Max@Math Revolution wrote:[GMAT math practice question]
If 0.02 < x < 0.04 and 100 < y < 250, which of the following could be the value of (y-x)/(xy)?
A. 10
B. 20
C. 30
D. 50
E. 100
We can use a nice (and often tested) fraction property that says:
(a - b)/c = a/c - bc
So, (y-x)/(xy) = y/xy - x/xy
=
1/x - 1/y
That's better!
So, we're now looking for a possible value of
1/x - 1/y
Let's look at some EXTREME values.
We can MAXIMIZE the value of
1/x - 1/y by MAXIMIZING the value of 1/x , and MINIMIZING the value of 1/y
1/x is maximized when the value of
x is a small as possible
We're told that 0.02 < x < 0.04, so the smallest value of x is just a tiny bit bigger than 0.02
To make things easier on ourselves, let's see what happens when x = 0.02
ASIDE: 0.02 = 1/50
When x = 0.02, we see that 1/x =1/0.02 = 1/(1/50) =
50
Conversely, 1/y is minimized when the value of
y is a big as possible
We're told that 100 < y < 250, so the biggest value of y is just a tiny bit less than 250
To make things easier on ourselves, let's see what happens when y = 250
We get: 1/y = 1/250 =
0.004
So, the MAXIMUM value of
1/x - 1/y =
50 -
0.004 =
49.996
So, b]1/x - 1/y[/b] must be LESS THAN
49.996
At this point, we can see that the correct answer must be C.
How do we know this?
We already know that the MAXIMUM value
1/x - 1/y is approximately
49.996
IF we were to also find the MINIMUM value of
1/x - 1/y, then we'd have a range of possible values for
1/x - 1/y
The range would look like this:
some smaller value <
1/x - 1/y <
49.996
Since there can be only 1 correct answer, the correct answer must be biggest value that is less than
49.996
Answer: C
Cheers,
Brent
