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If # represents one of the operations +, -, and x, is

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Manager
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If # represents one of the operations +, -, and x, is [#permalink] New post 11 Apr 2006, 05:52
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A
B
C
D
E

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If # represents one of the operations +, -, and x, is k#(L+m)=(k#L)+(k#m) for all numbers k, L, and m?

(1) k#1 is not equal to 1#k for some numbers k
(2) # represents subtraction

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 [#permalink] New post 11 Apr 2006, 06:11
Answer is D.

Statement 2 is obvious enough.

Statement 1: Because we know that # only represents addition, subtraction and multiplication, and NOT division, statement 1 tells us that # must represent subtraction. 1#k and k#1 will be the same if # represents multiplication or addition.
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 [#permalink] New post 11 Apr 2006, 07:05
I get the answer as E.

If k, l and M = 0, then the two sides of equation are equal.
For other numbers, they are unequal.

Well, but the question is

"is k#(L+m)=(k#L)+(k#m) for all numbers k, L, and m". And the answer is NO.
This means each statement is sufficient. Hence changing my answer to D.

Last edited by remgeo on 12 Apr 2006, 01:51, edited 1 time in total.
  [#permalink] 11 Apr 2006, 07:05
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If # represents one of the operations +, -, and x, is

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