If x and y are positive integers such that their sum is a CONSTANT:
The GREATEST possible value of xy will be yielded when x and y are AS CLOSE TO EACH OTHER AS POSSIBLE.
The LEAST possible value of xy will be yielded when x and y are AS FAR FROM EACH OTHER AS POSSIBLE.
Given x+y=100, where x and y are positive integers:
Greatest option for xy = 50*50 = 2500
Least option for xy = 1*99 = 99
In short:
To MAXIMIZE the product, MINIMIZE the difference.
To MINIMIZE the product, MAXIMIZE the difference.
Bunuel wrote:
A rectangle with integer side lengths has perimeter 10. What is the greatest number of these rectangles that can be cut from a piece of paper with width 24 and length 60?
A. 144
B. 180
C. 240
D. 360
E. 480
A rectangle with integer side lengths has perimeter 10:2L + 2W = 10
L+W = 5
What is the greatest number of these rectangles that can be cut from a piece of paper with width 24 and length 60?To maximize the number of rectangles, we must minimize the value of LW -- the area of each rectangle.
As noted above:
To minimize the product of L and W, we must maximize the difference between L and W, as follows:
L=4, W=1, area = 4*1 = 4
Thus:
Greatest number of rectangles \(= \frac{paper-area}{rectangle-area} = \frac{24*60}{4} = 360\)
_________________
GMAT and GRE Tutor for over 20 years
Recent success stories for my students:admissions into Booth, Kellogg, HBS, Wharton, Tuck, Fuqua, Emory and others.
Available for live sessions in NYC and remotely all over the world
For more information, please email me at GMATGuruNY at gmail