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# For what value of x between -1 and 5

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Retired Moderator
Joined: 27 May 2014
Posts: 525
GMAT 1: 730 Q49 V41
For what value of x between -1 and 5  [#permalink]

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09 Oct 2017, 09:29
1
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:30) correct 32% (01:13) wrong based on 139 sessions

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For what value of x between -1 and 5 inclusive, is the value x^2 - 7x + 10 the smallest?

(A) -1
(B) 0
(C) 2
(D) 3
(E) 5

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For what value of x between -1 and 5  [#permalink]

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09 Oct 2017, 09:37
saswata4s wrote:
For what value of x between -1 and 5 inclusive, is the value x^2 - 7x + 10 the smallest?

(A) -1
(B) 0
(C) 2
(D) 3
(E) 5

$$x^2 - 7x + 10 = (x-5)(x-2)$$

For option A, B, C & E, this equation is either positive or 0. For Option D the equation is negative and hence the lowest

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Re: For what value of x between -1 and 5  [#permalink]

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09 Oct 2017, 09:46
Answer D. The equation gets simplified as (x-5)(x-2). So at 2&5, the equation is 0 so C & E options are out. Only for option D will the value be less than 0.

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Re: For what value of x between -1 and 5  [#permalink]

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12 Oct 2017, 17:14
saswata4s wrote:
For what value of x between -1 and 5 inclusive, is the value x^2 - 7x + 10 the smallest?

(A) -1
(B) 0
(C) 2
(D) 3
(E) 5

Let’s factor the given equation:

(x - 5)(x - 2)

We see that when x is 5 or 2, one of the factors will be 0; thus, the value of the expression is 0.

When x is -1 or 0, both factors will be negative, and thus the value of the expression is positive.

Finally, when x is 3, one factor is positive while the other is negative, and thus the value of the expression is negative.

We see, then, that the value of the expression is smallest when x = 3.

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Re: For what value of x between -1 and 5  [#permalink]

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12 Oct 2017, 17:35
$$x^2$$-7x+2= (x-5)(x-2)

Put A in the above equation: (-1-5)(-1-2)= 18
Put B in the above equation: (0-5)(0-2)= 10
Put C in the above equation: (2-5)(2-2)= 0
Put D in the above equation: (3-5)(3-2)= -2 (Smallest Value)
Put E in the above equation: (5-5)(5-2)= 0

Kudos please if you like my explanation!

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Re: For what value of x between -1 and 5  [#permalink]

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13 Oct 2017, 00:45
2
saswata4s wrote:
For what value of x between -1 and 5 inclusive, is the value x^2 - 7x + 10 the smallest?

(A) -1
(B) 0
(C) 2
(D) 3
(E) 5

Note that the given expression is a quadratic and its graph will be an upward facing parabola. So the minimum will be at x = -b/2a.
x = -(-7)/2*1 = 3.5
Of the given options, 3 is closest to 3.5 so that is where the expression will be minimum.
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Re: For what value of x between -1 and 5 &nbs [#permalink] 13 Oct 2017, 00:45
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