What is the result when x is rounded to the nearest hundredt

Question

What is the result when x is rounded to the nearest hundredth?

(1) When x is rounded to the nearest thousandth the result is 0.455.
(2) The thousandth digit of x is 5.

KarishmaB · Accepted Answer

Responding to a pm:

When you round off to the hundredth digit, you look at only the thousandth digit i.e. you focus only on the next digit.

Say x = .4546
When you round it to the nearest hundredth digit, you get x = .45 (not .46). The reason is that the thousandth digit is 4 which is less than 5. 0.4546 is closer to 0.45 than it is to 0.46
You do not follow a sequence of roundings to arrive at x = .455 and then x = .46

Say x = .4553
Now when you round to the nearest hundredth, you get x = .46 because the thousandth digit is 5. .4553 is closer to .46 than to .45

Therefore statement 1 is not sufficient alone. If you round off x to thousandth and get .455, you do not know whether x was .4546 or .4553 initially (or similar). Hence you do not know what you will get when you round it to nearest hundredth. Statement 2 tells you that the thousandth digit was 5 so now you know that x was .4553 (or similar) and it will be rounded to .46

AKProdigy87 · Answer

I believe the answer is  C .

Statement 1: When x is rounded to the nearest thousandth the result is 0.455.

Two cases.

Case 1: Thousandths digit is 5 (0.4550 <= x < 0.4555). Then x rounded to the nearest hundredth would be 0.46.
Case 2: Thousandths digit is 4 (0.4545 < x < 0.4550). Then x rounded to the nearest hundredth would be 0.45.

Therefore, insufficient.

Statement 2: The thousandths digit of x is 5.

Doesn't give any information about any of the other digits of x. Insufficient.

Evaluting Both Statements.

Since we know that the thousandths digit of x is 5, this falls under Case 1. X rounded to the nearest hundredths digit if 0.46. Therefore, sufficient.

Augustus · Answer

No. 
If the thousandths digit is 4, e.g. 0.4549, the nearest thousandth is 0.455 and the nearest hundredth is 0.45
If the thousandths digit is 5, e.g. 0.4551, the nearest thousandth is 0.455 and the nearest hundredth is 0.46.

Therefore we need the information from (2) to state that x rounded to the nearest hundredth is 0.46, so the answer is C.

chetan2u · Answer

C
..
(1) when x is rounded to the nearest thousandth, the result is .455 ....
   means the no could be .4546 or .4552...  
ans in first case will be .45 and in 2nd case .46  
not suff..
(2) the thousandths digit of x is 5 .... 
 nothing given abt hundredths digit .... 
not suff

combined 
we know the no is .4551,.4552,.4553,.4554...  in each case ans is .46 so hundredth digit is 6 ..
.suff
 hope it helped!

gmatcracker2010 · Answer

Apology for repeat query.

But I still feel the OA should A. Look at the Q. What is the result after X rounded off to nearest hundredth ie. Two digits after the decimal. 
As explained by many, it is possible to ans this using only Statement 1 as follows:
Cases:
1. If the number is 0.4549 after rounding off to nearest hundredth it is 0.46
2. If the number 0.455 after rounding off to nearest hundredth it is 0.46
3. If the number 0.455 after rounding off to nearest hundredth it is 0.46
In any of the above cases the final rounding number remains same ie. 0.455. Is my logic correct or am I missing something?

Bunuel · Answer

Red part is not correct: 0.4549 rounded to the nearest hundredth = 0.45, since the  first  dropped 4 is less than 5.

Rounding rules

Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep.

Example:
5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5.
5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5.
5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5.

Hope it helps.

shashankp27 · Answer

Karishma , I may be little off on this one but as per stm1 : whatever was the value of X , when it was rounded to nearest thousandth it became .455 so when i round this to nearest hundredth shoudn't it become .46 ?

suppose X was .4549 so when it is rounded(round up ) to the nearest thousandth it becomes .455 and when finally rounded to nearest hundredth it becomes .46

suppose X was .4554 so when it is rounded( round down) to the nearest thousandth it becomes .455 and when finally rounded to nearest hundredth it becomes .46

Am is missing something here ? can you please elaborate a bit as to why both statements are needed.

I guess , my Question is why should we bother about the digit after the Thousandth digit when stmt1 clearly says that the thousandth digit (post round off) is 5 and asks about the Hundreth digit.

KarishmaB · Answer

When you have to round a number to the hundredth, you do not have to first round it off to thousandth and then to hundredth. You have to directly round it off to the hundredth.
Forget process. Think logic. Is 0.4549 closer to .45 or .46? It is closer to 0.45 so you will round it off to 0.45
The digit right next to the last digit you want is the only important one. It is incorrect to round off numbers in steps. If you want to round off till hundredth, it has to be done in a single step.

bagdbmba · Answer

Hi Karishma,
So answer would be C I think...Please confirm!

Bunuel · Answer

Merging topics.

Yes, the correct answer is C.

KarishmaB · Answer

Yes, that's correct.

KarishmaB · Answer

Responding to a pm:

You do need the original value to get the "further rounded" value in this case. But it will not always be so.

If you are given that rounded to the nearest thousandth, x = 0.452.
Here, it doesn't matter what the original value of x is. 
Rounded to the nearest hundredth, the value of x will be 0.45.

Why? Because the actual value of x could be something like 0.4517 or 0.4523. The thousandth digit will be either 1 or 2. In either case, the hundredth digit will remain 5.

GMATinsight · Answer

Please find the solution as attached.

JeffTargetTestPrep · Answer

We need to answer the question:

x rounded to the nearest hundredth = ?

Statement One Alone:

=> When x is rounded to the nearest thousandth the result is 0.455.

If x = 0.4551, then x rounded to the nearest thousandth is 0.455, and x rounded to the nearest hundredth is 0.46.

Whereas, is x = 0.4549, then x rounded to the nearest thousandth is 0.455, and x rounded to the nearest hundredth is 0.45.

Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> The thousandth digit of x is 5.

We don’t know the digits of x that are left to the thousandth digit. Statement two is not sufficient. Eliminate answer choice B.

Statements One And Two Together:

Since x must be in the interval 0.455 ≤ x < 0.4555, x rounded to the nearest hundredth is equal to 0.46.

The two statements together are sufficient.

Answer: C

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What is the result when x is rounded to the nearest hundredt

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