22. Is xy < 1?
(1) x + y = 1
(2) x^2 + y^2 = 1
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vipulgoyal
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srcc25anu
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St1: x+y=1
Case 1: x = 1, y = 0 x+y = 1 and xy = 0; Is XY < 1? Yes
Case 2: x = 0.8, y = 0.2 x+y = 1 and xy = .16; Is XY < 1? Yes
sufficient
St2: x^2 + y^2 = 1
x = 1, y = 0 x^2 + y^2 = 1 and xy = 0; Is XY < 1? Yes
x = 0.8, y = 0.6 x^2 + y^2 = 1 and xy = .48; Is XY < 1? Yes
sufficient
Hence D
Case 1: x = 1, y = 0 x+y = 1 and xy = 0; Is XY < 1? Yes
Case 2: x = 0.8, y = 0.2 x+y = 1 and xy = .16; Is XY < 1? Yes
sufficient
St2: x^2 + y^2 = 1
x = 1, y = 0 x^2 + y^2 = 1 and xy = 0; Is XY < 1? Yes
x = 0.8, y = 0.6 x^2 + y^2 = 1 and xy = .48; Is XY < 1? Yes
sufficient
Hence D
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GMATGuruNY
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If x + y = k, where k is a constant, then the greatest possible value of xy occurs when x=y.
Example: x + y = 10
If x=5 and y=5, then xy = 25.
If x=4 and y=6, then xy = 24.
If x=3 and y=7, then xy = 21.
As the distance between x and y INCREASES, the product of x and y DECREASES.
Thus, the greatest possible value of xy occurs when x=y=5.
Here, the greatest possible value of xy occurs when x = y = 1/2:
xy = (1/2)(1/2) = 1/4.
Thus, xy < 1.
SUFFICIENT.
Statement 2: x² + y² = 1
Here, the greatest possible value of x²y² occurs when x² = y² = 1/2:
x²y² = (1/2)(1/2)
(xy)² = (1/2)²
xy = 1/2.
Thus, xy < 1.
SUFFICIENT.
The correct answer is D.
Example: x + y = 10
If x=5 and y=5, then xy = 25.
If x=4 and y=6, then xy = 24.
If x=3 and y=7, then xy = 21.
As the distance between x and y INCREASES, the product of x and y DECREASES.
Thus, the greatest possible value of xy occurs when x=y=5.
Statement 1: x + y = 1vipulgoyal wrote:22. Is xy < 1?
(1) x + y = 1
(2) x^2 + y^2 = 1
Here, the greatest possible value of xy occurs when x = y = 1/2:
xy = (1/2)(1/2) = 1/4.
Thus, xy < 1.
SUFFICIENT.
Statement 2: x² + y² = 1
Here, the greatest possible value of x²y² occurs when x² = y² = 1/2:
x²y² = (1/2)(1/2)
(xy)² = (1/2)²
xy = 1/2.
Thus, xy < 1.
SUFFICIENT.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
