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# If 0 < x ≤ 1, then which one of the following is the maximum

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Manager
Joined: 27 Jul 2011
Posts: 58
If 0 < x ≤ 1, then which one of the following is the maximum  [#permalink]

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21 Nov 2013, 03:22
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Difficulty:

15% (low)

Question Stats:

76% (01:10) correct 24% (00:49) wrong based on 238 sessions

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If 0 < x ≤ 1, then which one of the following is the maximum value of (x – 1)^2 + x ?

(A) –2
(B) –1
(C) 0
(D) 1
(E) 2
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Joined: 02 Sep 2009
Posts: 47978
Re: If 0 < x ≤ 1, then which one of the following is the maximum  [#permalink]

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21 Nov 2013, 03:42
5
smartyman wrote:
If 0 < x ≤ 1, then which one of the following is the maximum value of (x – 1)^2 + x ?

(A) –2
(B) –1
(C) 0
(D) 1
(E) 2

If you cannot spot that the maximum value of (x – 1)^2 + x for 0 < x ≤ 1 is when x=1 --> (x – 1)^2 + x = 1 you can do the following:

Since 0 < x ≤ 1, then (x – 1)^2 + x is positive --> discard A, B and C.

For the same reason: (x – 1)^2 is a non-negative fraction less than 1.

Thus (x – 1)^2 + x = (non-negative fraction less than 1) + (0 < x ≤ 1) < 2. Discard E.

Only D is left.

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Re: If 0 < x ≤ 1, then which one of the following is the maximum  [#permalink]

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21 Nov 2013, 03:42
1
smartyman wrote:
If 0 < x ≤ 1, then which one of the following is the maximum value of (x – 1)^2 + x ?

(A) –2
(B) –1
(C) 0
(D) 1
(E) 2

As x is a positive entity, the sum of the given expression can never be negative or zero.Eliminate all except D and E.

There are many ways to ascertain the maximum value now.

For example,
The given expression results as$$x^2-x+1 \to x(x-1)+1$$

For x=1, we have the sum as 1

For 0< x<1, we have the expression as : 1-(a negative quantity)

Thus, maximum value is for x=1.

D.
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Re: If 0 < x ≤ 1, then which one of the following is the maximum  [#permalink]

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27 Jul 2014, 14:49
1
Bunuel wrote:
smartyman wrote:
If 0 < x ≤ 1, then which one of the following is the maximum value of (x – 1)^2 + x ?

(A) –2
(B) –1
(C) 0
(D) 1
(E) 2

If you cannot spot that the maximum value of (x – 1)^2 + x for 0 < x ≤ 1 is when x=1 --> (x – 1)^2 + x = 1 you can do the following:

Since 0 < x ≤ 1, then (x – 1)^2 + x is positive --> discard A, B and C.

For the same reason: (x – 1)^2 is a non-negative fraction less than 1.

Thus (x – 1)^2 + x = (non-negative fraction less than 1) + (0 < x ≤ 1) < 2. Discard E.

Only D is left.

I like the way you discard E. Thanks. +1 kudos
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Re: If 0 < x ≤ 1, then which one of the following is the maximum  [#permalink]

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31 Jul 2014, 00:49
1
Given that 0 < x ≤ 1

Placing value of x = 1 in the above equation:

$$(1-1)^2 + 1 = 1$$

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Re: If 0 < x ≤ 1, then which one of the following is the maximum  [#permalink]

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26 Sep 2017, 03:35
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If 0 < x ≤ 1, then which one of the following is the maximum &nbs [#permalink] 26 Sep 2017, 03:35
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