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# For which values of x is the following inequality true: x^2 < 2x.

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Math Expert
Joined: 02 Sep 2009
Posts: 55148
For which values of x is the following inequality true: x^2 < 2x.  [#permalink]

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17 Apr 2019, 22:07
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Difficulty:

25% (medium)

Question Stats:

69% (01:12) correct 31% (00:56) wrong based on 26 sessions

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For which values of x is the following inequality true: x^2 < 2x.

(A) x < 0
(B) 0 < x < 2
(C) –2 < x < 2
(D) x < 2
(E) x > 2

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Re: For which values of x is the following inequality true: x^2 < 2x.  [#permalink]

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18 Apr 2019, 12:25
Bunuel wrote:
For which values of x is the following inequality true: x^2 < 2x.

(A) x < 0
(B) 0 < x < 2
(C) –2 < x < 2
(D) x < 2
(E) x > 2

x^2 < 2x
x(x-2)<1
x<1 and x<2
IMO range falls under 0 < x < 2
IMO B
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Joined: 24 Jun 2018
Posts: 34
Re: For which values of x is the following inequality true: x^2 < 2x.  [#permalink]

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18 Apr 2019, 15:50
Bunuel wrote:
For which values of x is the following inequality true: x^2 < 2x.

(A) x < 0
(B) 0 < x < 2
(C) –2 < x < 2
(D) x < 2
(E) x > 2

Looking at the options in the question, it is easy to use options rather than solve the problem:

A) x<0

Let x=-3
Then we get 9<-6. Not good.

Let x =-2
We get, 4<-4. Not good.

B) 0 < x < 2

Let x = 1
We get, 1<2. Good

C) –2 < x < 2
Let x =-1
We get, 1<-2. Not good

D) x<2

In the above options, we already tried for x<2 and see that inequality holds good for until x is between 0 & 2 but less than 0, it doesnt hold good.

E) x>2

Let x =3
Then 9<6. Not good.

Hence option B
Re: For which values of x is the following inequality true: x^2 < 2x.   [#permalink] 18 Apr 2019, 15:50
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