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# Let m be a positive integer with 5 digits. If rounding m to the neares

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Math Expert
Joined: 02 Sep 2009
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Let m be a positive integer with 5 digits. If rounding m to the neares  [#permalink]

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25 Dec 2016, 02:43
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Let m be a positive integer with 5 digits. If rounding m to the nearest 10 yields 11110, what is m?

(1) m is a multiple of 10.
(2) Reversing the digits of m results in a smaller number.

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Joined: 13 Oct 2016
Posts: 363
GPA: 3.98
Re: Let m be a positive integer with 5 digits. If rounding m to the neares  [#permalink]

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25 Dec 2016, 05:06
3
Bunuel wrote:
Let m be a positive integer with 5 digits. If rounding m to the nearest 10 yields 11110, what is m?

(1) m is a multiple of 10.
(2) Reversing the digits of m results in a smaller number.

"rounding m to the nearest 10". If I understood this correctly last two digits of our m could be 05, 06, 07, 08, 09, 10, 11, 12, 13, 14.

(1) m is a multiple of 10

We have only one option from the list 11110. Sufficient.

(2) Reversing the digits of m results in a smaller number

We can get 50111 > 11105, 60111 > 11106, ... , 90111 > 11109, 21111 > 11112, 31111 > 11113.

11111 = 11111 and only one option 01111 < 11110 Sufficient.

Please correct me if I'm wrong.
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Joined: 04 Mar 2016
Posts: 43
Location: India
Re: Let m be a positive integer with 5 digits. If rounding m to the neares  [#permalink]

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25 Dec 2016, 05:16
1
1) Rounding m to nearest 10 means...11105 <=m<= 11115 ... In this range only 1 no is a multiple of 10 . So and is m= 11110.
But I am confused if a nearest ten can be considered as rounded to itself.

2) In the same range as above
11105 <=m< =11115, again only if the no is 11110 then reverse is 1111 which is less, else all other nos do not satisfy this.

So answer is either B or D

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!
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Location: India
Re: Let m be a positive integer with 5 digits. If rounding m to the neares  [#permalink]

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25 Dec 2016, 05:18
vitaliyGMAT wrote:
Bunuel wrote:
Let m be a positive integer with 5 digits. If rounding m to the nearest 10 yields 11110, what is m?

(1) m is a multiple of 10.
(2) Reversing the digits of m results in a smaller number.

"rounding m to the nearest 10". If I understood this correctly last two digits of our m could be 05, 06, 07, 08, 09, 10, 11, 12, 13, 14.

(1) m is a multiple of 10

We have only one option from the list 11110. Sufficient.

(2) Reversing the digits of m results in a smaller number

We can get 50111 > 11105, 60111 > 11106, ... , 90111 > 11109, 21111 > 11112, 31111 > 11113.

11111 = 11111 and only one option 01111 < 11110 Sufficient.

Please correct me if I'm wrong.

But can 11110 be rounded to itself ??

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!
Senior Manager
Joined: 13 Oct 2016
Posts: 363
GPA: 3.98
Re: Let m be a positive integer with 5 digits. If rounding m to the neares  [#permalink]

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25 Dec 2016, 07:34
Omkar.kamat wrote:
vitaliyGMAT wrote:
Bunuel wrote:
Let m be a positive integer with 5 digits. If rounding m to the nearest 10 yields 11110, what is m?

(1) m is a multiple of 10.
(2) Reversing the digits of m results in a smaller number.

"rounding m to the nearest 10". If I understood this correctly last two digits of our m could be 05, 06, 07, 08, 09, 10, 11, 12, 13, 14.

(1) m is a multiple of 10

We have only one option from the list 11110. Sufficient.

(2) Reversing the digits of m results in a smaller number

We can get 50111 > 11105, 60111 > 11106, ... , 90111 > 11109, 21111 > 11112, 31111 > 11113.

11111 = 11111 and only one option 01111 < 11110 Sufficient.

Please correct me if I'm wrong.

But can 11110 be rounded to itself ??

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!

I don’t know for sure. I’ve met several GMAT questions on this forum which started with the line “… integers x and y …” and intuitively I took that as if x and y should be different integers, but the only way those questions could be solved eventually was that x ought to be identical to y. In this question, I guess, we have general case with bunch of numbers which are rounded to the nearest ten, and if the number has last two digits as 10 then it will be rounded to itself. But, this is my guess. Let’s wait for Bunuel's post or official answer.
Math Expert
Joined: 02 Aug 2009
Posts: 7763
Re: Let m be a positive integer with 5 digits. If rounding m to the neares  [#permalink]

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25 Dec 2016, 08:04
1
Omkar.kamat wrote:
vitaliyGMAT wrote:
Bunuel wrote:
Let m be a positive integer with 5 digits. If rounding m to the nearest 10 yields 11110, what is m?

(1) m is a multiple of 10.
(2) Reversing the digits of m results in a smaller number.

"rounding m to the nearest 10". If I understood this correctly last two digits of our m could be 05, 06, 07, 08, 09, 10, 11, 12, 13, 14.

(1) m is a multiple of 10

We have only one option from the list 11110. Sufficient.

(2) Reversing the digits of m results in a smaller number

We can get 50111 > 11105, 60111 > 11106, ... , 90111 > 11109, 21111 > 11112, 31111 > 11113.

11111 = 11111 and only one option 01111 < 11110 Sufficient.

Please correct me if I'm wrong.

But can 11110 be rounded to itself ??

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!

Hi,

Rounding to nearest 10 means the nearest multiple of 10..
The number could be anything...
If it is already a multiple of 10, the nearest multiple of 10 will be itself...
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Joined: 13 Oct 2016
Posts: 363
GPA: 3.98
Re: Let m be a positive integer with 5 digits. If rounding m to the neares  [#permalink]

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25 Dec 2016, 08:14
Quote:
Hi,

Rounding to nearest 10 means the nearest multiple of 10..
The number could be anything...
If it is already a multiple of 10, the nearest multiple of 10 will be itself...

Thank you for explanation!
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Posts: 2609
Schools: Boston U '20 (M)
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Let m be a positive integer with 5 digits. If rounding m to the neares  [#permalink]

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25 Dec 2016, 09:05
chetan2u wrote:
Omkar.kamat wrote:
vitaliyGMAT wrote:
"rounding m to the nearest 10". If I understood this correctly last two digits of our m could be 05, 06, 07, 08, 09, 10, 11, 12, 13, 14.

(1) m is a multiple of 10

We have only one option from the list 11110. Sufficient.

(2) Reversing the digits of m results in a smaller number

We can get 50111 > 11105, 60111 > 11106, ... , 90111 > 11109, 21111 > 11112, 31111 > 11113.

11111 = 11111 and only one option 01111 < 11110 Sufficient.

Please correct me if I'm wrong.

But can 11110 be rounded to itself ??

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!

Hi,

Rounding to nearest 10 means the nearest multiple of 10..
The number could be anything...
If it is already a multiple of 10, the nearest multiple of 10 will be itself...

Hi chetan2u
Can you please post a solution to this one=> 25-integers-are-written-on-a-board-are-there-at-least-two-consecutive-195899.html

A couple of people have also posted the query after my post which has further increased my curiosity.

Regards
Stone Cold

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Re: Let m be a positive integer with 5 digits. If rounding m to the neares  [#permalink]

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14 Aug 2018, 11:39
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Re: Let m be a positive integer with 5 digits. If rounding m to the neares   [#permalink] 14 Aug 2018, 11:39
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