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Two points are on the opposite sides of a square who sides

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Two points are on the opposite sides of a square who sides  [#permalink]

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New post 26 Jul 2014, 11:24
3
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (00:55) correct 28% (00:56) wrong based on 111 sessions

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Two points are on the opposite sides of a square who side measures 4. Which of the following could be the distance between these two points?

(A) 3.8
(B) 5
(C) 6
(D) 7
(E) 9
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Re: Two points are on the opposite sides of a square who sides  [#permalink]

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New post 26 Jul 2014, 11:46
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1
Reni wrote:
Two points are on the opposite sides of a square who side measures 4. Which of the following could be the distance between these two points?

(A)3.8
(B)5
(C)6
(D)7
(E)9



The shortest distance between any two points which are on opposite sides of a square is the length of the side of the square.
The longest distance between any two points which are on a square is the length of the diagonal of the square.
Attachment:
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So, the distance between these two points must be more than or equal to 4 and less than or equal to \(\sqrt{4^2+4^2}<6\). The only option which fall into this range is B.

Answer: B.
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Re: Two points are on the opposite sides of a square who sides  [#permalink]

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New post 04 Feb 2016, 00:00
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Hi All,

With a bit of logic, and using the answer choices as reference, you can answer this question without having to do ANY calculations.

We're told that two points are on the opposite sides of a square whose sides are 4. We're asked which of the following COULD be the distance between these two points.

Since we don't know exactly where the two points are, we should start with what would be the SHORTEST distance between them, then we can work 'up' from there.

If the points were at the exact some 'place' on opposite sides, then they would be the same distance as the length of a side: 4. That length is the SHORTEST distance between possible points, so Answer A is impossible. As we slide either (or both) points along the sides of the square, the distance will become GREATER than 4. So we could move one (or both) of the points so that they were 4.1 apart (or 4.2 or 4.325, etc.). Logically, the answer CANNOT be 6, because if 6 were a possibility, then 5 would ALSO be a possibility. Since there's only one correct answer to this question, it MUST be the smallest number that is greater than 4...

Final Answer:

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Re: Two points are on the opposite sides of a square who sides  [#permalink]

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New post 27 Jul 2018, 16:39
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Two points are on the opposite sides of a square who sides &nbs [#permalink] 27 Jul 2018, 16:39
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