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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # M is a positive two-digit number. When the digits are reversed, the nu

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Math Expert V
Joined: 02 Sep 2009
Posts: 56257
M is a positive two-digit number. When the digits are reversed, the nu  [#permalink]

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Difficulty:   15% (low)

Question Stats: 86% (01:15) correct 14% (01:42) wrong based on 32 sessions

### HideShow timer Statistics M is a positive two-digit number. When the digits are reversed, the number is N. If K = M + N, which of the following is true?

A. K must be even
B. K cannot be square
C. K cannot be divisible by 13
D. K must be divisible by 11
E. If M is even then K must be even

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NUS School Moderator D
Joined: 18 Jul 2018
Posts: 982
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: M is a positive two-digit number. When the digits are reversed, the nu  [#permalink]

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M is a two digit positive integer. Let M = 10a+b.
Then N = 10b+a
M+N = 11a+11b = 11(a+b).
Hence K must be divisible by 11.

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VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: M is a positive two-digit number. When the digits are reversed, the nu  [#permalink]

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Bunuel wrote:
M is a positive two-digit number. When the digits are reversed, the number is N. If K = M + N, which of the following is true?

A. K must be even
B. K cannot be square
C. K cannot be divisible by 13
D. K must be divisible by 11
E. If M is even then K must be even

Given M=10x+y & N=10y+x (digits x and y are reversed)

K=M+N=10x+y+10y+x=11x+11y=11(x+y)

A. K must be even
It depends on the value of x and y
True: x=Odd, y=odd
False: x=Odd, y=even

B. K cannot be square
It depends on the value of x and y
True: x=5, y=other than 6
False: x=5, y=6

C. K cannot be divisible by 13
It depends on the value of x and y
True: x=2, y=2
False: x=7, y=6

D.K must be divisible by 11
True: K is a multiple of 11 as k=11(x+y)
keep it.

E. If M is even then K must be even
Let M=12 then N=21
K=M+N=33 not an even number

Ans. (D)
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Rise above the storm, you will find the sunshine Re: M is a positive two-digit number. When the digits are reversed, the nu   [#permalink] 22 Aug 2018, 02:04
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