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Intern  Joined: 05 Oct 2013
Posts: 21
GMAT 1: 650 Q49 V30 If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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18 00:00

Difficulty:   95% (hard)

Question Stats: 49% (02:24) correct 51% (02:31) wrong based on 395 sessions

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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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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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GMAT 1: 710 Q49 V37 Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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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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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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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

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

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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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GMAT 1: 670 Q46 V35 GMAT 2: 640 Q46 V31 Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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1
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  [#permalink]

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Please can anyone help to understand the rounding concept.

Posted from my mobile device
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Joined: 02 Sep 2009
Posts: 53831
Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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Srija221 wrote:
Please can anyone help to understand the rounding concept.

Posted from my mobile device

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.

So, according to the above 8.35y rounded to the nearest tenth will be 8.4 irrespective of the value of y.

For mote on this check the following posts:
Math: Number Theory
Rounding Rules on the GMAT: Slip to the Side and Look for a Five!

3. Fractions, Decimals, Ratios and Proportions

For more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: If n is an integer between 100 and 900, what is the tens dig  [#permalink]

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For the above question..The only solutions with the statement 1
545 rounded off to nearest tens digit is 550 ...rounded off to nearest 100 is 600
When 545 is rounded off to nearest 100 the number is 500.
Thus the final and initial answers are different.

545, 546, 547, 548 and 549
So the tens digit has to be 4.

Posted from my mobile device Re: If n is an integer between 100 and 900, what is the tens dig   [#permalink] 22 Aug 2018, 09:29
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# If n is an integer between 100 and 900, what is the tens dig

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