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16 Sep 2014, 00:55
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What is the difference between the lengths of diagonals of parallelogram \(ABCD\) (\(BD \gt AC\))?
(1) \(AB - BC = 2\)
(2) \(\angle ABC = 30\) degrees
(1) \(AB - BC = 2\)
(2) \(\angle ABC = 30\) degrees
16 Sep 2014, 00:55
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Official Solution:
Statement (1) by itself is insufficient. The parallelogram can be close to a rectangle (then its diagonals would differ insignificantly) or it can be very oblique (then the difference between the lengths of its diagonals would be substantial).
Statement (2) by itself is insufficient. There are no limitations on the size of the parallelogram and thus no limitation on the difference between the lengths of its diagonals.
Statements (1) and (2) combined are insufficient. S1 and S2 also do not prevent the parallelogram from getting arbitrarily large (due to S1, it will look more like a rhombus as it gets larger). Hence, there is no limitation on the difference between the lengths of its diagonals either.
Answer: E
Statement (1) by itself is insufficient. The parallelogram can be close to a rectangle (then its diagonals would differ insignificantly) or it can be very oblique (then the difference between the lengths of its diagonals would be substantial).
Statement (2) by itself is insufficient. There are no limitations on the size of the parallelogram and thus no limitation on the difference between the lengths of its diagonals.
Statements (1) and (2) combined are insufficient. S1 and S2 also do not prevent the parallelogram from getting arbitrarily large (due to S1, it will look more like a rhombus as it gets larger). Hence, there is no limitation on the difference between the lengths of its diagonals either.
Answer: E
30 Oct 2016, 05:48
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Can you provide a more detailed explaination?
