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If n is an integer between 100 and 900, what is the tens dig

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If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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New post 10 Nov 2013, 23:00
1
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A
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Question Stats:

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If n is an integer between 100 and 900, what is the tens digit of n?

(1) If n is rounded to the nearest ten and the result is then rounded to the nearest hundred, the final value differs from the result of rounding n to the nearest hundred.

(2) The tens digit of n is half the units digit of n and is twice the hundreds digit of n.
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Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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New post 10 Nov 2013, 23:10
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1
Hi,


100<n<900.

Statement 1:

ABC rounded to nearest ten and then to the nearest hundred differs from ABC rounded to nearest 100.

The middle value will depended on the unit digits.

For example :
554 --> 550 ---> 500 (Applying If n is rounded to the nearest ten and the result is then rounded to the nearest hundred).
554 ---> 600 (Applying the result of rounding n to the nearest hundred).

Hundredth Digit is definitely 5 and the Unit Digit varies between 1 to 5 inclusive.

So the statement 1 is sufficient.

Statement 2:

124, 248 etc- Insufficient.


So the answer is A.
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Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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New post 11 Nov 2013, 08:21
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Gnpth wrote:
100<n<900.

cStatement 1:[/b][/u]

ABC rounded to nearest ten and then to the nearest hundred differs from ABC rounded to nearest 100.

The middle value will depended on the unit digits.

For example :
554 --> 550 ---> 500 (Applying If n is rounded to the nearest ten and the result is then rounded to the nearest hundred).
554 ---> 600 (Applying the result of rounding n to the nearest hundred).

Hundredth Digit is definitely 5 and the Unit Digit varies between 1 to 5 inclusive.


I don't think you got it right.

We care about the tens digit, not the hundreds digit.
The right example would be:
545 --> 550 ---> 600 (Applying If n is rounded to the nearest ten and the result is then rounded to the nearest hundred).
545 ---> 500 (Applying the result of rounding n to the nearest hundred).

Another example would be:
345 --> 350 ---> 400 (Applying If n is rounded to the nearest ten and the result is then rounded to the nearest hundred).
345 ---> 300 (Applying the result of rounding n to the nearest hundred).


So, the tens digit has to be 4. Hence, Statement 1 is sufficient.
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Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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New post 11 Nov 2013, 23:12
amyjohn wrote:
If n is an integer between 100 and 900, what is the tens digit of n?

(1) If n is rounded to the nearest ten and the result is then rounded to the nearest hundred, the final value differs from the result of rounding n to the nearest hundred.

(2) The tens digit of n is half the units digit of n and is twice the hundreds digit of n.



Hi Amyjohn,

Got it wrong the first time as I did not understand the St 1 completely

For St 1 let us take n= 567 ---->Rounded to nearest ten----->570 and then rounded to nearest hundred : 600
n=567, rounded directly to nearest hundred: 600 : No difference in the above 2 final values

Consider n= 543----->540 ---->500
n= 543------> 500 Again no difference in final values

now if n= 548----> 550-----.600
or 548----->500 (rounded to nearest hundred)

Hence tens digit has to be 4.

For St 2 : we have either 124 or 248

So A has to be the answer
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Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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New post 17 Nov 2016, 22:02
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amyjohn wrote:
If n is an integer between 100 and 900, what is the tens digit of n?

(1) If n is rounded to the nearest ten and the result is then rounded to the nearest hundred, the final value differs from the result of rounding n to the nearest hundred.

(2) The tens digit of n is half the units digit of n and is twice the hundreds digit of n.


Check solution

Answer: Option A
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Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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New post 20 Oct 2017, 13:09
who decided that 350 is rounded up and not down?
is that common knowledge?
I though that you can round 350 both to 400 or 300
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Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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New post 20 Oct 2017, 16:34
omer1kau wrote:
who decided that 350 is rounded up and not down?
is that common knowledge?
I though that you can round 350 both to 400 or 300


u have to round anything 5+ up b/c then rounding cancels itself out in mass

ie if you round DOWN at 5, then anything ending in

0
1
2
3
4
5

is rounded DOWN

and anything ending in

6
7
8
9

is rounded up.

in aggregate this would push measurement down since there are more round-down #s than round-up


by rounding up when 5 u balance it out
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Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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New post 20 Dec 2017, 18:21
Hi All,

The first Fact in this DS question is rather 'densely' worded, so you would likely find it helpful to TEST VALUES so that you can clarify what is 'allowed' and what is not.

We're told that N is an integer and that 100 < N < 900. We're asked for the TENS DIGIT of N.

1) If N is rounded to the nearest ten and the result is then rounded to the nearest hundred, the final value DIFFERS from the result of rounding N to the nearest hundred.

With this Fact, we're told to round TWICE (first to the nearest 10 and THEN to the nearest 100). Consider a couple of examples....

IF.... N = 425
Rounding to the nearest ten.... 430.... then rounding to the nearest hundred.... 400

vs.

Just rounding to the nearest hundred... 400

The two 'end' results would be the SAME, but Fact 1 states that they have to be DIFFERENT. So... what type of value of N would lead to different results... You need a number that would naturally round 'down' but rounds 'up' if you round it in two steps...

IF.... N = 445
Rounding to the nearest ten.... 450.... then rounding to the nearest hundred.... 500

vs.

Just rounding to the nearest hundred... 400

Now the results are DIFFERENT. This type of result will only occur when the TENS digit is 4 AND the UNITS DIGIT is 5 or higher (you can try as many examples as you like and you'll see). Thus, the answer to the question is ALWAYS FOUR.
Fact 1 is SUFFICIENT.

2) The tens digit of N is half the units digit of N and is twice the hundreds digit of N.

IF....
N = 124, then the answer to the question is TWO.
N = 248, then the answer to the question is FOUR.
Fact 2 is INSUFFICIENT.

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Re: If n is an integer between 100 and 900, what is the tens dig &nbs [#permalink] 20 Dec 2017, 18:21
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