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For all positive integers m and n, the expression m △ n represents the

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For all positive integers m and n, the expression m △ n represents the [#permalink]

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New post 21 Dec 2016, 18:06
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For all positive integers m and n, the expression m △ n represents the remainder when m+n is divided by m-n. What is the value of
((19△9)△2) - (19△(9△2)) ?

(A) -8

(B) -6

(C) -4

(D) 4

(E) 6
[Reveal] Spoiler: OA

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Last edited by Vyshak on 23 Dec 2016, 20:33, edited 1 time in total.
Corrected OA
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Re: For all positive integers m and n, the expression m △ n represents the [#permalink]

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New post 22 Dec 2016, 01:58
MathRevolution wrote:
For all positive integers m and n, the expression m △ n represents the remainder when m+n is divided by m-n. What is the value of
((19△9)△2) - (19△(9△2)) ?

(A) -8

(B) -6

(C) -4

(D) 4

(E) 6



I solved it as:
(19△9)△2) gives 4
(19△(9△2) gives 8
So, 4-8 should be -4.
Ans C.

Please someone explain what I am missing.
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Re: For all positive integers m and n, the expression m △ n represents the [#permalink]

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New post 22 Dec 2016, 02:31
I too get -4 as answer.
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Re: For all positive integers m and n, the expression m △ n represents the [#permalink]

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New post 23 Dec 2016, 01:28
Since m△n represents the remainder of m+n divided by m-n,
19△9 represents the remainder of (19+9) divided by (19-9), which is the remainder of 28 divided by 10. Then, from 28=10(2)+8, the remainder becomes 8, and thus 19△9=8.
8△2 represents the remainder of (8+2) divided by (8-2), which is the remainder of 10 divided by 6. Then, from 10=6(1)+4, the remainder becomes 4, and thus 8△2=4.
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Re: For all positive integers m and n, the expression m △ n represents the [#permalink]

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New post 23 Dec 2016, 09:38
It looks like you may have forgot to include the second part of the express which is "minus 8."
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Re: For all positive integers m and n, the expression m △ n represents the [#permalink]

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New post 10 Jan 2017, 22:03
shashank1tripathi wrote:
MathRevolution wrote:
For all positive integers m and n, the expression m △ n represents the remainder when m+n is divided by m-n. What is the value of
((19△9)△2) - (19△(9△2)) ?

(A) -8

(B) -6

(C) -4

(D) 4

(E) 6



I solved it as:
(19△9)△2) gives 4
(19△(9△2) gives 8
So, 4-8 should be -4.
Ans C.

Please someone explain what I am missing.


Hi shashank1tripathi,

Your solution is correct.

Happy Studying!
Math Revolution
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See our Youtube demo

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Re: For all positive integers m and n, the expression m △ n represents the [#permalink]

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New post 20 Feb 2017, 18:00
I believe the answer is C- For all positive integers m and n, the expression m △ n represents the remainder when m+n is divided by m-n. What is the value of
((19△9)△2) - (19△(9△2)) ?- well, you have plug in 19 for M and 9 for N. For example

19+9/19-9
28-10= r8
8△2
8+2/8-2
10/6
r4

9+2/9-2
11/7
r4
19△4
19+4/19-4
23/15
r8

Conclusion:
4-8= -4
Re: For all positive integers m and n, the expression m △ n represents the   [#permalink] 20 Feb 2017, 18:00
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