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Source: — Problem Solving |

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by Brent@GMATPrepNow » Fri Aug 10, 2012 8:42 am
shanice wrote:If y=4+(x-3)^2, then y is least when x

A)14
B)13
C)0
D)3
E)4

Answer is D.

I don't understand what the question is asking. Can someone explain, please?
We want to minimize the value of 4+(x-3)^2
To do this, we need to minimize the value of (x-3)^2
Notice that (any number)^2 > 0
So, the smallest value possible of (any number)^2 is 0

(x-3)^2 = 0 when x=3.
So, the value of 4+(x-3)^2 is minimized when x=3.

Answer = D

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Brent

PS: Be sure to use the Spoiler function to hide the correct answer so that others can try answering the question without seeing the answer.
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by GMATGuruNY » Fri Aug 10, 2012 8:48 am
shanice wrote:If y=4+(x-3)^2, then y is least when x

A)14
B)13
C)0
D)3
E)4

Answer is D.

I don't understand what the question is asking. Can someone explain, please?
To MINIMIZE y, we must MINIMIZE the value of 4 + (x-3)².
Since the square of a value cannot be negative, the least possible value of (x-3)² is 0.
(x-3)² = 0 when x=3.
Thus, y will be its least possible value when x=3:
y = 4 + (x-3)² = 4 + (3-3)² = 4.
If x is any value other than 3, the value of y will INCREASE.

The correct answer is D.
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by truplayer256 » Fri Aug 10, 2012 9:37 am
y = 4 + (x - 3)^2

Note that y is always going to increase or stay the same no matter what since (x - 3)^2 is ALWAYS going to be positive. Therefore, the only obvious choice for the least value of y is 4 and this occurs when x = 3.

If you have taken calculus before, you can also use differentiation to come up with your answer:

dy/dx = 2(x - 3) = 0 => x = 3
This means that a minimum occurs when x = 3.

The best choice is D.
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