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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8437
GMAT 1: 760 Q51 V42
GPA: 3.82
For all positive integers m and n, the expression m △ n represents the  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 80% (01:45) correct 20% (02:32) wrong based on 152 sessions

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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

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Originally posted by MathRevolution on 21 Dec 2016, 19:06.
Last edited by Vyshak on 23 Dec 2016, 21:33, 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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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.
Current Student S
Joined: 23 Jul 2015
Posts: 139
Re: For all positive integers m and n, the expression m △ n represents the  [#permalink]

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I too get -4 as answer.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8437
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: For all positive integers m and n, the expression m △ n represents the  [#permalink]

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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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It looks like you may have forgot to include the second part of the express which is "minus 8."
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8437
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: For all positive integers m and n, the expression m △ n represents the  [#permalink]

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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,

Happy Studying!
Math Revolution
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Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: For all positive integers m and n, the expression m △ n represents the  [#permalink]

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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
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4219
For all positive integers m and n, the expression m △ n represents the  [#permalink]

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Top Contributor
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

19∆9 = the remainder when (19+9) is divided by (19-9)
= the remainder when 28 is divided by 10
= 8

So, (19∆9)∆2 = 8∆2
= the remainder when (8+2) is divided by (8-2)
= the remainder when 10 is divided by 6
= 4
-------------------------------------------------------------
9∆2 = the remainder when (9+2) is divided by (9-2)
= the remainder when 11 is divided by 7
= 4

So, 19∆(9∆2) = 19∆4
= the remainder when (19+4) is divided by (19-4)
= the remainder when 23 is divided by 15
= 8
-------------------------------------------------------------

We get: ((19∆9)∆2) - (19∆(9∆2))
= 4 - 8
= -4

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