i simplified the equation given in question and came to the question asking me is f>0?cyrwr1 wrote:Given: f not equal to 1, is f^2/(f-1) > f ?
1) f is not an integer
2) f > 0
Please list your work and conclusion, I came to two answers.
cyrwr1 wrote:Hey Gokhra,
I had gotten E too but checked it a different way with rewriting it as:
is f^2> f^2-f ?
When you put in a positive >1, you get the result yes
when you put in a positive <1, you get the result yes too
say you use a 1/2, you would get is 1/4 > (1/4-1/2) ? and then have 1/4 > -1/4, that too is true.
so I am so confused about the solution. Unless my logic is incorrect, I cannot decide between choice B and E
Your logic is incorrect. This is not a valid way to rewrite the inequality. I assume you got this by multiplying both sides of the inequality by (f-1)? This is only valid for positive values of f-1. Remember that when you multiply both sides of an inequality by a negative number you have to flip the direction of the inequality sign. f-1 could represent a negative value also, so when you rewrite it this way, you are essentially assuming f-1 is positive, and then you lose information about what happens when f-1 is negative. You should generally avoid multiplying or dividing both sides of an inequality by a variable for this reason. Notice that in my solution, I avoided doing any multiplication or division across the inequality sign when I rewrote it. If you do that, you can be sure you are preserving all of the original solutions (and non-solutions).cyrwr1 wrote:Hey Gokhra,
I had gotten E too but checked it a different way with rewriting it as:
is f^2> f^2-f ?
Unless my logic is incorrect, I cannot decide between choice B and E
cyrwr1 wrote:Hey Gokhra,
I had gotten E too but checked it a different way with rewriting it as:
is f^2> f^2-f ?
When you put in a positive >1, you get the result yes
when you put in a positive <1, you get the result yes too
say you use a 1/2, you would get is 1/4 > (1/4-1/2) ? and then have 1/4 > -1/4, that too is true.
so I am so confused about the solution. Unless my logic is incorrect, I cannot decide between choice B and E
As always, a cool explanation. Thanks.GmatMathPro wrote:Your logic is incorrect. This is not a valid way to rewrite the inequality. I assume you got this by multiplying both sides of the inequality by (f-1)? This is only valid for positive values of f-1. Remember that when you multiply both sides of an inequality by a negative number you have to flip the direction of the inequality sign. f-1 could represent a negative value also, so when you rewrite it this way, you are essentially assuming f-1 is positive, and then you lose information about what happens when f-1 is negative. You should generally avoid multiplying or dividing both sides of an inequality by a variable for this reason. Notice that in my solution, I avoided doing any multiplication or division across the inequality sign when I rewrote it. If you do that, you can be sure you are preserving all of the original solutions (and non-solutions).cyrwr1 wrote:Hey Gokhra,
I had gotten E too but checked it a different way with rewriting it as:
is f^2> f^2-f ?
Unless my logic is incorrect, I cannot decide between choice B and E
You CAN do it by multiplying both sides by f-1, but you have to be careful. To do it, you would have to break it down into cases. First, assume that f-1 is positive, or f-1>0 or f>1, and multiply to get f^2>f^2-f, which simplifies to f>0, but we are assuming that f>1, so we cannot include the numbers from 0 to 1 in the solution set. For this case, the solution is f>1.
Now, let's assume f-1<0 or f<1. Now when we multiply by f-1 we have to reverse the inequality sign because we are multiplying both sides by a negative: f^2<f^2-f which simplifies to f<0. We are also assuming that f<1, so all f that satisfy f<0 AND f<1 will be in the solution set, which is just f<0.
Combining, we get f<0 or f>1 for our solution set.
