J = x rounded to the nearest TENTH, and K = x

Question

J = x rounded to the nearest TENTH, and K = x rounded to the nearest THOUSANDTH. If 0 < x < 1, what is the greatest possible value of J – K?

A) 0.005
B) 0.0055
C) 0.05
D) 0.0505
E) 0.0555

GMATGuruNY · Accepted Answer

Since J = x rounded to the nearest tenth, J = 0.a (where a is a digit 0-9).
Since K = x rounded to the nearest thousandth,  K = 0.bcd  (where b, c and d are any digits 0-9).
The value of K implies that J-K can have at most three digits to the right of the decimal.
Eliminate B, D and E.

To maximize J-K, we want x to round UP to the nearest tenth (so that J is as big as possible) but round DOWN to the nearest thousandth (so that K is as small as possible).
One option:
x = 0.0501. with the result that J = 0.1 and K = 0.050.
In this case, J-K = 0.1 - 0.05 = 0.05.
Since option C can be the value of J-K, eliminate A, which is smaller.

C

pushpitkc · Answer

Hi  chandra004

The difference between an integer(x) rounded to its nearest tenth and thousandth must be maximum. 
Also, the integer(x) needs to be in between 0 & 1. For this to be true, the tenth must be the maximum 
possible (which is 0.9**) & thousandth must be the minimum possible(which is be 0.**0)

Therefore, the integer x has to be 0.850. The reason the hundredth' digit is 5 as we need the maximum difference.

Hope this helps you!

pushpitkc · Answer

Since 0 < x < 1, x = 0.8502(Since we need the greatest possible value of J - K)

When x is rounded to the nearest tenth, we will get 0.9(which is the value of J)
When x is rounded to the nearest thousandth, we will get 0.850(which is the value of K)

Therefore, the greatest possible difference between J and K is 0.900 - 0.850 =  0.05(Option C)

chandra004 · Answer

Hello  pushpitkc 
I didn't understand your solution. How did you choose x as 0.8502. Please elaborate.

Kem12 · Answer

Hi
I agree that J should be 0.9 but I'm still not clear about K... Why Can't K be 0.001 if K is rounded up to the nearest thousandth? 0.850 seems rounded up to the nearest hundredth to me since it has zero in the thousandth place. Could you please help me out here. I'm confused.

Posted from my mobile device

laknaouiwarda1 · Answer

i didn't understand the solution, please explain more. thank you

srishti246 · Answer

The greatest possible value of J-K is when J = x is considered to be the highest possible number between 0 and 1 i.e. 0.9 (rounded to the nearest 10th) and when K = x is considered to be the lowest possible number between 0 and 1 i.e. 0.001 (rounded to the nearest 1000th). This gives as J-K = 0.899. This tells us two things:

1. There can be a maximum of three digits to the right of the decimal.
2. Max possible value of the difference is 0.899. So the real difference in the options can be any number less or equal to 0.899

Let's eliminate the options now. B, D, and E have more than 3 digits to the right of the decimal so eliminate these options. Compare and select the highest possible value between option A and C to get the right answer basis what is asked. Hence, Option C is the right answer.

Hope this resolves your doubt.

Regor60 · Answer

This is a misunderstanding.

X is a SINGLE number of 4 or more decimal places.

One X isn't selected to represent J and a different X selected to represent K.

architectodicta · Answer

I solved it this way: We need the max J possible given that 0

pappal · Answer

wouldn't the greatest difference be when we choose something like 
x=0.845B where B=0 to 4
J=0.9
k=0.845
j-k=0.9-0.845=0.055
however no such choice is provided and through elimination we could get the correct choice but not the correct answer.
thanks for any corrections in advance.

architectodicta · Answer

Hi,

If x=0.845B, this rounded to the nearest tenth would be 0.8

That way, the difference would be negative.

In order to make the X go up we need that 0.8(4) a 5, and since X is less than one the max X would be 0.(9)5 that rounds to 1, not 0,85.

About the K, it's already equals X we just can make it with the least value possible by choosing the last digit: 0,95X, in this case would be 0.

I believe that's it.

pappal · Answer

hello 
rule for rounding up decimal says that if any digit is greater than or equal to 5, then immediate preceding digit is increased by 1 OR if its less than 5 then the preceding digit is left as it is.
so 0.845B rounded to the nearest thousandths place is 0.845, to nearest hundredths is 0.85 and to the nearest tenths is 0.9.

SamiMartinez · Answer

AI gave this - I guess using .02 still works well even though everyone is using .08?

Step 2: To maximize J - K

We want J as large as possible and K as small as possible for the same x.

That means:
 • x should be just below the midpoint where rounding to the tenth jumps up.
 • At that same x, K should round down as much as possible.

⸻

Step 3: Examine the boundary near a tenth

Consider the transition point between J = 0.1 and J = 0.2.
That boundary is at x = 0.15.

Just below 0.15 (say 0.149499...),
 • Rounding to the nearest tenth gives J = 0.1? No — 0.1495 rounds up to 0.1? Actually, wait:
 • 0.15 rounds up to 0.2,
 • anything less than 0.15 rounds down to 0.1.

So just below 0.15 → J = 0.1.

But we want J > K, so we want J = 0.2 while K still rounds down smaller.

For J = 0.2, x must be at least 0.15.

So take x = just at or above 0.15 → J = 0.2.

Now make K as small as possible — just before it rounds up to 0.150.
At x = 0.1495, K = 0.150; at x = 0.149499..., K = 0.149.

⸻

Step 4: Compute the difference

Take x = 0.149499...

Then:
 • J = 0.2
 • K = 0.149

J - K = 0.2 - 0.149 = 0.051

But since the smallest possible K in that region is actually 0.1495 (rounds up), the greatest possible difference before K bumps up is slightly less than 0.051 — approximately 0.0505.

J = x rounded to the nearest TENTH, and K = x

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

J = x rounded to the nearest TENTH, and K = x

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards