Substitute y =
I. 1/(2x)
II. – 2/x
III. 3/x
in the x^2y^2 - xy equation.
Only II and II will equal 6
I) 1/2x
x^2 * (1/2x)^2 - x*1/2x is not equal to 6
II) – 2/x
X^2 ( -2/X)^2 - X (-2/X)
= 4+2
=6
Could be true
III) 3/x
X^2 (3/X)^2 - X * 3/X
= 9 - 3
=6
COULD BE TRUE
Hence E)
Question 11 (nov. 14th)
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Source: Beat The GMAT — Problem Solving |
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jaybrium
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My technique for this problem, wasn't the best, but it lead me to the correct answer:
x^2y^2-xy = 6
you can factor out xy, therefore:
xy(xy-1) = 6
xy has to be an integer, so the product of a certain integer and that integer minus 1 = 6, so I figured the intgers could be 3 and 2
so
X = 3; y=1
or
x=1; y=3
from here I just plugged in X into the options:
I. 1/(2x) = 1/6 or 1/3; no good- eliminate A, C, & D
** only B & E remain, II must work
III. 3/x = 1 or 3, this works- choose E
If my post causes more harm than, good I apologize. Once I realized that I couldn't simply isolate y, I realized this problem had a solution that wasn't intuitive to me, so I tried the best I could and it worked (in under two minutes). I think that's the moral of my story.
Naturally Cramya has an great solution- use hers for this type of problem
Thanks Cramya!
x^2y^2-xy = 6
you can factor out xy, therefore:
xy(xy-1) = 6
xy has to be an integer, so the product of a certain integer and that integer minus 1 = 6, so I figured the intgers could be 3 and 2
so
X = 3; y=1
or
x=1; y=3
from here I just plugged in X into the options:
I. 1/(2x) = 1/6 or 1/3; no good- eliminate A, C, & D
** only B & E remain, II must work
III. 3/x = 1 or 3, this works- choose E
If my post causes more harm than, good I apologize. Once I realized that I couldn't simply isolate y, I realized this problem had a solution that wasn't intuitive to me, so I tried the best I could and it worked (in under two minutes). I think that's the moral of my story.
Naturally Cramya has an great solution- use hers for this type of problem
Thanks Cramya!- Jay
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iamcste
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Perfect ! I just wanted to do this...dmateer25 wrote:x^2 y^2 - xy = 6
xy(xy - 1) = 6
xy=3 or xy=-2 because these are only two possible solutions to the equation
so y=3/x and y=-2/x
E
I am sure you got xy=3 and xy=-2 from options right
