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Consider the binary operation # defined by a#b = 10a + b, where the op

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Consider the binary operation # defined by a#b = 10a + b, where the op  [#permalink]

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New post 21 Mar 2018, 23:11
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67% (01:09) correct 33% (01:07) wrong based on 38 sessions

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Consider the binary operation # defined by a#b = 10a + b, where the operations on the right side of the equal sign denote the standard arithmetic operations. Suppose M = x#y and N = y#x, where x and y are positive integers, which of the following must be a factor of M + N ?

(A) 14
(B) 11
(C) 10
(D) 9
(E) 6

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Re: Consider the binary operation # defined by a#b = 10a + b, where the op  [#permalink]

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New post 21 Mar 2018, 23:18
Bunuel wrote:
Consider the binary operation # defined by a#b = 10a + b, where the operations on the right side of the equal sign denote the standard arithmetic operations. Suppose M = x#y and N = y=x, where x and y are positive integers, which of the following must be a factor of M + N ?

(A) 14
(B) 11
(C) 10
(D) 9
(E) 6

I believe N = y#x here

Then M+N becomes 11a+11b
B
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Re: Consider the binary operation # defined by a#b = 10a + b, where the op  [#permalink]

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New post Updated on: 22 Mar 2018, 02:07

Solution



It seems there is a typing error, it should be N= y# x.

Working out:

    • M= x # y= 10x + y
    • N= y # x= 10y + x
    • M+N= (10x + y) + (10y + x) = 11(x + y)

    • Hence, (M+N) is always a factor of 11.

Answer: B
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Originally posted by EgmatQuantExpert on 22 Mar 2018, 01:06.
Last edited by EgmatQuantExpert on 22 Mar 2018, 02:07, edited 3 times in total.
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Joined: 07 Dec 2017
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Re: Consider the binary operation # defined by a#b = 10a + b, where the op  [#permalink]

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New post 22 Mar 2018, 01:08
Bunuel wrote:
Consider the binary operation # defined by a#b = 10a + b, where the operations on the right side of the equal sign denote the standard arithmetic operations. Suppose M = x#y and N = y=x, where x and y are positive integers, which of the following must be a factor of M + N ?

(A) 14
(B) 11
(C) 10
(D) 9
(E) 6


As there are only variables in the equation, we'll pick easy numbers.
This is an Alternative approach.

Say x = y = 1. Then x#y = 10+1 = 11 and y#x = 1+10 = 11
Then M+N=22. Only (B) , 11, is a factor of 22.

(B) is our answer.
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Re: Consider the binary operation # defined by a#b = 10a + b, where the op &nbs [#permalink] 22 Mar 2018, 01:08
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