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

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Math Expert
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What is the units digit of the three-digit integer N ? [#permalink]

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07 Sep 2015, 22:45
4
15
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Difficulty:

55% (hard)

Question Stats:

57% (01:41) correct 43% (01:29) wrong based on 240 sessions

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

(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.

Kudos for a correct solution.

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Re: What is the units digit of the three-digit integer N ? [#permalink]

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08 Sep 2015, 01:28
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.
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Re: What is the units digit of the three-digit integer N ? [#permalink]

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Updated on: 08 Sep 2015, 13:03
Solution:

1) The values can be in the range[546,554]. Insufficeint
2) Many possible values.Insufficient./

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

Option E

Originally posted by anudeep133 on 08 Sep 2015, 04:21.
Last edited by anudeep133 on 08 Sep 2015, 13:03, edited 2 times in total.
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Re: What is the units digit of the three-digit integer N ? [#permalink]

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08 Sep 2015, 04:29
dominicraj wrote:
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.

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.
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Re: What is the units digit of the three-digit integer N ? [#permalink]

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08 Sep 2015, 04:34
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.
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Re: What is the units digit of the three-digit integer N ? [#permalink]

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08 Sep 2015, 04:39
dominicraj wrote:
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.

Yes, you are right.Thanks.
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Re: What is the units digit of the three-digit integer N ? [#permalink]

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08 Sep 2015, 12:58
Bunuel wrote:
What is the units digit of the three-digit integer N ?

(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.

Kudos for a correct solution.

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.
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Re: What is the units digit of the three-digit integer N ? [#permalink]

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08 Sep 2015, 22:05
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
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Re: What is the units digit of the three-digit integer N ? [#permalink]

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10 Sep 2015, 13:55
3
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.
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Re: What is the units digit of the three-digit integer N ? [#permalink]

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10 Sep 2015, 14:49
2
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.

Solid question Bunuel. +1
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Re: What is the units digit of the three-digit integer N ? [#permalink]

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23 Feb 2017, 05:41
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
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Re: What is the units digit of the three-digit integer N ? [#permalink]

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28 Feb 2018, 21:40
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.

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Re: What is the units digit of the three-digit integer N ? [#permalink]

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02 Mar 2018, 23:11
Bunuel wrote:
What is the units digit of the three-digit integer N ?

(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.

Kudos for a correct solution.

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.
Re: What is the units digit of the three-digit integer N ?   [#permalink] 02 Mar 2018, 23:11
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