A circle is drawn within the interior of a rectangle.

[EnriqueR905]

Hello, I received this question in my last CAT but I could not visualize the shape and the reasoning behind the answer.This is the question:

A circle is drawn within the interior of a rectangle. Does the circle occupy more than one-half of the rectangle’s area?

(1) The rectangle’s length is more than twice its width.

(2) If the rectangle’s length and width were each reduced by 25% and the circle unchanged, the circle would still fit into the interior of the new rectangle.

Correct Answer: E

Thank You.

[Sage Pearce-Higgins]

Please see my reply to this thread: https://www.manhattanprep.com/gmat/foru ... 33247.html

[RonPurewal]

Hello, I received this question in my last CAT but I could not visualize the shape and the reasoning behind the answer.This is the question:

hi,
on this forum, it's not acceptable to just post a problem and say "please advise", or "i had no idea how to solve this".

1/
first of all, this is almost certainly not true.
you probably started the problem in some way, and then got stuck at some very specific point(s) along the way.

2/
in the unlikely event that this actually is true—i.e., if you actually looked at this problem and thought, "wow, i have NO idea how to do this at all"—then you're better off leaving the problem and returning to it later.
if we just posted an answer key—which you should have anyway—that wouldn't help you develop your problem-solving skills—and then you'd waste the problem!

so...
please post specifics about the issue(s) you're having with the problem.
what was your approach?
what did you understand?
what didn't you understand?
where did you get stuck?
did you try any alternate approaches?
etc.

thanks.

[EnriqueR905]

My approach for this question was the following:

Since we are told that the circle is inside the rectangle, clearly the circle's area is smaller than the rectangle's area.Based, on that, I need to find the relationship of both areas, therefore, i need the area of the circle divided by the area of the rectangle or a relationship between both.

statement a: they are giving me the relationship between the length (horizontal line) and width(vertical line). I got and equation that stated that L>2W.With this i could not do anything.So a was out.

statement b: since we know that 3/4 of the L and 3/4 of the W we could get a relationship, let's say that L=8 and W=4, we would have an area of 32 and it's half would be 16. If we use these numbers and reduce the L and W by 25% we would have 3 and 6 and using the formula we would get an area of 18. This does not help me to understand the solve the answer because 16 or 17 can still be the area of the circle.So b was also out.

Together, we have the relationship L>2W and having L=16 and W=4, we get and area of 128 and its half would be 64. If we reduce it by 3/4 we would have 12 and 3 which multiplied gives me 46 which far smaller than half of the area, making C the answer but that was not the case.

[RonPurewal]

ok, well, you have the wrong "correct answer" to this question -- so, you may want to start over from scratch with this one. (:

the actual answer to this problem is D -- each individual statement is sufficient.

did you even look at the answer key?
i understand it's possible to confuse the letters "d" and "e"... but, had you looked at the answer key, you would have realized that you were mistaken in concluding that the individual statements were insufficient.