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If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (
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15 Feb 2021, 07:03
15 Feb 2021, 07:03
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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.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 9.
B. 12.
C. 15.
D. 16.
E. 18.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (
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15 Feb 2021, 07:26
15 Feb 2021, 07:26
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Carcass 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.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 9.
B. 12.
C. 15.
D. 16.
E. 18.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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: C
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Re: If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (
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15 Feb 2021, 07:32
15 Feb 2021, 07:32
Carcass 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.
A. 9.
B. 12.
C. 15.
D. 16.
E. 18.
\((2X + Y)(2Z + W) = 4XZ + 2XW + 2ZY + YW\)
Rearrange;
\((2X + Y)(2Z + W) = 4XZ + YW + 2(XW + ZY)\)
\((2X + Y)(2Z + W) = 3 + 2(6) = 15\)
Hence, option C
