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# On segment WZ above, if WY = 21, XZ = 26, and YZ is twice WX, what is

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Math Expert
Joined: 02 Sep 2009
Posts: 56267
On segment WZ above, if WY = 21, XZ = 26, and YZ is twice WX, what is  [#permalink]

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12 Jul 2017, 23:40
1
5
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:17) correct 30% (02:16) wrong based on 125 sessions

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On segment WZ above, if WY = 21, XZ = 26, and YZ is twice WX, what is the value of XY?

(A) 5
(B) 10
(C) 11
(D) 16
(E) It cannot be determined from the information given

Attachment:

2017-07-13_1039.png [ 2.7 KiB | Viewed 2775 times ]

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Re: On segment WZ above, if WY = 21, XZ = 26, and YZ is twice WX, what is  [#permalink]

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13 Jul 2017, 00:56
1
Let WX = a, XY = b, YZ = c
So, we have to find the value of b.

From the diagram given in the question stem, we can deduce the following information :
a+b = 21
b+c = 26
c = 2a

Substituting this value of c in the equation, we will get the following equations
2a + b = 26
a + b = 21
Solving for a = 5.

From this information, we can say b=16(Option D)
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Re: On segment WZ above, if WY = 21, XZ = 26, and YZ is twice WX, what is  [#permalink]

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13 Jul 2017, 00:58
Bunuel wrote:

On segment WZ above, if WY = 21, XZ = 26, and YZ is twice WX, what is the value of XY?

(A) 5
(B) 10
(C) 11
(D) 16
(E) It cannot be determined from the information given

Attachment:
2017-07-13_1039.png

Let WX = p
So, YZ = 2p
Let xy = q

WY = p+q = 21
XZ = q +2p = 26
Solving from 2 equations above we get p = 5,
q = 16 = XY

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On segment WZ above, if WY = 21, XZ = 26, and YZ is twice WX, what is  [#permalink]

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13 Jul 2017, 09:31
1
Bunuel wrote:

On segment WZ above, if WY = 21, XZ = 26, and YZ is twice WX, what is the value of XY?

(A) 5
(B) 10
(C) 11
(D) 16
(E) It cannot be determined from the information given

Attachment:
2017-07-13_1039.png

$$\frac{YZ}{WX}$$ = $$\frac{2}{1}$$. Let WX = x, thus YZ =2x

W__x__X__________________Y____2x____Z

Once written this way, scrutinize XY for a relationship to some given value(s) and for XY's relationship to the other two segments.

XY + YZ = XZ
XY + WX = WY

We have values and variables for all of them except XY. We have WY = 21, XZ = 26, WX = x, and YZ = 2x. Substitute in equations above, then subtract lower from upper.

XY + 2x = 26
XY + x = 21
----->x = 5

We have x = 5. To find XY, just use x = 5 in either equation.

XY + 5 = 21
XY = 16

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Re: On segment WZ above, if WY = 21, XZ = 26, and YZ is twice WX, what is  [#permalink]

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16 Aug 2018, 12:54
2WX+XY=26
2WX+2XY=42 (Twice of WX+XY=21)
So, XY=16

Re: On segment WZ above, if WY = 21, XZ = 26, and YZ is twice WX, what is   [#permalink] 16 Aug 2018, 12:54
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