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Math Expert V
Joined: 02 Sep 2009
Posts: 58312
A positive number x has the property that x% of x is 4. What is x?  [#permalink]

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A positive number x has the property that x% of x is 4. What is x?

(A) 2
(B) 4
(C) 10
(D) 20
(E) 40

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Location: India
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Re: A positive number x has the property that x% of x is 4. What is x?  [#permalink]

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Bunuel wrote:
A positive number x has the property that x% of x is 4. What is x?

(A) 2
(B) 4
(C) 10
(D) 20
(E) 40

given
x/100 * x =4
or say
x^2 = 4*100
x = 2* 10
x= 20
IMO D
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4000
Re: A positive number x has the property that x% of x is 4. What is x?  [#permalink]

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Top Contributor
Bunuel wrote:
A positive number x has the property that x% of x is 4. What is x?

(A) 2
(B) 4
(C) 10
(D) 20
(E) 40

APPROACH #1: Algebra
Given: x% of x is 4
Rewrite as: x/100 of x = 4
Rewrite as: (x/100)(x) = 4
Simplify: x²/100 = 4
Multiply both sides by 100 to get: x² = 400
So, EITHER x = 20 OR x = -20

We're told that x is POSITIVE, so x must be 20

APPROACH #2: Test answer choices
A) Does 2% of 2 = 4? No, 2% of 2 will be less than 2
B) Does 4% of 4 = 4? No, 4% of 4 will be less than 4
C) Does 10% of 10 = 4? No, 10% of 10 = 1
D) Does 20% of 20 = 4? YES!

Cheers,
Brent
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Re: A positive number x has the property that x% of x is 4. What is x?  [#permalink]

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Bunuel wrote:
A positive number x has the property that x% of x is 4. What is x?

(A) 2
(B) 4
(C) 10
(D) 20
(E) 40

Just as we can express 25% as 25/100, we can express x% as x/100. In the phrase “x% of x is 4,” we recall that the word “of” means multiply and “is” means equals. Thus, we can create the equation:

(x/100)(x) = 4

x^2 = 400

x = 20

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: A positive number x has the property that x% of x is 4. What is x?   [#permalink] 27 Mar 2019, 19:01
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