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If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression

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If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression [#permalink]

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New post 07 Jun 2016, 07:30
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4
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:10) correct 20% (01:59) wrong based on 143 sessions

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Kudos [?]: 132782 [0], given: 12372

Senior Manager
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Joined: 20 Feb 2015
Posts: 388

Kudos [?]: 106 [0], given: 10

Concentration: Strategy, General Management
Re: If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression [#permalink]

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New post 07 Jun 2016, 07:44
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(2x+y)*(2z+w) = 3+2(6) =15

Kudos [?]: 106 [0], given: 10

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Kudos [?]: 78 [0], given: 13

Location: United States
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WE: Information Technology (Computer Software)
Re: If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression [#permalink]

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New post 07 Jun 2016, 08:06
(2X + Y)(2Z + W) = 4XZ + YW + 2XW + 2YZ = 4XZ + YW + 2(XW + YZ) = 3 + 2*6 = 15. Hence C.

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Re: If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression [#permalink]

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New post 15 Jun 2016, 12:25
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Top Contributor
Bunuel wrote:
If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)?

A. 9.
B. 12.
C. 15.
D. 16.
E. 18.


We want the value of (2X + Y)(2Z + W)
Expand this to get: (2X + Y)(2Z + W) = 4XZ + 2XW + 2YZ + YW
= 4XZ + YW + 2XW + 2YZ [I rearranged the terms]
= 3 + 2XW + 2YZ [replaced 4XZ + YW with 3]
= 3 + 2(XW + YZ) factored out a 2
= 3 + 2(6)
= 3 + 12
= 15

Answer:
[Reveal] Spoiler:
C



Related Resource
Here's a video explaining the FOIL method for expanding the product of two binomials:

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Re: If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression [#permalink]

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New post 21 Oct 2017, 21:09
Bunuel wrote:
If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)?

A. 9.
B. 12.
C. 15.
D. 16.
E. 18.


(2X + Y)(2Z + W) = 4XZ + 2ZY + 2WX + WY
= 4XZ + YW + 2(XW + YZ)
= 3 + 2*6
= 15

Answer C
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Re: If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression   [#permalink] 21 Oct 2017, 21:09
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If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression

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