What is the units digit of the three-digit integer N ?

Question

(1) When N is rounded to the nearest hundred, the result is 50 less than the result when N is rounded to the nearest ten.
(2) N is divisible by 4.

sehej · Accepted Answer

I'd go with C.

(1) When N is rounded to the nearest hundred, the result is 50 less than the result when N is rounded to the nearest ten.

Since the result is 50 less - it means the number N is being rounded down rather than being rounded up. The maximum we can round down is 49 (Example - 249 rounded to nearest hundred is 200). So let's assume the tens digit of N is 4.

But the difference is 50. So we want the number N rounded up when it's rounded to the nearest ten. Which means if N has a units digit \(=>5\) it will round up. (Same example above - 249 rounded to the nearest ten is 250)

Hence the difference between the two resultant numbers is 50 (\(250 - 200\)). But N could have any units digit among \(5,6,7,8,9\). Therefore, \(Insufficient\)

(2) N is divisible by 4.

This implies that the last two digits of N must be divisible by 4. The units digit could be \(0,4,8,2,6\).

Hence \(Insufficient\) by itself.

Combining both we know that the tens digit is 4 and that the units digit must be greater than 4. The only viable option that remains is \(8\). 8 is the units digit for N.

Hence, \(C\)

Harish - Your method is correct. However the question stem specifically states that the number rounded to nearest hundred is 50 LESS THAN the number rounded to the nearest ten. Therefore, the instance of 52 as the last two digits does not apply. I think

Waiting for OA.

dominicraj · Answer

It is E IMO.

As per option A: number should be anywhere between X45 and X55. Also X45 and X55 are not included in that(where X stands for hundredth digit)

As per option B: we can have any number which has last two digits divisible by 4.

If we use both A and B we have X48 and X52 as the contenders. Hence we still cant answer the question despite using both.

Regards,
Dom.

anudeep133 · Answer

Solution:

1) The values can be in the range . Insufficeint
2) Many possible values.Insufficient./

Combined : We have two values 548 and 552. So, insufficient.

Option E

anudeep133 · Answer

Hi Dom, I think the no. can only be on of these {545,546,547,548,549,555,556,557,558,559}. Take x51 as an example. When rounded to tens it will be X5 and when rounded to hundreds it will be x+1. So, the difference should be 50. 10X+5-X-1=50 ==> 9X=46. Not possible. Please correct me if i am wrong.

dominicraj · Answer

Hi anudeep,

we cannot have numbers beyond X55.. in my opinion.

reason being when you make it to nearest tens the number becomes X60...

and to nearest hundreds... (X+1)00.. the difference between them becomes 40. which goes against option A.

Regards,
Dom.

anudeep133 · Answer

Yes, you are right.Thanks.

harishbiyani8888 · Answer

I started with  statement 2  as it seemed much easier.

N can be any 3 digit number divisible by 4, and we have more than one unit digit in this case. Ex - 0, 4, 8 etc. So not sufficient.

Statement 1  : the last two digits N can be 46 47 48 49 51 52 53 54.

So, when you round off any of the above numbers to the nearest 100 and the nearest tens, the difference is 50.

For ex: 451 - Nearest 100 digit is 500, nearest 10 digit is 450, so difference = 50. Not sufficient.

On combining, both the statements we still are left with 48 and 52 (last two digits divisible by 4)

SO E.

PAVEL1987 · Answer

Guys, please correct me if 'm wrong, but it seems to me that you can't consider nos. over X50 under statement no.1, cause othervise when rounded to hundred we will get 50 more not less

BASSLJ · Answer

Im going to go with C.

Statement 1) When N is rounded to the nearest hundred, the result is 50 less than the result when N is rounded to the nearest ten.

Under this assumption, the tens digit has to be less that 5 so N rounds down. Then the units digit would have to be 5 through 9 so that it rounds up. So for example, N could be 149 through 145. (i.e. 149 rounds down to 100 if rounding to nearest 100 & 149 rounds up to 150 if rounding to nearest 10.) But since we have multiple numbers that we can use, statement 1 in insufficient.

Statement 2) N is divisible by 4

Ignoring statement 1, N could could have several solutions again. Example 104, 108, 112 etc. With no other info, statement 1 is insufficient.

