4) If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of the following is true?
A) x > y > z
B) y > x > z"¨
C) y > z > x"¨
D) z > y > x
E) z > x > y
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NeilWatson
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Compare x and y in terms of a COMMON POWER.NeilWatson wrote:4) If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of the following is true?
A) x > y > z
B) y > x > z"¨
C) y > z > x"¨
D) z > y > x
E) z > x > y
x³ = 25:
Thus:
(x³)² = 25²
x� = 625.
y� = 64:
Thus:
y² = 8
y² = 2³
(y²)³ = (2³)³
y� = 2�
y� = 512.
Since x� > y�, x > y.
Eliminate B, C and D.
Compare y and z in terms of a COMMON POWER.
y² = 2³:
Thus:
(y²)� = (2³)�
y¹� = 2¹�
y¹� = 2¹� * 2�
y¹� = 1024 * 32
y¹� ≈ 32000.
z� = 216:
Thus:
(z�)² = 216²
z¹� ≈ 40000.
Since z¹� > y¹�, z > y.
Eliminate A.
The correct answer is E.
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Hi NeilWatson,
This is something of a convoluted, layered "math" question, and you're not likely to see it on Test Day. It can be solved with comparative math though - instead of calculating the exact values of X, Y and Z, you can deduce which is bigger or smaller by pattern comparison.
First, let's do a quick estimation...
3^3 = 27
3^4 = 81
3^5 = 243
X^3 = 25, so X is a little less than 3
Y^4 = 64, so Y is a little less than 3 (or a little bigger than -3)
Z^5 = 216, so Z is a little less than 3
We're told that XY > 0, so we're forced to consider only the positive value of Y.
X, Y and Z are all pretty close to one another, so we have to look for something that will differentiate them (and help us to figure out which is bigger when we look at any 2 of them)
X^3 = (X)(X)(X) = 25
Y^4 = (Y)(Y)(Y)(Y) = 64
Since the values of X and Y are pretty close, multiplying by the "extra" Y is what turns 25 into 64.....
64/25 = about 2.5
This does NOT mean that Y = 2.5, but it DOES mean that Y MUST be farther away from 3 than X is.
So X > Y
Y^4 = (Y)(Y)(Y)(Y) = 64
Z^5 = (Z)(Z)(Z)(Z)(Z) = 216
The values of Y and Z are also pretty close, so multiplying by the "extra" Z is what turns 64 into 216....
216/64 = more than 3
This does NOT mean that Z is greater than 3, but it DOES mean that Z MUST be closer to 3 than Y is.
So Z > Y
From here, the answer choices provide us with a great way "out" of this question. Since Y is smaller than both X and Z, the only answer that makes sense is....E
GMAT assassins aren't born, they're made,
Rich
This is something of a convoluted, layered "math" question, and you're not likely to see it on Test Day. It can be solved with comparative math though - instead of calculating the exact values of X, Y and Z, you can deduce which is bigger or smaller by pattern comparison.
First, let's do a quick estimation...
3^3 = 27
3^4 = 81
3^5 = 243
X^3 = 25, so X is a little less than 3
Y^4 = 64, so Y is a little less than 3 (or a little bigger than -3)
Z^5 = 216, so Z is a little less than 3
We're told that XY > 0, so we're forced to consider only the positive value of Y.
X, Y and Z are all pretty close to one another, so we have to look for something that will differentiate them (and help us to figure out which is bigger when we look at any 2 of them)
X^3 = (X)(X)(X) = 25
Y^4 = (Y)(Y)(Y)(Y) = 64
Since the values of X and Y are pretty close, multiplying by the "extra" Y is what turns 25 into 64.....
64/25 = about 2.5
This does NOT mean that Y = 2.5, but it DOES mean that Y MUST be farther away from 3 than X is.
So X > Y
Y^4 = (Y)(Y)(Y)(Y) = 64
Z^5 = (Z)(Z)(Z)(Z)(Z) = 216
The values of Y and Z are also pretty close, so multiplying by the "extra" Z is what turns 64 into 216....
216/64 = more than 3
This does NOT mean that Z is greater than 3, but it DOES mean that Z MUST be closer to 3 than Y is.
So Z > Y
From here, the answer choices provide us with a great way "out" of this question. Since Y is smaller than both X and Z, the only answer that makes sense is....E
GMAT assassins aren't born, they're made,
Rich
