[email protected] wrote:What's the difference between x/y>1 and x>y?
I thought the answer was " no difference"
But, according to GMAT Prep, there is a difference.
In x/y>1, both x & y have to be + or -.
But there is no such criteria in x>y.
I am still not convinced.
Do help!!
Regards,
mukherjee
When we multiply each side of an inequality by a NEGATIVE value, we must FLIP the direction of the inequality.
If x/y > 1 and y<0, then multiplying each side by y -- a negative value -- requires that we FLIP > to <:
x/y > 1
y * x/y < y * 1
x < y.
Since y<0, the following relationship is implied:
x < y < 0.
Examples for x and y:
x = -2 and y = -1, with the result that x/y = -2/-1 = 2.
x = -10 and y = -2, with the result that x/y = -10/-2 = 5.
And so on.
If x/y > 1 and y>0, then multiplying each side by y -- a positive value -- does NOT affect the direction of the inequality:
x/y > 1
y * x/y > y * 1
x > y.
Since y>0, the following relationship is implied:
x > y > 0.
Examples for x and y:
x = 2 and y = 1, with the result that x/y = 2/1 = 2.
x = 10 and y = 2, with the result that x/y = 10/2 = 5.
And so on.
Thus, x/y > 1 does NOT imply that x>y.
Rather, x/y > 1 implies that EITHER x>y>0 OR that x<y<0.
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