Hi,
Got stuck by this.Pl help:
Q-Given that 2^x = 4^y = 8^z and xyz=288,what is the value of (1/2x)+(1/4y)+(1/8z).
A) 18/74
B) 18/96
C) 11/74
D) 11/96
OA is D.
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sandipgumtya
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Matt@VeritasPrep
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Let's start by simplifying the exponents.
2ˣ = 4ʸ = 8ᶻ
is really
2ˣ = (2²)ʸ = (2³)ᶻ
so
x = 2y = 3z
we also have
xyz = 288
Now just do substitution. Since x = 2y and z = (2/3)y, we have
xyz = 2y*y*(2/3)y = 288
That gives y = 6
From this, x = 12 and z = 4.
The sum at the end is 1/24 + 1/24 + 1/32, or 11/96.
2ˣ = 4ʸ = 8ᶻ
is really
2ˣ = (2²)ʸ = (2³)ᶻ
so
x = 2y = 3z
we also have
xyz = 288
Now just do substitution. Since x = 2y and z = (2/3)y, we have
xyz = 2y*y*(2/3)y = 288
That gives y = 6
From this, x = 12 and z = 4.
The sum at the end is 1/24 + 1/24 + 1/32, or 11/96.
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sandipgumtya
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GMATGuruNY
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The problem should read as follows:
In this case, x=6, y=3 and z=2.
Implication:
x:y:z = 6:3:2.
Test multiples of this ratio until a product of 288 is yielded:
6*3*2 = 36.
12*6*4 = 288.
The option in red works.
Since x=12, y=6, and z=4, we get:
1/(2x) + 1/(4y) + 1/(8z) = 1/24 + 1/24 + 1/32 = 4/96 + 4/96 + 3/96 = 11/96.
The correct answer is D.
Let 2ˣ = 4ʸ = 8ᶻ = 64.If 2ˣ = 4ʸ = 8ᶻ and xyz=288, what is the value of 1/(2x) + 1/(4y) + 1/(8z)?
A) 18/74
B) 18/96
C) 11/74
D) 11/96
In this case, x=6, y=3 and z=2.
Implication:
x:y:z = 6:3:2.
Test multiples of this ratio until a product of 288 is yielded:
6*3*2 = 36.
12*6*4 = 288.
The option in red works.
Since x=12, y=6, and z=4, we get:
1/(2x) + 1/(4y) + 1/(8z) = 1/24 + 1/24 + 1/32 = 4/96 + 4/96 + 3/96 = 11/96.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
