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Set of all values of d

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by gmattesttaker2 » Mon May 19, 2014 7:08 pm
Hello,

Can you please help with this:

Which of the following inequalities indicates the set of all values of d for which the lengths of the three sides of a triangle can be 3,4, and d?

A) 0<d<1
B) 0<d<5
C) 0<d<7
D) 1<d<5
E) 1<d<7

OA: E

Thanks,
Sri
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by Brent@GMATPrepNow » Mon May 19, 2014 8:09 pm
gmattesttaker2 wrote: Which of the following inequalities indicates the set of all values of d for which the lengths of the three sides of a triangle can be 3,4, and d?

A) 0<d<1
B) 0<d<5
C) 0<d<7
D) 1<d<5
E) 1<d<7
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
difference between sides A and B < third side < sum of sides A and B

So, 4 - 3 < d < 4 + 3
Simplify: 1 < d < 7
Answer: E

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Brent
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by [email protected] » Mon May 19, 2014 8:40 pm
Hi Sri,

This question is actually written in such a way that if you know a bit about triangles, then you can logically eliminate all the wrong answers. Here's how.

The question does NOT state that the third side has to be an integer, so we have to keep an open mind about non-integers.

Notice how three of the answers are 0 < d. These 3 answers imply that the missing side could be "just above 0"; for practical purposes, the ONLY type of triangles that allow for that possibility are isosceles triangles - the two sides that we're given would have to be the SAME LENGTH for this option to exist. With sides of 3 and 4, we CANNOT have a side that's "just above 0." Eliminate A, B and C.

With the Pythagorean Theorem comes the "Magic Pythagorean Triples", one of which is the 3/4/5 right triangle. With sides of 3 and 4, the missing side COULD be a 5, so we need an answer that accounts for that possibility. Eliminate D.

Final Answer: E

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Rich
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