachment 2015-06-02_1757.png is no longer available

MANHATTAN GMAT OFFICIAL SOLUTION:

Redraw the diagram and label as much as possible. Using the rules about a transversal (line m) intersecting parallel lines (in this case, two sets of parallel lines), we can label at least two more angles y° and z°: We have labeled three angles that form a straight line at the intersection of k1, l1, and m, so x + y + z = 180. Since x = 180 – (y + z), the rephrased question is “What is the value of x or the value of (y + z)?"

(1) INSUFFICIENT: Substitute x = 3z – y into x + y + z = 180 and simplify:
(3z – y) + y + z = 180
4z = 180
z = 45
This provides neither the value of x nor the value of (y + z).

(2) INSUFFICIENT: Simplify the expression.
(y – z)^2 = 225
(y – z) = –15 or 15, so |y – z| = 15.
This provides neither the value of x nor the value of (y + z).

(1) & (2) INSUFFICIENT: There are two solutions as indicated by the absolute value in (2):
y – z = 15: OR y – z = –15:
y = 15 + z OR y = –15 + z
y = 15 + 45 OR y = –15 + 45
y = 60 OR y = 30
y + z = 60 + 45 = 105 OR y + z = 30 + 45 = 75

The correct answer is E, because even with both statements, we cannot tell whether x = y + z = 75 or 105.

Attachment: 2015-06-08_1438.png [ 25.78 KiB | Viewed 3819 times ]

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Re: In the figure above, lines k1 and k2 are parallel to each other, lines  [#permalink]

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_________________ Re: In the figure above, lines k1 and k2 are parallel to each other, lines   [#permalink] 18 Jul 2019, 09:44
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