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

Question

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.

sathishkumar434 · Accepted Answer

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.

Gnpth · Answer

Hi, 100 550 ---> 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.

WoundedTiger · Answer

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

GMATinsight · Answer

Check solution

Answer: Option A

omer1kau · Answer

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

halibr331 · Answer

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

EMPOWERgmatRichC · Answer

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.

Final Answer:  A

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

Srija221 · Answer

Please can anyone help to understand the rounding concept.

Posted from my mobile device

Bunuel · Answer

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  
     Theory   
 GMAT Shortcut: Adding to the Numerator and Denominator 
 Rounding Rules on the GMAT: Slip to the Side and Look for a Five! 
 How to Identify Terminating Decimals on the GMAT 
 Rounding Up Some Official GMAT Questions! 
 Terminating Decimals in Data Sufficiency on the GMAT 
 GMAT Quantitative: Ratio and Proportions 
 Ratios in GMAT Data Sufficiency 
 Why You Should Convert Fractions to Decimals on the GMAT 
 Use This Strategy for Fractions and Save Time on GMAT Test Day 
 Variations On The GMAT - All In One Topic 
     Questions   
 Terminating and Recurring Decimals 
 Units digits, exponents, remainders problems 
 DS Questions 
 PS Questions

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

Hope it helps.

Srija221 · Answer

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

bumpbot · Answer

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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

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