1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS
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x=a.bc --> b=?

(1) x=a.b5. Clearly insufficient to determine b.

(2) x, rounded to nearest tenth is 54.5 --> x can be for example 54.54 (meaning that c<5) OR 54.46 (meaning that c>=5). Not sufficient.

(1)+(2) c=5>=5, hence x=54.45... --> b=4. Sufficient.

Answer: C.
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Obviously (1) alone is not enough, so is BCE
What is about information (2) rounded to the nearest tenth, is 54,5
So the number no rounded is 54,49X where X integer > 4 or 54,50X where X integer <5
So the the tenth digit can be 4 or 5, the information (2) alone is not enough to answer to this question.
However since in the 1st information the undredths digit of x is 5, so the tenth digit is 4
Therefore the correct answer is C

Thanks Guys

OA is C

I was messing up with my rounding off concepts
Now I fixed'em ryt

hope didnt fix it to any particular value ....just kidding mate...happens with all of us some or the other time...

Need a quick clarification on this. (I guess I don't need a clarification anymore, just thought i'd add the note below)

What is Number x, rounded to the nearest tenth here?

if x = 54.550000 ~ 54.6
if x = 54.458000 ~ 54.5

I guess I figured it out as I was typing this itself.

Note: When the digit 5, 6, 7, 8, or 9 appears in the ones place, round up; when the digit 0, 1, 2, 3, or 4 appears in the ones place, round down

hundredth digit is after decimal??? 132===> hundredths is 1, tenth 3 and one-2
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Thanks for clarifying this.
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hats off to your mathematics bunuel !!! what so ever type of problem it may be you always have a solution for it.

Hi Bunuel,
Sorry for the silly question but how do we know its asking tenths digit after or before decimal?

TENTH digit is Always to the Right of the decimal.
TENS digit is Always to the left of the decimal.

is this question asking about tenth digit or decimal point?
i think it should be tenth decimal point,
and after rounding off it comes as 54.5 hence tenth decimal 0.5 remained as it is as hundredth digit was less than or equal to 5,
e.g number was 54.55, I round it off , it becomes 54.5, if the number was 54.56, i round it off it becomes 54.6

if you dont consider first statement then there are two possibilities 54.47 will also become 54.5 and 54.52 will also become 54.5
hence we need both statements

Hope i m making sense
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we have to find tenths digit of a number x

(1) hundredths digit 0f x is 5
we can not find tenths digit from it, hence insufficient

(2) Number x, rounded to the nearest tenth, is 54.5[/quote]
here, we have two cases, if no is 54.50 to 54.54 then tenths digit is 5
and if no is 54.45 to 54.49 then tenths digit is 4
therefore (2) alone is not sufficient

using (1) and (2) together
we clearly have no as 54.45, giving us tenths digit as 4
both statements together gives a unique answer

Answer C

Kudos, if you like the explanation

Hi All,

In this prompt, we're asked for the TENTHS digit of X? This question asks for the digit that is to the IMMEDIATE RIGHT of the decimal point.

Fact 1: The hundredths digit of X is 5

This tells us NOTHING about the tenths digit - that digit could be any integer from 0 to 9, inclusive.

eg.
X = _.05
X = _.15
X = _.25
...
X = _.95
Fact 1 is INSUFFICIENT

Fact 2: Number X, rounded to the nearest tenth, is 54.5

This Fact discusses ROUNDING. If the hundredths digit is 0-4, then we 'round down'; if the hundredths digit is 5-9, then we 'round up.'

eg.
IF.....
X = 54.49, then we would 'round up' to 54.5

X = 54.53, then we would 'round down' to 54.5

Thus, the tenths digit could be 4 or 5.
Fact 2 is INSUFFICIENT

Combined, we know...
The hundredths digit of X is 5
Number X, rounded to the nearest tenth, is 54.5

Since the hundredths digit is 5, that means that we would have to round UP to get to 54.5. Thus, X could only be 54.45
Combined, SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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the key point here is 'number x'.

As it is mentioned that it is a number and not an integer you can assume x = 0.abc and I guess rest of the problem can be referred from any of the well explained answers above.

right

Please read the whole thread. For example, this post: https://gmatclub.com/forum/what-is-the- ... ml#p722510
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It is not mentioned anywhere in the second statement that X was rounded "UP" to the nearest tenths digit.

As per general rules of mathematics, we can round 54.45 & 54.55 both to the 54.5 as there is no mention of rounding "UP" or "Down".

So, In my opinion the answer should be (E).

Hi TumharaFaizal,

When using 'rounding rules' the digits 0, 1, 2, 3 and 4 are 'rounded down' while the digits 5, 6, 7, 8 and 9 are 'rounded up.'

Thus, when rounding to the nearest TENTH,
54.45 would become 54.5 but....
54.55 would also be 'rounded up' (and become 54.6).

GMAT assassins aren't born, they're made,
Rich
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