Bob plans to draw a square ABCD with a point O on the side AB but is

Question

Bob plans to draw a square ABCD with a point O on the side AB but is not successful. Why is Bob unable to draw the square?

(1) The length of OD is twice that of OC.

(2) The length of OD is 4 cm.

prady80 · Answer

Imagine that the point is the point A then ratio of OD to OC would be side : diagonal.
Assume that ABCD is a square, then that ratio comes out the be s:s \sqrt{2} which is 1: \sqrt{2}. 
Since diagonal is of maximum length in a square, the max ratio will always be 1: \sqrt{2}.
There is not point on the side of the square which can exceed this ratio if it has to be on the side of square.
1: 2 greater than 1:\sqrt{2}. Therefore, Statement 1 is sufficient to prove that a square cannot be drawn.
Statement 2 does not provide any valuable additional information and hence is insufficient.

CounterSniper · Answer

(1) The length of OD is twice that of OC.

the largest distance between any two points within a square is the diagonal.

if the side of the square is A then the diagonal is Aroot2, as per the question though OD=2OC .The square is thus not possible to draw with the given criteria . Thus sufficient

(2) The length of OD is 4 cm.

insufficient.

Nunuboy1994 · Answer

I got this question right through intuition but can someone diagram it for me? I don't actually understand the logic behind this question.

Sanjay2043 · Answer

The longest line we can inscribe in a square is its diagnol(BD). let length of a side of square is a. Then diagnol (BD) = aroot2 (45-45-90).
Now lets draw point O near to B making OC approximately equal to BC (OC=a). Now according to question OD=2OC but we know that BD is the longest and its value is just aroot 2. So a square cannot be drawn.

bhargavasrikantha · Answer

what if the point is between A and B but not on A/B. since question states Point O is on side of AB. So the location is not clarified.

if that's the case, 1 is insufficient.

Even 2 is insufficient and ofcourse both are still insufficient. In my view answer is E. Can someone advice on my approach?

amanvermagmat · Answer

Hello

The MAX ratio of OD to OC you will get will be when point O coincides with point B. Because in that case OD will be diagonal and OC will be the side, and thus the required ratio will be √2 : 1.

If instead you take point somewhere else between A and B then OD : OC will be less than √2 : 1.

So if the Max possible ratio in this case of a square is √2 : 1,then it can never be 2:1.

That's why statement 1 is sufficient

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Bob plans to draw a square ABCD with a point O on the side AB but is

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Bob plans to draw a square ABCD with a point O on the side AB but is

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