The value of x^y is how many times the value of [(x^y)(x^(y+1))(x^(y+2))(x^(y+3))]/x?
A. x^y
B. x^(4y+5)
C. x^(4y+6)
D. x^(-3y-5)
E. x^(-4y-5)
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dimochka
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When you're multiplying numbers with the same base and different exponents, you simply need to add all the exponents together. Similarly, dividing by a number with the same base means subtracting that exponent.
As such, the expression can be simplified to:
[(x^y)(x^(y+1))(x^(y+2))(x^(y+3))]/x = x^(y+y+1+y+2+y+3) / x^1 = x^(y+y+1+y+2+y+3-1) = x^(4y+5)
Notice that the question does not simply ask you to simplify the expression, but rather asking you to compare it in size to x^y
x^y / x^(4y+5) = x^(y-4y-5).
Simplify to get D as the answer.
As such, the expression can be simplified to:
[(x^y)(x^(y+1))(x^(y+2))(x^(y+3))]/x = x^(y+y+1+y+2+y+3) / x^1 = x^(y+y+1+y+2+y+3-1) = x^(4y+5)
Notice that the question does not simply ask you to simplify the expression, but rather asking you to compare it in size to x^y
x^y / x^(4y+5) = x^(y-4y-5).
Simplify to get D as the answer.
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GMATGuruNY
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Let x=2 and y=1.Rospino wrote:The value of x^y is how many times the value of [(x^y)(x^(y+1))(x^(y+2))(x^(y+3))]/x?
A. x^y
B. x^(4y+5)
C. x^(4y+6)
D. x^(-3y-5)
E. x^(-4y-5)
Then:
x^y = 2^1 = 2.
[(x^y)(x^(y+1))(x^(y+2))(x^(y+3))]/x = (2^1)(2^2)(2^3)(2^4)/2 = 2^9.
Dividing the two results, we get:
2/(2^9) = 2^(-8). This is our target.
Now we plug x=2 and y=1 into the answers to see which yields our target of 2^(-8).
A quick scan reveals that only answer choice D works:
x^(-3y-5) = 2^(-3*1 - 5) = 2^(-8).
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
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