Combining the statements) Since we know the 3 digit N is divisible by 4, it will not matter what the hundreds digit is for N. (From the rules of division, we only have to prove the last 2 digits in a number is divisible by 4 to prove that the entire number is also divisible by 4.) Therefore, we can use the numbers we came up in working statement 1 - 149, 148, 147, 146, and 145. Of these numbers, only 148 is divisible by 4.

Therefore C is the answer.

Solid question Bunuel. +1

KrishnakumarKA1 · Answer

PROMPT ANALYSIS

N is an natural number.

SUPERSET

N can range from 100 to 999.

TRANSLATION

In order to find N we need:
1# exact value of N
2# any relation or equation to determine N.

STATEMENT ANALYSIS

St 1: n will be either 151-155, 251-255, 351-355 …….851-855 INSUFFICIENT
St 2: n can be any 3 digit number divisible by 4. INSUFFICIENT

St 1& St 2: n could be 152, 252,352, 452……..852. We can see that the units digit in each case is 2. SUFFICIENT

Option C

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

With digit problems, it’s generally a good idea to rephrase the given statements into lists of possibilities. If possible, you should make an exhaustive list.

(1) INSUFFICIENT: When N is rounded to the nearest hundred, the result ends with “00”. Therefore, according to this statement, N rounded to the nearest ten yields a number ending with “50”. Furthermore, since the value rounded to the nearest hundred is lower, N must round down to the nearest hundred. Using basic facts about rounding, we can deduce from these two facts that the last two digits of N are somewhere between 45 and 49(inclusive). This range includes five possible units digits (5 through 9), so this statement is INSUFFICIENT.

(2) INSUFFICIENT: This statement tells us only that N is a three-digit multiple of 4. This is not enough information to determine the units digit of N.

(1) and (2): SUFFICIENT: An integer is divisible by 4 if its last two digits are divisible by 4. (The hundreds digit doesn’t matter, since 100 is a multiple of 4.) Of the options allowed by statement (1) for the last two digits – 45, 46, 47, 48, and 49 – only 48 is divisible by 4. Therefore, the last two digits of N are 48. Therefore, the units digit of N is 8; SUFFICIENT.

The correct answer is C.

rishabhmishra · Answer

IMO C  statement 1 to make 50 difference then hundredth digit will be any no. except 9 as no. is 3 digit 
tense digit will be 1 to 4 any number and unit digit will be 6 to 9 any number so insufficient.
statement 2 n divisible by 4 then n can be 400, 404,408, 412 etc insufficient.
combing both we know divisibility rule of 4 i.e last 2 digit is divisible by 4 then unit digit will be 8 only from 6 to 9 and hence sufficient.

kajumba900 · Answer

My solution:

Statement 1:

By rounding our number to the closest hundred we know that we end up with a lower number and by rounding to the closest ten we end up with a higher number. For this to be true the number we are looking for has to be lower than X5X and higher than XX4. Now, by taking into consideration that the two possible roundings have to create a gap of 50 we can quickly see that only X45 - X49 satisfies this condition. Ex. 145, 146, 147, 148, 149. As such we have five possible unit digits -  not sufficient

Statement 2:

There are endless three-digit numbers that are divisible by 4. Ex. 120, 644, 888...  Not sufficient

Statement 1 & 2 combined:

So going back to the set from S1 we can remove odd numbers directly, we are then left with X46 and X48, and only X48 will be divisible by 4. As such the unit digit has to be 8.

Answer: C

purvibagmar · Answer

But in case of 246- nearest 100 is 200 and nearest 10 is 250 thus giving the difference of 50 and 246 is divisible by 4.
Here the units digit is 6. So then there is no definite answer right?
If you can please tell me if this is right or if I am missing something?

Bunuel · Answer

246 is not divisible by 4:

246/4 = 61.5.

Stella5200 · Answer

Statement 1:

Take a number with a 3 handle.

Range where it rounds to a 50: 345, 346, 347, 348, 349, (anything above will round to 400)
All round to 300

This alone not enough no unique solution -   Insufficient

Statement 2:

Div by 4. Cool. Requirement is last 2 ending numbers need to be div by 4. Plenty in the mix of all 3 digit numbers. Also they can end as 16,32,48 etc... all diff units place. No unique solution   Insufficient

Statement 1 and 2:

Take the same 3 handle range again: 345, 346, 347, 348, 349
How many div by 4: Only 348. 8 is the digit. This will repeat for all ranges. We have a unique solution -   Sufficient

What is the units digit of the three-digit integer N ?

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