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

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Joined: 02 Sep 2009
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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
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (01:09) correct 19% (01:48) wrong based on 177 sessions

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Director
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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 07 Jun 2016, 07:44
1
(2x+y)*(2z+w) = 3+2(6) =15
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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 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
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:


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 &nbs [#permalink] 21 Oct 2017, 21:09
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