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M is a positive two-digit number. When the digits are reversed, the nu

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M is a positive two-digit number. When the digits are reversed, the nu  [#permalink]

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New post 22 Aug 2018, 01:47
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A
B
C
D
E

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  15% (low)

Question Stats:

89% (01:06) correct 11% (01:53) wrong based on 28 sessions

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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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Re: M is a positive two-digit number. When the digits are reversed, the nu  [#permalink]

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New post 22 Aug 2018, 01:59
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.

D is the answer

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Re: M is a positive two-digit number. When the digits are reversed, the nu  [#permalink]

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New post 22 Aug 2018, 02:04
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
Discard

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
Discard

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
Discard

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
Discard

Ans. (D)
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Re: M is a positive two-digit number. When the digits are reversed, the nu &nbs [#permalink] 22 Aug 2018, 02:04
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