Problem Solving

AAPL wrote:For all positive integers m and n, the expression $$m \triangle n$$ represents the reminder when m+n is divided by m-n. What is the value of $$((19\triangle9)\triangle2)-(19\triangle(9\triangle2))?$$

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

Answer: C

Cheers,
Brent