If 0<x<y, is y-x < 0.00005

[massi2884]

If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000

I can't find the solution because I transform 1/60,000 into 1/6x10^5, which I transform into 6^10^-5. Can you tell me where I'm wrong? OA is C. Thanks

Source: GMATPrep Question Pack 1

[mathbyvemuri]

If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000

first consider statement-2:
y<1/15,000 => y - 1/60,000 < 1/15,000 - 1/60,000
from statement-1, as x>1/60,000,
y-x < 1/15,000 - 1/60,000
=> y-x < 1/15,000 (1-1/4)
=> y-x < 1/15,000 (3/4)
=> y-x < 1/20,000
=> y-x < 1/2 * 10^(-4)
=> y-x < 0.00005
=> y-x is definitely less than 0.0005 as 0.0005 is greater than 0.00005
As both statements are used, answer is C

[massi2884]

Hi, thanks for your reply. However, I don't understand your last sentence: "y-x is definitely less than 0.0005 as 0.0005 is greater than 0.00005".
Isn't y-x < 0.00005 already what we were looking for?
Thanks.

[Anurag@Gurome]

If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000

I can't find the solution because I transform 1/60,000 into 1/6x10^5, which I transform into 6^10^-5. Can you tell me where I'm wrong? OA is C. Thanks

Source: GMATPrep Question Pack 1

0.00005 = 5/100000 = (5 * 6)/(6 * 100000) = 3/60,000
1/15000 = 4/(4 * 15000) = 4/60,000

(1) x > (1/60,000)
If x = 2/60,000 and y = 3/60,000, then y - x = 3/60,000 - 2/60,000 = 1/60,000 < 0.00005
If x = 2/60,000 and y = 5/60,000, then y - x = 5/60,000 - 2/60,000 = 3/60,000 = 0.00005
No definite answer; NOT sufficient.

(2) y < 1/15,000
If x = 2/60,000 and y = 3/60,000, then y - x = 3/60,000 - 2/60,000 = 1/60,000 < 0.00005
If x = 1/1,20,000 and y = 7/1,20,000, then y - x = 7/1,20,000- 1/1,20,000 = 6/1,20,000 = 3/60,000 = 0.00005
No definite answer; NOT sufficient.

Combining (1) and (2), x > 1/60,000 and y < 1/15,000
OR -x < -1/60,000 and y < 1/15,000
Now the inequalities are in the same direction, so we can add them to get the range of y - x.
y - x < (1/15,000 - 1/60,000)
y - x < 3/60,000
y - x < 0.00005; SUFFICIENT.

The correct answer is C.

[mathbyvemuri]

Hi, thanks for your reply. However, I don't understand your last sentence: "y-x is definitely less than 0.0005 as 0.0005 is greater than 0.00005".
Isn't y-x < 0.00005 already what we were looking for?
Thanks.

It's a simple logic: If x < 10, we can definitely say that x < 20 as well.
Similarly, as we got here that, y-x < 0.00005, it's sure that y-x < 0.0005

[Stuart@KaplanGMAT]

If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000

I can't find the solution because I transform 1/60,000 into 1/6x10^5, which I transform into 6^10^-5. Can you tell me where I'm wrong? OA is C. Thanks

Source: GMATPrep Question Pack 1

Sometimes brute force is the key to happiness on the GMAT.

(1) doesn't give us any information about the upper boundary of y, so there's no way it's sufficient by itself: eliminate A and D.

(2) gives us an upper boundary on y AND we already know that x > 0, so it's actually possible that (2) is sufficient alone. Time to pick up your pencil and do some long division!

1/15000 = 1 divided by 15000 = .00006666 (and so on...)

Since x must be greater than 0, we know that y - x is less than .000066 - 0 or:

y - x < .000066. Could it be less than .00005? YES. Could it be greater than .00005? YES. Accordingly, (2) is insufficient: eliminate B.

Since we need to combine, let's calculate the limit on x:

1/60000 = 1 divided by 60000 = .0000166 (6s going on forever).

To get the limit on the biggest possible value of y-x, we choose the biggest possible y and the smallest possible x, i.e. y=.000066 and x=.000016. Since .000066 - .000016 = .00005, y-x MUST be less than .00005. Together sufficient, choose C!

The quicker you can do the long division, the quicker you can answer the question (I brute forced it in about 75 seconds).