Re: SAT question
- From: "Pubkeybreaker" <Robert_silverman@xxxxxxxxxxxx>
- Date: 2 Mar 2006 04:46:26 -0800
"If a triangle has sides ABC which one of the folowing is true.
A.) C= A+B
B.) C= A-B
C.) C+2 = A+B+3
D.) C+3 = A+B+2
E.) C= 2A+B "
The problem, as stated is nonsense.
(1) When one says 'sides ABC' one is applying LABELS to the sides.
This is
not the same as saying that the LENGTHS are A, B, C.
Indeed, the problem does not even state the DOMAIN for the
variables A,B,C.
for example, A,B.C might be VECTORS (A triangle certainly can
be formed
from 3 vectors, making both A.) and B.) true)
however, we will assume LENGTHS of A,B,C
(2) the problem does not distinguish, 'for all' A,B,C vs 'for
some' A,B,C,
Both A.) and B.) are permissible. One gets a DEGENERATE triangle
(with area 0), but a degenerate triangle is still a triangle. The
problem, if
correctly posed should state specifically: 'non-degenerate triangle'.
Some might
argue this point. It is somewhat a matter of definition.
Note that A.) and B.) are EQUIVALENT statements. It asserts that
the length
of one side equals the sum of the other two.
C.) and E.) are clearly not permissible. D.) clearly is. for SOME
A,B,C. but not
for ALL A,B,C. (take an equilateral triangle with A=B=C = 2, for
example. However,
A=B=C=1 does work)
The problem, as stated, is meaningless gibberish. There is also a
difference
between 'is true' and 'can be true'. I would take 'is true' to
mean FOR ALL
A,B,C, whereas 'can be true' would mean 'FOR SOME A,B,C'. In the
first
interpretation there is no correct answer.
.
- References:
- SAT question
- From: jennifer
- SAT question
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