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26 Jan 2019, 12:33
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2y - x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?
(A) 2
(B) 1
(C) 0
(D) -1
(E) - 2
I understand how to get to the answer (D) but I can't figure out how to simplify the equation and feel like I am missing something. anyone know how to simplify 2y - x = 2xy into x in terms of y and can explain the steps? Thanks!
(A) 2
(B) 1
(C) 0
(D) -1
(E) - 2
I understand how to get to the answer (D) but I can't figure out how to simplify the equation and feel like I am missing something. anyone know how to simplify 2y - x = 2xy into x in terms of y and can explain the steps? Thanks!
26 Jan 2019, 12:53
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Hi HanktheTank,
We're given three pieces of information to work with:
1) 2Y - X = 2(X)(Y)
2) X ≠ 0
3) X and Y are both INTEGERS
We're asked which of the following could equal Y. You can approach this question in a number of different ways. Here's how you can put X in terms of Y:
2Y - X = 2(X)(Y)
To start, let's put all the Xs on the 'right side':
2Y = 2(X)(Y) + X
Next, factor out the X:
2Y = (X)(2Y + 1)
Now, isolate the X:
(2Y)/(2Y+1) = X
At this point, we can compare the 5 answer choices to this equation (try plugging each value in for Y and solve). Remember that X CANNOT be 0 and BOTH X and Y must be INTEGERS. Only one of the 5 answer choices will fit all of those restrictions.
GMAT assassins aren't born, they're made,
Rich
We're given three pieces of information to work with:
1) 2Y - X = 2(X)(Y)
2) X ≠ 0
3) X and Y are both INTEGERS
We're asked which of the following could equal Y. You can approach this question in a number of different ways. Here's how you can put X in terms of Y:
2Y - X = 2(X)(Y)
To start, let's put all the Xs on the 'right side':
2Y = 2(X)(Y) + X
Next, factor out the X:
2Y = (X)(2Y + 1)
Now, isolate the X:
(2Y)/(2Y+1) = X
At this point, we can compare the 5 answer choices to this equation (try plugging each value in for Y and solve). Remember that X CANNOT be 0 and BOTH X and Y must be INTEGERS. Only one of the 5 answer choices will fit all of those restrictions.
GMAT assassins aren't born, they're made,
Rich
26 Jan 2019, 13:02
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It can be written as
x = 2y /(2y+1)
Then I think its fairly easy to sub y and see what gives an integer for x.
x = 2y /(2y+1)
Then I think its fairly easy to sub y and see what gives an integer for x.
