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# If the figure above shows the diagonal of two rectangles, is the inner

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Math Expert
Joined: 02 Sep 2009
Posts: 55271
If the figure above shows the diagonal of two rectangles, is the inner  [#permalink]

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14 Sep 2018, 01:59
00:00

Difficulty:

55% (hard)

Question Stats:

55% (00:58) correct 45% (01:08) wrong based on 25 sessions

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If the figure above shows the diagonal of two rectangles, is the inner rectangle a square?

(1) The outer rectangle is not a square.
(2) O is the midpoint of the diagonal.

Attachment:

image009.jpg [ 3.76 KiB | Viewed 496 times ]

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Re: If the figure above shows the diagonal of two rectangles, is the inner  [#permalink]

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14 Sep 2018, 23:32
Bunuel wrote:

If the figure above shows the diagonal of two rectangles, is the inner rectangle a square?

(1) The outer rectangle is not a square.
(2) O is the midpoint of the diagonal.

Attachment:
image009.jpg

As per the figure both the rectangles must be similar figures i.e. ratio of their sides will be a constant

Question: is the inner rectangle a square?

Statement 1: The outer rectangle is not a square.
i.e. Inner rectangle also is NOT square hence
SUFFICIENT

Statement 2: O is the midpoint of the diagonal.

But sinmce we don't know about the relationship between lengths of sides hence
NOT SUFFICIENT

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Re: If the figure above shows the diagonal of two rectangles, is the inner  [#permalink]

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15 Sep 2018, 00:15
1
Bunuel wrote:

If the figure above shows the diagonal of two rectangles, is the inner rectangle a square?

(1) The outer rectangle is not a square.
(2) O is the midpoint of the diagonal.

Attachment:
image009.jpg

Questions dealing with regular polygons can often be solved by drawing, and not exact calculations.
This is an Alternative approach.

(1)
Let's draw the larger square first. Then the smaller rectangle has its corner somewhere on the diagonal of the larger square. No what point on the diagonal we pick to be the corner of the smaller rectangle, we can see that it is a square!
Sufficient!

(2)
This time, let's try making the outer rectangle 'very wide' or 'a perfect square'. Once again, just using our eyes, we can SEE that if the outer rectangle is very wide the inner rectangle is not a square and if it is a perfect square it is.
Insufficient.

Important note:
When can we trust a drawing?
With regular polygons, we already know all the angles of the shape, meaning that the property we can change is its size: we can make it larger or smaller. That means that properties such as symmetry, or the ratio between lengths in the shape are constant, no matter how we draw the shape. This means we can trust our eyes and have no need for an involved, exact solution.
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Re: If the figure above shows the diagonal of two rectangles, is the inner   [#permalink] 15 Sep 2018, 00:15
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