Problem Solving

If 0.02<x<0.1 and 1000<y<10,000, which of the following could be the value of (y-x)/xy?

(A) 1.5
(B) 15
(C) 150
(D) 1,500
(E) 15,000

aj5105 wrote:If 0.02<x<0.1 and 1000<y<10,000, which of the following could be the value of (y-x)/xy?

(A) 1.5
(B) 15
(C) 150
(D) 1,500
(E) 15,000

The maximum value x -y can take is when x is max and y is min. Take x =10000 and y = .02
x -y=9999.98

For denominator make x and y the smallest

.02 x 1000=20

20
9999.98/20< 50. ( At this point I would choose B on the real GMAT test since 1.5 is too far away)

to test 1.5 make y-x smallest and xy biggest

1000-.1=999.9/9999.999 x .1= 999.9/9999.99< 1. (This confirms my instinct.

Choose B

This is how I solved.

I split (y - x) / xy as 1/x - 1/y.

I found the maximum value and the minimum value. After rounding the decimals I got the range 1 to 50. [spoiler](B) [/spoiler] is the only number in that range.

aj5105 wrote:If 0.02<x<0.1 and 1000<y<10,000, which of the following could be the value of (y-x)/xy?

(A) 1.5
(B) 15
(C) 150
(D) 1,500
(E) 15,000

(y-x)/xy
= y/xy - x/xy
= 1/x - 1/y

0.02 < x < 0.1, so the range for 1/x will be:

1/0.1 < 1/x < 1/0.02
10 < 1/x < 50

1000<y<10,000, so the range for 1/y will be:

1/10,000 < 1/y < 1/1000
0.0001 < 1/y < 0.001

since the possible values for 1/y is so much more smaller than 1/x, we can safely approximate the following:

1/x - 1/y &#8776; 1/x

therefore, the range for (1/x - 1/y) is approximately 10 < 1/x - 1/y < 50. looking through the answer choices, only choice B fits within this range.

-BM-

smart solution as always. thanks BM

i guess fastest wud be wht AJ mentioned...i solved in the same way in less than 30 sec

to get the constraints take min of x and max of y and visa-versa.

we get the range as

10< (y-x/xy ) < 50

Thus B